Matrix3f.java

/*
 * (C) Copyright 2015-2018 Richard Greenlees

 Permission is hereby granted, free of charge, to any person obtaining a copy
 of this software and associated documentation files (the "Software"), to deal
 in the Software without restriction, including without limitation the rights
 to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 copies of the Software, and to permit persons to whom the Software is
 furnished to do so, subject to the following conditions:

 The above copyright notice and this permission notice shall be included in
 all copies or substantial portions of the Software.

 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 THE SOFTWARE.

 */
package org.joml;

import java.io.Externalizable;
import java.io.IOException;
import java.io.ObjectInput;
import java.io.ObjectOutput;
//#ifdef __HAS_NIO__
import java.nio.ByteBuffer;
import java.nio.FloatBuffer;
//#endif
import java.text.DecimalFormat;
import java.text.NumberFormat;

//#ifdef __GWT__
import com.google.gwt.typedarrays.shared.Float32Array;
//#endif

/**
 * Contains the definition of a 3x3 matrix of floats, and associated functions to transform
 * it. The matrix is column-major to match OpenGL's interpretation, and it looks like this:
 * <p>
 *      m00  m10  m20<br>
 *      m01  m11  m21<br>
 *      m02  m12  m22<br>
 * 
 * @author Richard Greenlees
 * @author Kai Burjack
 */
public class Matrix3f implements Externalizable, Matrix3fc {

    private static final long serialVersionUID = 1L;

    public float m00, m01, m02;
    public float m10, m11, m12;
    public float m20, m21, m22;

    /**
     * Create a new {@link Matrix3f} and set it to {@link #identity() identity}.
     */
    public Matrix3f() {
        m00 = 1.0f;
        m11 = 1.0f;
        m22 = 1.0f;
    }

    /**
     * Create a new {@link Matrix3f} and make it a copy of the given matrix.
     * 
     * @param mat
     *          the {@link Matrix3fc} to copy the values from
     */
    public Matrix3f(Matrix3fc mat) {
        if (mat instanceof Matrix3f) {
            MemUtil.INSTANCE.copy((Matrix3f) mat, this);
        } else {
            setMatrix3fc(mat);
        }
    }

    /**
     * Create a new {@link Matrix3f} and make it a copy of the upper left 3x3 of the given {@link Matrix4fc}.
     * 
     * @param mat
     *          the {@link Matrix4fc} to copy the values from
     */
    public Matrix3f(Matrix4fc mat) {
        if (mat instanceof Matrix4f) {
            MemUtil.INSTANCE.copy((Matrix4f) mat, this);
        } else {
            setMatrix4fc(mat);
        }
    }

    /**
     * Create a new 3x3 matrix using the supplied float values. The order of the parameter is column-major, 
     * so the first three parameters specify the three elements of the first column.
     * 
     * @param m00
     *          the value of m00
     * @param m01
     *          the value of m01
     * @param m02
     *          the value of m02
     * @param m10
     *          the value of m10
     * @param m11
     *          the value of m11
     * @param m12
     *          the value of m12
     * @param m20
     *          the value of m20
     * @param m21
     *          the value of m21
     * @param m22
     *          the value of m22
     */
    public Matrix3f(float m00, float m01, float m02,
                    float m10, float m11, float m12, 
                    float m20, float m21, float m22) {
        this.m00 = m00;
        this.m01 = m01;
        this.m02 = m02;
        this.m10 = m10;
        this.m11 = m11;
        this.m12 = m12;
        this.m20 = m20;
        this.m21 = m21;
        this.m22 = m22;
    }

//#ifdef __HAS_NIO__
    /**
     * Create a new {@link Matrix3f} by reading its 9 float components from the given {@link FloatBuffer}
     * at the buffer's current position.
     * <p>
     * That FloatBuffer is expected to hold the values in column-major order.
     * <p>
     * The buffer's position will not be changed by this method.
     * 
     * @param buffer
     *          the {@link FloatBuffer} to read the matrix values from
     */
    public Matrix3f(FloatBuffer buffer) {
        MemUtil.INSTANCE.get(this, buffer.position(), buffer);
    }
//#endif

    /**
     * Create a new {@link Matrix3f} and initialize its three columns using the supplied vectors.
     * 
     * @param col0
     *          the first column
     * @param col1
     *          the second column
     * @param col2
     *          the third column
     */
    public Matrix3f(Vector3fc col0, Vector3fc col1, Vector3fc col2) {
        if (col0 instanceof Vector3f &&
            col1 instanceof Vector3f &&
            col2 instanceof Vector3f) {
            MemUtil.INSTANCE.set(this, (Vector3f) col0, (Vector3f) col1, (Vector3f) col2);
        } else {
            setVector3fc(col0, col1, col2);
        }
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#m00()
     */
    public float m00() {
        return m00;
    }
    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#m01()
     */
    public float m01() {
        return m01;
    }
    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#m02()
     */
    public float m02() {
        return m02;
    }
    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#m10()
     */
    public float m10() {
        return m10;
    }
    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#m11()
     */
    public float m11() {
        return m11;
    }
    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#m12()
     */
    public float m12() {
        return m12;
    }
    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#m20()
     */
    public float m20() {
        return m20;
    }
    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#m21()
     */
    public float m21() {
        return m21;
    }
    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#m22()
     */
    public float m22() {
        return m22;
    }

    /**
     * Set the value of the matrix element at column 0 and row 0
     * 
     * @param m00
     *          the new value
     * @return the value of the matrix element
     */
    public Matrix3f m00(float m00) {
        this.m00 = m00;
        return this;
    }
    /**
     * Set the value of the matrix element at column 0 and row 1
     * 
     * @param m01
     *          the new value
     * @return the value of the matrix element
     */
    public Matrix3f m01(float m01) {
        this.m01 = m01;
        return this;
    }
    /**
     * Set the value of the matrix element at column 0 and row 2
     * 
     * @param m02
     *          the new value
     * @return the value of the matrix element
     */
    public Matrix3f m02(float m02) {
        this.m02 = m02;
        return this;
    }
    /**
     * Set the value of the matrix element at column 1 and row 0
     * 
     * @param m10
     *          the new value
     * @return the value of the matrix element
     */
    public Matrix3f m10(float m10) {
        this.m10 = m10;
        return this;
    }
    /**
     * Set the value of the matrix element at column 1 and row 1
     * 
     * @param m11
     *          the new value
     * @return the value of the matrix element
     */
    public Matrix3f m11(float m11) {
        this.m11 = m11;
        return this;
    }
    /**
     * Set the value of the matrix element at column 1 and row 2
     * 
     * @param m12
     *          the new value
     * @return the value of the matrix element
     */
    public Matrix3f m12(float m12) {
        this.m12 = m12;
        return this;
    }
    /**
     * Set the value of the matrix element at column 2 and row 0
     * 
     * @param m20
     *          the new value
     * @return the value of the matrix element
     */
    public Matrix3f m20(float m20) {
        this.m20 = m20;
        return this;
    }
    /**
     * Set the value of the matrix element at column 2 and row 1
     * 
     * @param m21
     *          the new value
     * @return the value of the matrix element
     */
    public Matrix3f m21(float m21) {
        this.m21 = m21;
        return this;
    }
    /**
     * Set the value of the matrix element at column 2 and row 2
     * 
     * @param m22
     *          the new value
     * @return the value of the matrix element
     */
    public Matrix3f m22(float m22) {
        this.m22 = m22;
        return this;
    }

    /**
     * Set the elements of this matrix to the ones in <code>m</code>.
     * 
     * @param m
     *          the matrix to copy the elements from
     * @return this
     */
    public Matrix3f set(Matrix3fc m) {
        if (m instanceof Matrix3f) {
            MemUtil.INSTANCE.copy((Matrix3f) m, this);
        } else {
            setMatrix3fc(m);
        }
        return this;
    }
    private void setMatrix3fc(Matrix3fc mat) {
        m00 = mat.m00();
        m01 = mat.m01();
        m02 = mat.m02();
        m10 = mat.m10();
        m11 = mat.m11();
        m12 = mat.m12();
        m20 = mat.m20();
        m21 = mat.m21();
        m22 = mat.m22();
    }

    /**
     * Set the elements of this matrix to the upper left 3x3 of the given {@link Matrix4fc}.
     *
     * @param mat
     *          the {@link Matrix4fc} to copy the values from
     * @return this
     */
    public Matrix3f set(Matrix4fc mat) {
        if (mat instanceof Matrix4f) {
            MemUtil.INSTANCE.copy((Matrix4f) mat, this);
        } else {
            setMatrix4fc(mat);
        }
        return this;
    }
    private void setMatrix4fc(Matrix4fc mat) {
        m00 = mat.m00();
        m01 = mat.m01();
        m02 = mat.m02();
        m10 = mat.m10();
        m11 = mat.m11();
        m12 = mat.m12();
        m20 = mat.m20();
        m21 = mat.m21();
        m22 = mat.m22();
    }

    /**
     * Set this matrix to be equivalent to the rotation specified by the given {@link AxisAngle4f}.
     * 
     * @param axisAngle
     *          the {@link AxisAngle4f}
     * @return this
     */
    public Matrix3f set(AxisAngle4f axisAngle) {
        float x = axisAngle.x;
        float y = axisAngle.y;
        float z = axisAngle.z;
        float angle = axisAngle.angle;
        float invLength = (float) (1.0 / Math.sqrt(x*x + y*y + z*z));
        x *= invLength;
        y *= invLength;
        z *= invLength;
        float s = (float) Math.sin(angle);
        float c = (float) Math.cosFromSin(s, angle);
        float omc = 1.0f - c;
        m00 = c + x*x*omc;
        m11 = c + y*y*omc;
        m22 = c + z*z*omc;
        float tmp1 = x*y*omc;
        float tmp2 = z*s;
        m10 = tmp1 - tmp2;
        m01 = tmp1 + tmp2;
        tmp1 = x*z*omc;
        tmp2 = y*s;
        m20 = tmp1 + tmp2;
        m02 = tmp1 - tmp2;
        tmp1 = y*z*omc;
        tmp2 = x*s;
        m21 = tmp1 - tmp2;
        m12 = tmp1 + tmp2;
        return this;
    }

    /**
     * Set this matrix to be equivalent to the rotation specified by the given {@link AxisAngle4d}.
     * 
     * @param axisAngle
     *          the {@link AxisAngle4d}
     * @return this
     */
    public Matrix3f set(AxisAngle4d axisAngle) {
        double x = axisAngle.x;
        double y = axisAngle.y;
        double z = axisAngle.z;
        double angle = axisAngle.angle;
        double invLength = 1.0 / Math.sqrt(x*x + y*y + z*z);
        x *= invLength;
        y *= invLength;
        z *= invLength;
        double s = Math.sin(angle);
        double c = Math.cosFromSin(s, angle);
        double omc = 1.0f - c;
        m00 = (float)(c + x*x*omc);
        m11 = (float)(c + y*y*omc);
        m22 = (float)(c + z*z*omc);
        double tmp1 = x*y*omc;
        double tmp2 = z*s;
        m10 = (float)(tmp1 - tmp2);
        m01 = (float)(tmp1 + tmp2);
        tmp1 = x*z*omc;
        tmp2 = y*s;
        m20 = (float)(tmp1 + tmp2);
        m02 = (float)(tmp1 - tmp2);
        tmp1 = y*z*omc;
        tmp2 = x*s;
        m21 = (float)(tmp1 - tmp2);
        m12 = (float)(tmp1 + tmp2);
        return this;
    }

    /**
     * Set this matrix to be equivalent to the rotation - and possibly scaling - specified by the given {@link Quaternionfc}.
     * <p>
     * This method is equivalent to calling: <tt>rotation(q)</tt>
     * <p>
     * Reference: <a href="http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToMatrix/">http://www.euclideanspace.com/</a>
     * 
     * @see #rotation(Quaternionfc)
     * 
     * @param q
     *          the {@link Quaternionfc}
     * @return this
     */
    public Matrix3f set(Quaternionfc q) {
        return rotation(q);
    }

    /**
     * Set this matrix to a rotation - and possibly scaling - equivalent to the given quaternion.
     * <p>
     * Reference: <a href="http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToMatrix/">http://www.euclideanspace.com/</a>
     * 
     * @param q
     *          the quaternion
     * @return this
     */
    public Matrix3f set(Quaterniondc q) {
        double w2 = q.w() * q.w();
        double x2 = q.x() * q.x();
        double y2 = q.y() * q.y();
        double z2 = q.z() * q.z();
        double zw = q.z() * q.w();
        double xy = q.x() * q.y();
        double xz = q.x() * q.z();
        double yw = q.y() * q.w();
        double yz = q.y() * q.z();
        double xw = q.x() * q.w();
        m00 = (float) (w2 + x2 - z2 - y2);
        m01 = (float) (xy + zw + zw + xy);
        m02 = (float) (xz - yw + xz - yw);
        m10 = (float) (-zw + xy - zw + xy);
        m11 = (float) (y2 - z2 + w2 - x2);
        m12 = (float) (yz + yz + xw + xw);
        m20 = (float) (yw + xz + xz + yw);
        m21 = (float) (yz + yz - xw - xw);
        m22 = (float) (z2 - y2 - x2 + w2);
        return this;
    }

    /**
     * Multiply this matrix by the supplied <code>right</code> matrix.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>R</code> the <code>right</code> matrix,
     * then the new matrix will be <code>M * R</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * R * v</code>, the
     * transformation of the right matrix will be applied first!
     * 
     * @param right
     *          the right operand of the matrix multiplication
     * @return this
     */
    public Matrix3f mul(Matrix3fc right) {
        return mul(right, this);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#mul(org.joml.Matrix3fc, org.joml.Matrix3f)
     */
    public Matrix3f mul(Matrix3fc right, Matrix3f dest) {
        float nm00 = m00 * right.m00() + m10 * right.m01() + m20 * right.m02();
        float nm01 = m01 * right.m00() + m11 * right.m01() + m21 * right.m02();
        float nm02 = m02 * right.m00() + m12 * right.m01() + m22 * right.m02();
        float nm10 = m00 * right.m10() + m10 * right.m11() + m20 * right.m12();
        float nm11 = m01 * right.m10() + m11 * right.m11() + m21 * right.m12();
        float nm12 = m02 * right.m10() + m12 * right.m11() + m22 * right.m12();
        float nm20 = m00 * right.m20() + m10 * right.m21() + m20 * right.m22();
        float nm21 = m01 * right.m20() + m11 * right.m21() + m21 * right.m22();
        float nm22 = m02 * right.m20() + m12 * right.m21() + m22 * right.m22();
        dest.m00 = nm00;
        dest.m01 = nm01;
        dest.m02 = nm02;
        dest.m10 = nm10;
        dest.m11 = nm11;
        dest.m12 = nm12;
        dest.m20 = nm20;
        dest.m21 = nm21;
        dest.m22 = nm22;
        return dest;
    }

    /**
     * Pre-multiply this matrix by the supplied <code>left</code> matrix and store the result in <code>this</code>.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>L</code> the <code>left</code> matrix,
     * then the new matrix will be <code>L * M</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>L * M * v</code>, the
     * transformation of <code>this</code> matrix will be applied first!
     *
     * @param left
     *          the left operand of the matrix multiplication
     * @return this
     */
    public Matrix3f mulLocal(Matrix3fc left) {
       return mulLocal(left, this);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#mulLocal(org.joml.Matrix3fc, org.joml.Matrix3f)
     */
    public Matrix3f mulLocal(Matrix3fc left, Matrix3f dest) {
        float nm00 = left.m00() * m00 + left.m10() * m01 + left.m20() * m02;
        float nm01 = left.m01() * m00 + left.m11() * m01 + left.m20() * m02;
        float nm10 = left.m00() * m10 + left.m10() * m11 + left.m20() * m12;
        float nm11 = left.m01() * m10 + left.m11() * m11 + left.m20() * m12;
        float nm20 = left.m00() * m20 + left.m10() * m21 + left.m20() * m22;
        float nm21 = left.m01() * m20 + left.m11() * m21 + left.m21() * m22;
        dest.m00 = nm00;
        dest.m01 = nm01;
        dest.m10 = nm10;
        dest.m11 = nm11;
        dest.m20 = nm20;
        dest.m21 = nm21;
        return dest;
    }

    /**
     * Set the values within this matrix to the supplied float values. The result looks like this:
     * <p>
     * m00, m10, m20<br>
     * m01, m11, m21<br>
     * m02, m12, m22<br>
     * 
     * @param m00
     *          the new value of m00
     * @param m01
     *          the new value of m01
     * @param m02
     *          the new value of m02
     * @param m10
     *          the new value of m10
     * @param m11
     *          the new value of m11
     * @param m12
     *          the new value of m12
     * @param m20
     *          the new value of m20
     * @param m21
     *          the new value of m21
     * @param m22
     *          the new value of m22
     * @return this
     */
    public Matrix3f set(float m00, float m01, float m02,
                        float m10, float m11, float m12, 
                        float m20, float m21, float m22) {
        this.m00 = m00;
        this.m01 = m01;
        this.m02 = m02;
        this.m10 = m10;
        this.m11 = m11;
        this.m12 = m12;
        this.m20 = m20;
        this.m21 = m21;
        this.m22 = m22;
        return this;
    }

    /**
     * Set the values in this matrix based on the supplied float array. The result looks like this:
     * <p>
     * 0, 3, 6<br>
     * 1, 4, 7<br>
     * 2, 5, 8<br>
     * 
     * This method only uses the first 9 values, all others are ignored.
     * 
     * @param m
     *          the array to read the matrix values from
     * @return this
     */
    public Matrix3f set(float m[]) {
        MemUtil.INSTANCE.copy(m, 0, this);
        return this;
    }

    /**
     * Set the three columns of this matrix to the supplied vectors, respectively.
     * 
     * @param col0
     *          the first column
     * @param col1
     *          the second column
     * @param col2
     *          the third column
     * @return this
     */
    public Matrix3f set(Vector3fc col0, Vector3fc col1, Vector3fc col2) {
        if (col0 instanceof Vector3f &&
            col1 instanceof Vector3f &&
            col2 instanceof Vector3f) {
            MemUtil.INSTANCE.set(this, (Vector3f) col0, (Vector3f) col1, (Vector3f) col2);
        } else {
            setVector3fc(col0, col1, col2);
        }
        return this;
    }
    private void setVector3fc(Vector3fc col0, Vector3fc col1, Vector3fc col2) {
        this.m00 = col0.x();
        this.m01 = col0.y();
        this.m02 = col0.z();
        this.m10 = col1.x();
        this.m11 = col1.y();
        this.m12 = col1.z();
        this.m20 = col2.x();
        this.m21 = col2.y();
        this.m22 = col2.z();
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#determinant()
     */
    public float determinant() {
        return (m00 * m11 - m01 * m10) * m22
             + (m02 * m10 - m00 * m12) * m21
             + (m01 * m12 - m02 * m11) * m20;
    }

    /**
     * Invert this matrix.
     *
     * @return this
     */
    public Matrix3f invert() {
        return invert(this);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#invert(org.joml.Matrix3f)
     */
    public Matrix3f invert(Matrix3f dest) {
        float s = determinant();
        // client must make sure that matrix is invertible
        s = 1.0f / s;
        float nm00 = (m11 * m22 - m21 * m12) * s;
        float nm01 = (m21 * m02 - m01 * m22) * s;
        float nm02 = (m01 * m12 - m11 * m02) * s;
        float nm10 = (m20 * m12 - m10 * m22) * s;
        float nm11 = (m00 * m22 - m20 * m02) * s;
        float nm12 = (m10 * m02 - m00 * m12) * s;
        float nm20 = (m10 * m21 - m20 * m11) * s;
        float nm21 = (m20 * m01 - m00 * m21) * s;
        float nm22 = (m00 * m11 - m10 * m01) * s;
        dest.m00 = nm00;
        dest.m01 = nm01;
        dest.m02 = nm02;
        dest.m10 = nm10;
        dest.m11 = nm11;
        dest.m12 = nm12;
        dest.m20 = nm20;
        dest.m21 = nm21;
        dest.m22 = nm22;
        return dest;
    }

    /**
     * Transpose this matrix.
     * 
     * @return this
     */
    public Matrix3f transpose() {
        return transpose(this);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#transpose(org.joml.Matrix3f)
     */
    public Matrix3f transpose(Matrix3f dest) {
        dest.set(m00, m10, m20,
                 m01, m11, m21,
                 m02, m12, m22);
        return dest;
    }

    /**
     * Return a string representation of this matrix.
     * <p>
     * This method creates a new {@link DecimalFormat} on every invocation with the format string "<tt>0.000E0;-</tt>".
     * 
     * @return the string representation
     */
    public String toString() {
        DecimalFormat formatter = new DecimalFormat(" 0.000E0;-");
        String str = toString(formatter);
        StringBuffer res = new StringBuffer();
        int eIndex = Integer.MIN_VALUE;
        for (int i = 0; i < str.length(); i++) {
            char c = str.charAt(i);
            if (c == 'E') {
                eIndex = i;
            } else if (c == ' ' && eIndex == i - 1) {
                // workaround Java 1.4 DecimalFormat bug
                res.append('+');
                continue;
            } else if (Character.isDigit(c) && eIndex == i - 1) {
                res.append('+');
            }
            res.append(c);
        }
        return res.toString();
    }

    /**
     * Return a string representation of this matrix by formatting the matrix elements with the given {@link NumberFormat}.
     * 
     * @param formatter
     *          the {@link NumberFormat} used to format the matrix values with
     * @return the string representation
     */
    public String toString(NumberFormat formatter) {
        return formatter.format(m00) + " " + formatter.format(m10) + " " + formatter.format(m20) + "\n"
             + formatter.format(m01) + " " + formatter.format(m11) + " " + formatter.format(m21) + "\n"
             + formatter.format(m02) + " " + formatter.format(m12) + " " + formatter.format(m22) + "\n";
    }

    /**
     * Get the current values of <code>this</code> matrix and store them into
     * <code>dest</code>.
     * <p>
     * This is the reverse method of {@link #set(Matrix3fc)} and allows to obtain
     * intermediate calculation results when chaining multiple transformations.
     * 
     * @see #set(Matrix3fc)
     * 
     * @param dest
     *          the destination matrix
     * @return the passed in destination
     */
    public Matrix3f get(Matrix3f dest) {
        return dest.set(this);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#get(org.joml.Matrix4f)
     */
    public Matrix4f get(Matrix4f dest) {
        return dest.set(this);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#getRotation(org.joml.AxisAngle4f)
     */
    public AxisAngle4f getRotation(AxisAngle4f dest) {
        return dest.set(this);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#getUnnormalizedRotation(org.joml.Quaternionf)
     */
    public Quaternionf getUnnormalizedRotation(Quaternionf dest) {
        return dest.setFromUnnormalized(this);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#getNormalizedRotation(org.joml.Quaternionf)
     */
    public Quaternionf getNormalizedRotation(Quaternionf dest) {
        return dest.setFromNormalized(this);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#getUnnormalizedRotation(org.joml.Quaterniond)
     */
    public Quaterniond getUnnormalizedRotation(Quaterniond dest) {
        return dest.setFromUnnormalized(this);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#getNormalizedRotation(org.joml.Quaterniond)
     */
    public Quaterniond getNormalizedRotation(Quaterniond dest) {
        return dest.setFromNormalized(this);
    }

//#ifdef __GWT__
    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#get(com.google.gwt.typedarrays.shared.Float32Array)
     */
    public Float32Array get(Float32Array buffer) {
        buffer.set(0,  m00);
        buffer.set(1,  m01);
        buffer.set(2,  m02);
        buffer.set(3,  m10);
        buffer.set(4,  m11);
        buffer.set(5,  m12);
        buffer.set(6,  m20);
        buffer.set(7,  m21);
        buffer.set(8,  m22);
        return buffer;
    }
    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#get(int, com.google.gwt.typedarrays.shared.Float32Array)
     */
    public Float32Array get(int index, Float32Array buffer) {
        buffer.set(index,    m00);
        buffer.set(index+1,  m01);
        buffer.set(index+2,  m02);
        buffer.set(index+3,  m10);
        buffer.set(index+4,  m11);
        buffer.set(index+5,  m12);
        buffer.set(index+6,  m20);
        buffer.set(index+7,  m21);
        buffer.set(index+8,  m22);
        return buffer;
    }
//#endif

//#ifdef __HAS_NIO__
    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#get(java.nio.FloatBuffer)
     */
    public FloatBuffer get(FloatBuffer buffer) {
        return get(buffer.position(), buffer);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#get(int, java.nio.FloatBuffer)
     */
    public FloatBuffer get(int index, FloatBuffer buffer) {
        MemUtil.INSTANCE.put(this, index, buffer);
        return buffer;
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#get(java.nio.ByteBuffer)
     */
    public ByteBuffer get(ByteBuffer buffer) {
        return get(buffer.position(), buffer);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#get(int, java.nio.ByteBuffer)
     */
    public ByteBuffer get(int index, ByteBuffer buffer) {
        MemUtil.INSTANCE.put(this, index, buffer);
        return buffer;
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#getTransposed(java.nio.FloatBuffer)
     */
    public FloatBuffer getTransposed(FloatBuffer buffer) {
        return getTransposed(buffer.position(), buffer);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#getTransposed(int, java.nio.FloatBuffer)
     */
    public FloatBuffer getTransposed(int index, FloatBuffer buffer) {
        MemUtil.INSTANCE.putTransposed(this, index, buffer);
        return buffer;
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#getTransposed(java.nio.ByteBuffer)
     */
    public ByteBuffer getTransposed(ByteBuffer buffer) {
        return getTransposed(buffer.position(), buffer);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#getTransposed(int, java.nio.ByteBuffer)
     */
    public ByteBuffer getTransposed(int index, ByteBuffer buffer) {
        MemUtil.INSTANCE.putTransposed(this, index, buffer);
        return buffer;
    }
//#endif

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#get(float[], int)
     */
    public float[] get(float[] arr, int offset) {
        MemUtil.INSTANCE.copy(this, arr, offset);
        return arr;
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#get(float[])
     */
    public float[] get(float[] arr) {
        return get(arr, 0);
    }

//#ifdef __HAS_NIO__
    /**
     * Set the values of this matrix by reading 9 float values from the given {@link FloatBuffer} in column-major order,
     * starting at its current position.
     * <p>
     * The FloatBuffer is expected to contain the values in column-major order.
     * <p>
     * The position of the FloatBuffer will not be changed by this method.
     * 
     * @param buffer
     *              the FloatBuffer to read the matrix values from in column-major order
     * @return this
     */
    public Matrix3f set(FloatBuffer buffer) {
        MemUtil.INSTANCE.get(this, buffer.position(), buffer);
        return this;
    }

    /**
     * Set the values of this matrix by reading 9 float values from the given {@link ByteBuffer} in column-major order,
     * starting at its current position.
     * <p>
     * The ByteBuffer is expected to contain the values in column-major order.
     * <p>
     * The position of the ByteBuffer will not be changed by this method.
     * 
     * @param buffer
     *              the ByteBuffer to read the matrix values from in column-major order
     * @return this
     */
    public Matrix3f set(ByteBuffer buffer) {
        MemUtil.INSTANCE.get(this, buffer.position(), buffer);
        return this;
    }
//#endif

    /**
     * Set all values within this matrix to zero.
     * 
     * @return this
     */
    public Matrix3f zero() {
        MemUtil.INSTANCE.zero(this);
        return this;
    }

    /**
     * Set this matrix to the identity.
     * 
     * @return this
     */
    public Matrix3f identity() {
        MemUtil.INSTANCE.identity(this);
        return this;
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#scale(org.joml.Vector3fc, org.joml.Matrix3f)
     */
    public Matrix3f scale(Vector3fc xyz, Matrix3f dest) {
        return scale(xyz.x(), xyz.y(), xyz.z(), dest);
    }

    /**
     * Apply scaling to this matrix by scaling the base axes by the given <tt>xyz.x</tt>,
     * <tt>xyz.y</tt> and <tt>xyz.z</tt> factors, respectively.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>S</code> the scaling matrix,
     * then the new matrix will be <code>M * S</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * S * v</code>, the
     * scaling will be applied first!
     * 
     * @param xyz
     *            the factors of the x, y and z component, respectively
     * @return this
     */
    public Matrix3f scale(Vector3fc xyz) {
        return scale(xyz.x(), xyz.y(), xyz.z(), this);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#scale(float, float, float, org.joml.Matrix3f)
     */
    public Matrix3f scale(float x, float y, float z, Matrix3f dest) {
        // scale matrix elements:
        // m00 = x, m11 = y, m22 = z
        // all others = 0
        dest.m00 = m00 * x;
        dest.m01 = m01 * x;
        dest.m02 = m02 * x;
        dest.m10 = m10 * y;
        dest.m11 = m11 * y;
        dest.m12 = m12 * y;
        dest.m20 = m20 * z;
        dest.m21 = m21 * z;
        dest.m22 = m22 * z;
        return dest;
    }

    /**
     * Apply scaling to this matrix by scaling the base axes by the given x,
     * y and z factors.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>S</code> the scaling matrix,
     * then the new matrix will be <code>M * S</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * S * v</code>
     * , the scaling will be applied first!
     * 
     * @param x
     *            the factor of the x component
     * @param y
     *            the factor of the y component
     * @param z
     *            the factor of the z component
     * @return this
     */
    public Matrix3f scale(float x, float y, float z) {
        return scale(x, y, z, this);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#scale(float, org.joml.Matrix3f)
     */
    public Matrix3f scale(float xyz, Matrix3f dest) {
        return scale(xyz, xyz, xyz, dest);
    }

    /**
     * Apply scaling to this matrix by uniformly scaling all base axes by the given <code>xyz</code> factor.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>S</code> the scaling matrix,
     * then the new matrix will be <code>M * S</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * S * v</code>
     * , the scaling will be applied first!
     * 
     * @see #scale(float, float, float)
     * 
     * @param xyz
     *            the factor for all components
     * @return this
     */
    public Matrix3f scale(float xyz) {
        return scale(xyz, xyz, xyz);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#scaleLocal(float, float, float, org.joml.Matrix3f)
     */
    public Matrix3f scaleLocal(float x, float y, float z, Matrix3f dest) {
        float nm00 = x * m00;
        float nm01 = y * m01;
        float nm02 = z * m02;
        float nm10 = x * m10;
        float nm11 = y * m11;
        float nm12 = z * m12;
        float nm20 = x * m20;
        float nm21 = y * m21;
        float nm22 = z * m22;
        dest.m00 = nm00;
        dest.m01 = nm01;
        dest.m02 = nm02;
        dest.m10 = nm10;
        dest.m11 = nm11;
        dest.m12 = nm12;
        dest.m20 = nm20;
        dest.m21 = nm21;
        dest.m22 = nm22;
        return dest;
    }

    /**
     * Pre-multiply scaling to this matrix by scaling the base axes by the given x,
     * y and z factors.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>S</code> the scaling matrix,
     * then the new matrix will be <code>S * M</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>S * M * v</code>, the
     * scaling will be applied last!
     * 
     * @param x
     *            the factor of the x component
     * @param y
     *            the factor of the y component
     * @param z
     *            the factor of the z component
     * @return this
     */
    public Matrix3f scaleLocal(float x, float y, float z) {
        return scaleLocal(x, y, z, this);
    }

    /**
     * Set this matrix to be a simple scale matrix, which scales all axes uniformly by the given factor.
     * <p>
     * The resulting matrix can be multiplied against another transformation
     * matrix to obtain an additional scaling.
     * <p>
     * In order to post-multiply a scaling transformation directly to a
     * matrix, use {@link #scale(float) scale()} instead.
     * 
     * @see #scale(float)
     * 
     * @param factor
     *             the scale factor in x, y and z
     * @return this
     */
    public Matrix3f scaling(float factor) {
        MemUtil.INSTANCE.zero(this);
        m00 = factor;
        m11 = factor;
        m22 = factor;
        return this;
    }

    /**
     * Set this matrix to be a simple scale matrix.
     * 
     * @param x
     *             the scale in x
     * @param y
     *             the scale in y
     * @param z
     *             the scale in z
     * @return this
     */
    public Matrix3f scaling(float x, float y, float z) {
        MemUtil.INSTANCE.zero(this);
        m00 = x;
        m11 = y;
        m22 = z;
        return this;
    }

    /**
     * Set this matrix to be a simple scale matrix which scales the base axes by <tt>xyz.x</tt>, <tt>xyz.y</tt> and <tt>xyz.z</tt> respectively.
     * <p>
     * The resulting matrix can be multiplied against another transformation
     * matrix to obtain an additional scaling.
     * <p>
     * In order to post-multiply a scaling transformation directly to a
     * matrix use {@link #scale(Vector3fc) scale()} instead.
     * 
     * @see #scale(Vector3fc)
     * 
     * @param xyz
     *             the scale in x, y and z respectively
     * @return this
     */
    public Matrix3f scaling(Vector3fc xyz) {
        return scaling(xyz.x(), xyz.y(), xyz.z());
    }

    /**
     * Set this matrix to a rotation matrix which rotates the given radians about a given axis.
     * <p>
     * The axis described by the <code>axis</code> vector needs to be a unit vector.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * The resulting matrix can be multiplied against another transformation
     * matrix to obtain an additional rotation.
     * <p>
     * In order to post-multiply a rotation transformation directly to a
     * matrix, use {@link #rotate(float, Vector3fc) rotate()} instead.
     * 
     * @see #rotate(float, Vector3fc)
     * 
     * @param angle
     *          the angle in radians
     * @param axis
     *          the axis to rotate about (needs to be {@link Vector3f#normalize() normalized})
     * @return this
     */
    public Matrix3f rotation(float angle, Vector3fc axis) {
        return rotation(angle, axis.x(), axis.y(), axis.z());
    }

    /**
     * Set this matrix to a rotation transformation using the given {@link AxisAngle4f}.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * The resulting matrix can be multiplied against another transformation
     * matrix to obtain an additional rotation.
     * <p>
     * In order to apply the rotation transformation to an existing transformation,
     * use {@link #rotate(AxisAngle4f) rotate()} instead.
     * <p>
     * Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Axis_and_angle">http://en.wikipedia.org</a>
     *
     * @see #rotate(AxisAngle4f)
     * 
     * @param axisAngle
     *          the {@link AxisAngle4f} (needs to be {@link AxisAngle4f#normalize() normalized})
     * @return this
     */
    public Matrix3f rotation(AxisAngle4f axisAngle) {
        return rotation(axisAngle.angle, axisAngle.x, axisAngle.y, axisAngle.z);
    }

    /**
     * Set this matrix to a rotation matrix which rotates the given radians about a given axis.
     * <p>
     * The axis described by the three components needs to be a unit vector.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * The resulting matrix can be multiplied against another transformation
     * matrix to obtain an additional rotation.
     * <p>
     * In order to apply the rotation transformation to an existing transformation,
     * use {@link #rotate(float, float, float, float) rotate()} instead.
     * <p>
     * Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle">http://en.wikipedia.org</a>
     * 
     * @see #rotate(float, float, float, float)
     * 
     * @param angle
     *          the angle in radians
     * @param x
     *          the x-component of the rotation axis
     * @param y
     *          the y-component of the rotation axis
     * @param z
     *          the z-component of the rotation axis
     * @return this
     */
    public Matrix3f rotation(float angle, float x, float y, float z) {
        float sin = (float) Math.sin(angle);
        float cos = (float) Math.cosFromSin(sin, angle);
        float C = 1.0f - cos;
        float xy = x * y, xz = x * z, yz = y * z;
        m00 = cos + x * x * C;
        m10 = xy * C - z * sin;
        m20 = xz * C + y * sin;
        m01 = xy * C + z * sin;
        m11 = cos + y * y * C;
        m21 = yz * C - x * sin;
        m02 = xz * C - y * sin;
        m12 = yz * C + x * sin;
        m22 = cos + z * z * C;
        return this;
    }

    /**
     * Set this matrix to a rotation transformation about the X axis.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations">http://en.wikipedia.org</a>
     * 
     * @param ang
     *            the angle in radians
     * @return this
     */
    public Matrix3f rotationX(float ang) {
        float sin, cos;
        sin = (float) Math.sin(ang);
        cos = (float) Math.cosFromSin(sin, ang);
        m00 = 1.0f;
        m01 = 0.0f;
        m02 = 0.0f;
        m10 = 0.0f;
        m11 = cos;
        m12 = sin;
        m20 = 0.0f;
        m21 = -sin;
        m22 = cos;
        return this;
    }

    /**
     * Set this matrix to a rotation transformation about the Y axis.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations">http://en.wikipedia.org</a>
     * 
     * @param ang
     *            the angle in radians
     * @return this
     */
    public Matrix3f rotationY(float ang) {
        float sin, cos;
        sin = (float) Math.sin(ang);
        cos = (float) Math.cosFromSin(sin, ang);
        m00 = cos;
        m01 = 0.0f;
        m02 = -sin;
        m10 = 0.0f;
        m11 = 1.0f;
        m12 = 0.0f;
        m20 = sin;
        m21 = 0.0f;
        m22 = cos;
        return this;
    }

    /**
     * Set this matrix to a rotation transformation about the Z axis.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations">http://en.wikipedia.org</a>
     * 
     * @param ang
     *            the angle in radians
     * @return this
     */
    public Matrix3f rotationZ(float ang) {
        float sin, cos;
        sin = (float) Math.sin(ang);
        cos = (float) Math.cosFromSin(sin, ang);
        m00 = cos;
        m01 = sin;
        m02 = 0.0f;
        m10 = -sin;
        m11 = cos;
        m12 = 0.0f;
        m20 = 0.0f;
        m21 = 0.0f;
        m22 = 1.0f;
        return this;
    }

    /**
     * Set this matrix to a rotation of <code>angleX</code> radians about the X axis, followed by a rotation
     * of <code>angleY</code> radians about the Y axis and followed by a rotation of <code>angleZ</code> radians about the Z axis.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * This method is equivalent to calling: <tt>rotationX(angleX).rotateY(angleY).rotateZ(angleZ)</tt>
     * 
     * @param angleX
     *            the angle to rotate about X
     * @param angleY
     *            the angle to rotate about Y
     * @param angleZ
     *            the angle to rotate about Z
     * @return this
     */
    public Matrix3f rotationXYZ(float angleX, float angleY, float angleZ) {
        float sinX = (float) Math.sin(angleX);
        float cosX = (float) Math.cosFromSin(sinX, angleX);
        float sinY = (float) Math.sin(angleY);
        float cosY = (float) Math.cosFromSin(sinY, angleY);
        float sinZ = (float) Math.sin(angleZ);
        float cosZ = (float) Math.cosFromSin(sinZ, angleZ);
        float m_sinX = -sinX;
        float m_sinY = -sinY;
        float m_sinZ = -sinZ;

        // rotateX
        float nm11 = cosX;
        float nm12 = sinX;
        float nm21 = m_sinX;
        float nm22 = cosX;
        // rotateY
        float nm00 = cosY;
        float nm01 = nm21 * m_sinY;
        float nm02 = nm22 * m_sinY;
        m20 = sinY;
        m21 = nm21 * cosY;
        m22 = nm22 * cosY;
        // rotateZ
        m00 = nm00 * cosZ;
        m01 = nm01 * cosZ + nm11 * sinZ;
        m02 = nm02 * cosZ + nm12 * sinZ;
        m10 = nm00 * m_sinZ;
        m11 = nm01 * m_sinZ + nm11 * cosZ;
        m12 = nm02 * m_sinZ + nm12 * cosZ;
        return this;
    }

    /**
     * Set this matrix to a rotation of <code>angleZ</code> radians about the Z axis, followed by a rotation
     * of <code>angleY</code> radians about the Y axis and followed by a rotation of <code>angleX</code> radians about the X axis.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * This method is equivalent to calling: <tt>rotationZ(angleZ).rotateY(angleY).rotateX(angleX)</tt>
     * 
     * @param angleZ
     *            the angle to rotate about Z
     * @param angleY
     *            the angle to rotate about Y
     * @param angleX
     *            the angle to rotate about X
     * @return this
     */
    public Matrix3f rotationZYX(float angleZ, float angleY, float angleX) {
        float sinX = (float) Math.sin(angleX);
        float cosX = (float) Math.cosFromSin(sinX, angleX);
        float sinY = (float) Math.sin(angleY);
        float cosY = (float) Math.cosFromSin(sinY, angleY);
        float sinZ = (float) Math.sin(angleZ);
        float cosZ = (float) Math.cosFromSin(sinZ, angleZ);
        float m_sinZ = -sinZ;
        float m_sinY = -sinY;
        float m_sinX = -sinX;

        // rotateZ
        float nm00 = cosZ;
        float nm01 = sinZ;
        float nm10 = m_sinZ;
        float nm11 = cosZ;
        // rotateY
        float nm20 = nm00 * sinY;
        float nm21 = nm01 * sinY;
        float nm22 = cosY;
        m00 = nm00 * cosY;
        m01 = nm01 * cosY;
        m02 = m_sinY;
        // rotateX
        m10 = nm10 * cosX + nm20 * sinX;
        m11 = nm11 * cosX + nm21 * sinX;
        m12 = nm22 * sinX;
        m20 = nm10 * m_sinX + nm20 * cosX;
        m21 = nm11 * m_sinX + nm21 * cosX;
        m22 = nm22 * cosX;
        return this;
    }

    /**
     * Set this matrix to a rotation of <code>angleY</code> radians about the Y axis, followed by a rotation
     * of <code>angleX</code> radians about the X axis and followed by a rotation of <code>angleZ</code> radians about the Z axis.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * This method is equivalent to calling: <tt>rotationY(angleY).rotateX(angleX).rotateZ(angleZ)</tt>
     * 
     * @param angleY
     *            the angle to rotate about Y
     * @param angleX
     *            the angle to rotate about X
     * @param angleZ
     *            the angle to rotate about Z
     * @return this
     */
    public Matrix3f rotationYXZ(float angleY, float angleX, float angleZ) {
        float sinX = (float) Math.sin(angleX);
        float cosX = (float) Math.cosFromSin(sinX, angleX);
        float sinY = (float) Math.sin(angleY);
        float cosY = (float) Math.cosFromSin(sinY, angleY);
        float sinZ = (float) Math.sin(angleZ);
        float cosZ = (float) Math.cosFromSin(sinZ, angleZ);
        float m_sinY = -sinY;
        float m_sinX = -sinX;
        float m_sinZ = -sinZ;

        // rotateY
        float nm00 = cosY;
        float nm02 = m_sinY;
        float nm20 = sinY;
        float nm22 = cosY;
        // rotateX
        float nm10 = nm20 * sinX;
        float nm11 = cosX;
        float nm12 = nm22 * sinX;
        m20 = nm20 * cosX;
        m21 = m_sinX;
        m22 = nm22 * cosX;
        // rotateZ
        m00 = nm00 * cosZ + nm10 * sinZ;
        m01 = nm11 * sinZ;
        m02 = nm02 * cosZ + nm12 * sinZ;
        m10 = nm00 * m_sinZ + nm10 * cosZ;
        m11 = nm11 * cosZ;
        m12 = nm02 * m_sinZ + nm12 * cosZ;
        return this;
    }

    /**
     * Set this matrix to the rotation - and possibly scaling - transformation of the given {@link Quaternionfc}.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * The resulting matrix can be multiplied against another transformation
     * matrix to obtain an additional rotation.
     * <p>
     * In order to apply the rotation transformation to an existing transformation,
     * use {@link #rotate(Quaternionfc) rotate()} instead.
     * <p>
     * Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Quaternion">http://en.wikipedia.org</a>
     * 
     * @see #rotate(Quaternionfc)
     * 
     * @param quat
     *          the {@link Quaternionfc}
     * @return this
     */
    public Matrix3f rotation(Quaternionfc quat) {
        float w2 = quat.w() * quat.w();
        float x2 = quat.x() * quat.x();
        float y2 = quat.y() * quat.y();
        float z2 = quat.z() * quat.z();
        float zw = quat.z() * quat.w();
        float xy = quat.x() * quat.y();
        float xz = quat.x() * quat.z();
        float yw = quat.y() * quat.w();
        float yz = quat.y() * quat.z();
        float xw = quat.x() * quat.w();
        m00 = w2 + x2 - z2 - y2;
        m01 = xy + zw + zw + xy;
        m02 = xz - yw + xz - yw;
        m10 = -zw + xy - zw + xy;
        m11 = y2 - z2 + w2 - x2;
        m12 = yz + yz + xw + xw;
        m20 = yw + xz + xz + yw;
        m21 = yz + yz - xw - xw;
        m22 = z2 - y2 - x2 + w2;
        return this;
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#transform(org.joml.Vector3f)
     */
    public Vector3f transform(Vector3f v) {
        return v.mul(this);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#transform(org.joml.Vector3fc, org.joml.Vector3f)
     */
    public Vector3f transform(Vector3fc v, Vector3f dest) {
        v.mul(this, dest);
        return dest;
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#transform(float, float, float, org.joml.Vector3f)
     */
    public Vector3f transform(float x, float y, float z, Vector3f dest) {
        dest.set(m00 * x + m10 * y + m20 * z,
                 m01 * x + m11 * y + m21 * z,
                 m02 * x + m12 * y + m22 * z);
        return dest;
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#transformTranspose(org.joml.Vector3f)
     */
    public Vector3f transformTranspose(Vector3f v) {
        return v.mulTranspose(this);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#transformTranspose(org.joml.Vector3fc, org.joml.Vector3f)
     */
    public Vector3f transformTranspose(Vector3fc v, Vector3f dest) {
        v.mulTranspose(this, dest);
        return dest;
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#transformTranspose(float, float, float, org.joml.Vector3f)
     */
    public Vector3f transformTranspose(float x, float y, float z, Vector3f dest) {
        dest.set(m00 * x + m01 * y + m02 * z,
                 m10 * x + m11 * y + m12 * z,
                 m20 * x + m21 * y + m22 * z);
        return dest;
    }

    public void writeExternal(ObjectOutput out) throws IOException {
        out.writeFloat(m00);
        out.writeFloat(m01);
        out.writeFloat(m02);
        out.writeFloat(m10);
        out.writeFloat(m11);
        out.writeFloat(m12);
        out.writeFloat(m20);
        out.writeFloat(m21);
        out.writeFloat(m22);
    }

    public void readExternal(ObjectInput in) throws IOException {
        m00 = in.readFloat();
        m01 = in.readFloat();
        m02 = in.readFloat();
        m10 = in.readFloat();
        m11 = in.readFloat();
        m12 = in.readFloat();
        m20 = in.readFloat();
        m21 = in.readFloat();
        m22 = in.readFloat();
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#rotateX(float, org.joml.Matrix3f)
     */
    public Matrix3f rotateX(float ang, Matrix3f dest) {
        float sin, cos;
        if (ang == (float) Math.PI || ang == -(float) Math.PI) {
            cos = -1.0f;
            sin = 0.0f;
        } else if (ang == (float) Math.PI * 0.5f || ang == -(float) Math.PI * 1.5f) {
            cos = 0.0f;
            sin = 1.0f;
        } else if (ang == (float) -Math.PI * 0.5f || ang == (float) Math.PI * 1.5f) {
            cos = 0.0f;
            sin = -1.0f;
        } else {
            sin = (float) Math.sin(ang);
            cos = (float) Math.cosFromSin(sin, ang);
        }
        float rm11 = cos;
        float rm21 = -sin;
        float rm12 = sin;
        float rm22 = cos;

        // add temporaries for dependent values
        float nm10 = m10 * rm11 + m20 * rm12;
        float nm11 = m11 * rm11 + m21 * rm12;
        float nm12 = m12 * rm11 + m22 * rm12;
        // set non-dependent values directly
        dest.m20 = m10 * rm21 + m20 * rm22;
        dest.m21 = m11 * rm21 + m21 * rm22;
        dest.m22 = m12 * rm21 + m22 * rm22;
        // set other values
        dest.m10 = nm10;
        dest.m11 = nm11;
        dest.m12 = nm12;
        dest.m00 = m00;
        dest.m01 = m01;
        dest.m02 = m02;

        return dest;
    }

    /**
     * Apply rotation about the X axis to this matrix by rotating the given amount of radians.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
     * then the new matrix will be <code>M * R</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * R * v</code>
     * , the rotation will be applied first!
     * <p>
     * Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations">http://en.wikipedia.org</a>
     * 
     * @param ang
     *            the angle in radians
     * @return this
     */
    public Matrix3f rotateX(float ang) {
        return rotateX(ang, this);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#rotateY(float, org.joml.Matrix3f)
     */
    public Matrix3f rotateY(float ang, Matrix3f dest) {
        float sin, cos;
        if (ang == (float) Math.PI || ang == -(float) Math.PI) {
            cos = -1.0f;
            sin = 0.0f;
        } else if (ang == (float) Math.PI * 0.5f || ang == -(float) Math.PI * 1.5f) {
            cos = 0.0f;
            sin = 1.0f;
        } else if (ang == (float) -Math.PI * 0.5f || ang == (float) Math.PI * 1.5f) {
            cos = 0.0f;
            sin = -1.0f;
        } else {
            sin = (float) Math.sin(ang);
            cos = (float) Math.cosFromSin(sin, ang);
        }
        float rm00 = cos;
        float rm20 = sin;
        float rm02 = -sin;
        float rm22 = cos;

        // add temporaries for dependent values
        float nm00 = m00 * rm00 + m20 * rm02;
        float nm01 = m01 * rm00 + m21 * rm02;
        float nm02 = m02 * rm00 + m22 * rm02;
        // set non-dependent values directly
        dest.m20 = m00 * rm20 + m20 * rm22;
        dest.m21 = m01 * rm20 + m21 * rm22;
        dest.m22 = m02 * rm20 + m22 * rm22;
        // set other values
        dest.m00 = nm00;
        dest.m01 = nm01;
        dest.m02 = nm02;
        dest.m10 = m10;
        dest.m11 = m11;
        dest.m12 = m12;

        return dest;
    }

    /**
     * Apply rotation about the Y axis to this matrix by rotating the given amount of radians.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
     * then the new matrix will be <code>M * R</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * R * v</code>
     * , the rotation will be applied first!
     * <p>
     * Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations">http://en.wikipedia.org</a>
     * 
     * @param ang
     *            the angle in radians
     * @return this
     */
    public Matrix3f rotateY(float ang) {
        return rotateY(ang, this);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#rotateZ(float, org.joml.Matrix3f)
     */
    public Matrix3f rotateZ(float ang, Matrix3f dest) {
        float sin, cos;
        if (ang == (float) Math.PI || ang == -(float) Math.PI) {
            cos = -1.0f;
            sin = 0.0f;
        } else if (ang == (float) Math.PI * 0.5f || ang == -(float) Math.PI * 1.5f) {
            cos = 0.0f;
            sin = 1.0f;
        } else if (ang == (float) -Math.PI * 0.5f || ang == (float) Math.PI * 1.5f) {
            cos = 0.0f;
            sin = -1.0f;
        } else {
            sin = (float) Math.sin(ang);
            cos = (float) Math.cosFromSin(sin, ang);
        }
        float rm00 = cos;
        float rm10 = -sin;
        float rm01 = sin;
        float rm11 = cos;

        // add temporaries for dependent values
        float nm00 = m00 * rm00 + m10 * rm01;
        float nm01 = m01 * rm00 + m11 * rm01;
        float nm02 = m02 * rm00 + m12 * rm01;
        // set non-dependent values directly
        dest.m10 = m00 * rm10 + m10 * rm11;
        dest.m11 = m01 * rm10 + m11 * rm11;
        dest.m12 = m02 * rm10 + m12 * rm11;
        // set other values
        dest.m00 = nm00;
        dest.m01 = nm01;
        dest.m02 = nm02;
        dest.m20 = m20;
        dest.m21 = m21;
        dest.m22 = m22;

        return dest;
    }

    /**
     * Apply rotation about the Z axis to this matrix by rotating the given amount of radians.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
     * then the new matrix will be <code>M * R</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * R * v</code>
     * , the rotation will be applied first!
     * <p>
     * Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations">http://en.wikipedia.org</a>
     * 
     * @param ang
     *            the angle in radians
     * @return this
     */
    public Matrix3f rotateZ(float ang) {
        return rotateZ(ang, this);
    }

    /**
     * Apply rotation of <code>angles.x</code> radians about the X axis, followed by a rotation of <code>angles.y</code> radians about the Y axis and
     * followed by a rotation of <code>angles.z</code> radians about the Z axis.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
     * then the new matrix will be <code>M * R</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * R * v</code>, the
     * rotation will be applied first!
     * <p>
     * This method is equivalent to calling: <tt>rotateX(angles.x).rotateY(angles.y).rotateZ(angles.z)</tt>
     * 
     * @param angles
     *            the Euler angles
     * @return this
     */
    public Matrix3f rotateXYZ(Vector3f angles) {
        return rotateXYZ(angles.x, angles.y, angles.z);
    }

    /**
     * Apply rotation of <code>angleX</code> radians about the X axis, followed by a rotation of <code>angleY</code> radians about the Y axis and
     * followed by a rotation of <code>angleZ</code> radians about the Z axis.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
     * then the new matrix will be <code>M * R</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * R * v</code>, the
     * rotation will be applied first!
     * <p>
     * This method is equivalent to calling: <tt>rotateX(angleX).rotateY(angleY).rotateZ(angleZ)</tt>
     * 
     * @param angleX
     *            the angle to rotate about X
     * @param angleY
     *            the angle to rotate about Y
     * @param angleZ
     *            the angle to rotate about Z
     * @return this
     */
    public Matrix3f rotateXYZ(float angleX, float angleY, float angleZ) {
        return rotateXYZ(angleX, angleY, angleZ, this);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#rotateXYZ(float, float, float, org.joml.Matrix3f)
     */
    public Matrix3f rotateXYZ(float angleX, float angleY, float angleZ, Matrix3f dest) {
        float sinX = (float) Math.sin(angleX);
        float cosX = (float) Math.cosFromSin(sinX, angleX);
        float sinY = (float) Math.sin(angleY);
        float cosY = (float) Math.cosFromSin(sinY, angleY);
        float sinZ = (float) Math.sin(angleZ);
        float cosZ = (float) Math.cosFromSin(sinZ, angleZ);
        float m_sinX = -sinX;
        float m_sinY = -sinY;
        float m_sinZ = -sinZ;

        // rotateX
        float nm10 = m10 * cosX + m20 * sinX;
        float nm11 = m11 * cosX + m21 * sinX;
        float nm12 = m12 * cosX + m22 * sinX;
        float nm20 = m10 * m_sinX + m20 * cosX;
        float nm21 = m11 * m_sinX + m21 * cosX;
        float nm22 = m12 * m_sinX + m22 * cosX;
        // rotateY
        float nm00 = m00 * cosY + nm20 * m_sinY;
        float nm01 = m01 * cosY + nm21 * m_sinY;
        float nm02 = m02 * cosY + nm22 * m_sinY;
        dest.m20 = m00 * sinY + nm20 * cosY;
        dest.m21 = m01 * sinY + nm21 * cosY;
        dest.m22 = m02 * sinY + nm22 * cosY;
        // rotateZ
        dest.m00 = nm00 * cosZ + nm10 * sinZ;
        dest.m01 = nm01 * cosZ + nm11 * sinZ;
        dest.m02 = nm02 * cosZ + nm12 * sinZ;
        dest.m10 = nm00 * m_sinZ + nm10 * cosZ;
        dest.m11 = nm01 * m_sinZ + nm11 * cosZ;
        dest.m12 = nm02 * m_sinZ + nm12 * cosZ;
        return dest;
    }

    /**
     * Apply rotation of <code>angles.z</code> radians about the Z axis, followed by a rotation of <code>angles.y</code> radians about the Y axis and
     * followed by a rotation of <code>angles.x</code> radians about the X axis.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
     * then the new matrix will be <code>M * R</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * R * v</code>, the
     * rotation will be applied first!
     * <p>
     * This method is equivalent to calling: <tt>rotateZ(angles.z).rotateY(angles.y).rotateX(angles.x)</tt>
     * 
     * @param angles
     *            the Euler angles
     * @return this
     */
    public Matrix3f rotateZYX(Vector3f angles) {
        return rotateZYX(angles.z, angles.y, angles.x);
    }

    /**
     * Apply rotation of <code>angleZ</code> radians about the Z axis, followed by a rotation of <code>angleY</code> radians about the Y axis and
     * followed by a rotation of <code>angleX</code> radians about the X axis.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
     * then the new matrix will be <code>M * R</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * R * v</code>, the
     * rotation will be applied first!
     * <p>
     * This method is equivalent to calling: <tt>rotateZ(angleZ).rotateY(angleY).rotateX(angleX)</tt>
     * 
     * @param angleZ
     *            the angle to rotate about Z
     * @param angleY
     *            the angle to rotate about Y
     * @param angleX
     *            the angle to rotate about X
     * @return this
     */
    public Matrix3f rotateZYX(float angleZ, float angleY, float angleX) {
        return rotateZYX(angleZ, angleY, angleX, this);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#rotateZYX(float, float, float, org.joml.Matrix3f)
     */
    public Matrix3f rotateZYX(float angleZ, float angleY, float angleX, Matrix3f dest) {
        float sinX = (float) Math.sin(angleX);
        float cosX = (float) Math.cosFromSin(sinX, angleX);
        float sinY = (float) Math.sin(angleY);
        float cosY = (float) Math.cosFromSin(sinY, angleY);
        float sinZ = (float) Math.sin(angleZ);
        float cosZ = (float) Math.cosFromSin(sinZ, angleZ);
        float m_sinZ = -sinZ;
        float m_sinY = -sinY;
        float m_sinX = -sinX;

        // rotateZ
        float nm00 = m00 * cosZ + m10 * sinZ;
        float nm01 = m01 * cosZ + m11 * sinZ;
        float nm02 = m02 * cosZ + m12 * sinZ;
        float nm10 = m00 * m_sinZ + m10 * cosZ;
        float nm11 = m01 * m_sinZ + m11 * cosZ;
        float nm12 = m02 * m_sinZ + m12 * cosZ;
        // rotateY
        float nm20 = nm00 * sinY + m20 * cosY;
        float nm21 = nm01 * sinY + m21 * cosY;
        float nm22 = nm02 * sinY + m22 * cosY;
        dest.m00 = nm00 * cosY + m20 * m_sinY;
        dest.m01 = nm01 * cosY + m21 * m_sinY;
        dest.m02 = nm02 * cosY + m22 * m_sinY;
        // rotateX
        dest.m10 = nm10 * cosX + nm20 * sinX;
        dest.m11 = nm11 * cosX + nm21 * sinX;
        dest.m12 = nm12 * cosX + nm22 * sinX;
        dest.m20 = nm10 * m_sinX + nm20 * cosX;
        dest.m21 = nm11 * m_sinX + nm21 * cosX;
        dest.m22 = nm12 * m_sinX + nm22 * cosX;
        return dest;
    }

    /**
     * Apply rotation of <code>angles.y</code> radians about the Y axis, followed by a rotation of <code>angles.x</code> radians about the X axis and
     * followed by a rotation of <code>angles.z</code> radians about the Z axis.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
     * then the new matrix will be <code>M * R</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * R * v</code>, the
     * rotation will be applied first!
     * <p>
     * This method is equivalent to calling: <tt>rotateY(angles.y).rotateX(angles.x).rotateZ(angles.z)</tt>
     * 
     * @param angles
     *            the Euler angles
     * @return this
     */
    public Matrix3f rotateYXZ(Vector3f angles) {
        return rotateYXZ(angles.y, angles.x, angles.z);
    }

    /**
     * Apply rotation of <code>angleY</code> radians about the Y axis, followed by a rotation of <code>angleX</code> radians about the X axis and
     * followed by a rotation of <code>angleZ</code> radians about the Z axis.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
     * then the new matrix will be <code>M * R</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * R * v</code>, the
     * rotation will be applied first!
     * <p>
     * This method is equivalent to calling: <tt>rotateY(angleY).rotateX(angleX).rotateZ(angleZ)</tt>
     * 
     * @param angleY
     *            the angle to rotate about Y
     * @param angleX
     *            the angle to rotate about X
     * @param angleZ
     *            the angle to rotate about Z
     * @return this
     */
    public Matrix3f rotateYXZ(float angleY, float angleX, float angleZ) {
        return rotateYXZ(angleY, angleX, angleZ, this);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#rotateYXZ(float, float, float, org.joml.Matrix3f)
     */
    public Matrix3f rotateYXZ(float angleY, float angleX, float angleZ, Matrix3f dest) {
        float sinX = (float) Math.sin(angleX);
        float cosX = (float) Math.cosFromSin(sinX, angleX);
        float sinY = (float) Math.sin(angleY);
        float cosY = (float) Math.cosFromSin(sinY, angleY);
        float sinZ = (float) Math.sin(angleZ);
        float cosZ = (float) Math.cosFromSin(sinZ, angleZ);
        float m_sinY = -sinY;
        float m_sinX = -sinX;
        float m_sinZ = -sinZ;

        // rotateY
        float nm20 = m00 * sinY + m20 * cosY;
        float nm21 = m01 * sinY + m21 * cosY;
        float nm22 = m02 * sinY + m22 * cosY;
        float nm00 = m00 * cosY + m20 * m_sinY;
        float nm01 = m01 * cosY + m21 * m_sinY;
        float nm02 = m02 * cosY + m22 * m_sinY;
        // rotateX
        float nm10 = m10 * cosX + nm20 * sinX;
        float nm11 = m11 * cosX + nm21 * sinX;
        float nm12 = m12 * cosX + nm22 * sinX;
        dest.m20 = m10 * m_sinX + nm20 * cosX;
        dest.m21 = m11 * m_sinX + nm21 * cosX;
        dest.m22 = m12 * m_sinX + nm22 * cosX;
        // rotateZ
        dest.m00 = nm00 * cosZ + nm10 * sinZ;
        dest.m01 = nm01 * cosZ + nm11 * sinZ;
        dest.m02 = nm02 * cosZ + nm12 * sinZ;
        dest.m10 = nm00 * m_sinZ + nm10 * cosZ;
        dest.m11 = nm01 * m_sinZ + nm11 * cosZ;
        dest.m12 = nm02 * m_sinZ + nm12 * cosZ;
        return dest;
    }

    /**
     * Apply rotation to this matrix by rotating the given amount of radians
     * about the given axis specified as x, y and z components.
     * <p>
     * The axis described by the three components needs to be a unit vector.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
     * then the new matrix will be <code>M * R</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * R * v</code>
     * , the rotation will be applied first!
     * <p>
     * Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle">http://en.wikipedia.org</a>
     * 
     * @param ang
     *            the angle in radians
     * @param x
     *            the x component of the axis
     * @param y
     *            the y component of the axis
     * @param z
     *            the z component of the axis
     * @return this
     */
    public Matrix3f rotate(float ang, float x, float y, float z) {
        return rotate(ang, x, y, z, this);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#rotate(float, float, float, float, org.joml.Matrix3f)
     */
    public Matrix3f rotate(float ang, float x, float y, float z, Matrix3f dest) {
        float s = (float) Math.sin(ang);
        float c = (float) Math.cosFromSin(s, ang);
        float C = 1.0f - c;

        // rotation matrix elements:
        // m30, m31, m32, m03, m13, m23 = 0
        float xx = x * x, xy = x * y, xz = x * z;
        float yy = y * y, yz = y * z;
        float zz = z * z;
        float rm00 = xx * C + c;
        float rm01 = xy * C + z * s;
        float rm02 = xz * C - y * s;
        float rm10 = xy * C - z * s;
        float rm11 = yy * C + c;
        float rm12 = yz * C + x * s;
        float rm20 = xz * C + y * s;
        float rm21 = yz * C - x * s;
        float rm22 = zz * C + c;

        // add temporaries for dependent values
        float nm00 = m00 * rm00 + m10 * rm01 + m20 * rm02;
        float nm01 = m01 * rm00 + m11 * rm01 + m21 * rm02;
        float nm02 = m02 * rm00 + m12 * rm01 + m22 * rm02;
        float nm10 = m00 * rm10 + m10 * rm11 + m20 * rm12;
        float nm11 = m01 * rm10 + m11 * rm11 + m21 * rm12;
        float nm12 = m02 * rm10 + m12 * rm11 + m22 * rm12;
        // set non-dependent values directly
        dest.m20 = m00 * rm20 + m10 * rm21 + m20 * rm22;
        dest.m21 = m01 * rm20 + m11 * rm21 + m21 * rm22;
        dest.m22 = m02 * rm20 + m12 * rm21 + m22 * rm22;
        // set other values
        dest.m00 = nm00;
        dest.m01 = nm01;
        dest.m02 = nm02;
        dest.m10 = nm10;
        dest.m11 = nm11;
        dest.m12 = nm12;

        return dest;
    }

    /**
     * Pre-multiply a rotation to this matrix by rotating the given amount of radians
     * about the specified <tt>(x, y, z)</tt> axis and store the result in <code>dest</code>.
     * <p>
     * The axis described by the three components needs to be a unit vector.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
     * then the new matrix will be <code>R * M</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>R * M * v</code>, the
     * rotation will be applied last!
     * <p>
     * In order to set the matrix to a rotation matrix without pre-multiplying the rotation
     * transformation, use {@link #rotation(float, float, float, float) rotation()}.
     * <p>
     * Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle">http://en.wikipedia.org</a>
     * 
     * @see #rotation(float, float, float, float)
     * 
     * @param ang
     *            the angle in radians
     * @param x
     *            the x component of the axis
     * @param y
     *            the y component of the axis
     * @param z
     *            the z component of the axis
     * @param dest
     *            will hold the result
     * @return dest
     */
    public Matrix3f rotateLocal(float ang, float x, float y, float z, Matrix3f dest) {
        float s = (float) Math.sin(ang);
        float c = (float) Math.cosFromSin(s, ang);
        float C = 1.0f - c;
        float xx = x * x, xy = x * y, xz = x * z;
        float yy = y * y, yz = y * z;
        float zz = z * z;
        float lm00 = xx * C + c;
        float lm01 = xy * C + z * s;
        float lm02 = xz * C - y * s;
        float lm10 = xy * C - z * s;
        float lm11 = yy * C + c;
        float lm12 = yz * C + x * s;
        float lm20 = xz * C + y * s;
        float lm21 = yz * C - x * s;
        float lm22 = zz * C + c;
        float nm00 = lm00 * m00 + lm10 * m01 + lm20 * m02;
        float nm01 = lm01 * m00 + lm11 * m01 + lm21 * m02;
        float nm02 = lm02 * m00 + lm12 * m01 + lm22 * m02;
        float nm10 = lm00 * m10 + lm10 * m11 + lm20 * m12;
        float nm11 = lm01 * m10 + lm11 * m11 + lm21 * m12;
        float nm12 = lm02 * m10 + lm12 * m11 + lm22 * m12;
        float nm20 = lm00 * m20 + lm10 * m21 + lm20 * m22;
        float nm21 = lm01 * m20 + lm11 * m21 + lm21 * m22;
        float nm22 = lm02 * m20 + lm12 * m21 + lm22 * m22;
        dest.m00 = nm00;
        dest.m01 = nm01;
        dest.m02 = nm02;
        dest.m10 = nm10;
        dest.m11 = nm11;
        dest.m12 = nm12;
        dest.m20 = nm20;
        dest.m21 = nm21;
        dest.m22 = nm22;
        return dest;
    }

    /**
     * Pre-multiply a rotation to this matrix by rotating the given amount of radians
     * about the specified <tt>(x, y, z)</tt> axis.
     * <p>
     * The axis described by the three components needs to be a unit vector.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
     * then the new matrix will be <code>R * M</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>R * M * v</code>, the
     * rotation will be applied last!
     * <p>
     * In order to set the matrix to a rotation matrix without pre-multiplying the rotation
     * transformation, use {@link #rotation(float, float, float, float) rotation()}.
     * <p>
     * Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle">http://en.wikipedia.org</a>
     * 
     * @see #rotation(float, float, float, float)
     * 
     * @param ang
     *            the angle in radians
     * @param x
     *            the x component of the axis
     * @param y
     *            the y component of the axis
     * @param z
     *            the z component of the axis
     * @return this
     */
    public Matrix3f rotateLocal(float ang, float x, float y, float z) {
        return rotateLocal(ang, x, y, z, this);
    }

    /**
     * Pre-multiply a rotation around the X axis to this matrix by rotating the given amount of radians
     * about the X axis and store the result in <code>dest</code>.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
     * then the new matrix will be <code>R * M</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>R * M * v</code>, the
     * rotation will be applied last!
     * <p>
     * In order to set the matrix to a rotation matrix without pre-multiplying the rotation
     * transformation, use {@link #rotationX(float) rotationX()}.
     * <p>
     * Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle">http://en.wikipedia.org</a>
     * 
     * @see #rotationX(float)
     * 
     * @param ang
     *            the angle in radians to rotate about the X axis
     * @param dest
     *            will hold the result
     * @return dest
     */
    public Matrix3f rotateLocalX(float ang, Matrix3f dest) {
        float sin = (float) Math.sin(ang);
        float cos = (float) Math.cosFromSin(sin, ang);
        float nm01 = cos * m01 - sin * m02;
        float nm02 = sin * m01 + cos * m02;
        float nm11 = cos * m11 - sin * m12;
        float nm12 = sin * m11 + cos * m12;
        float nm21 = cos * m21 - sin * m22;
        float nm22 = sin * m21 + cos * m22;
        dest.m00 = m00;
        dest.m01 = nm01;
        dest.m02 = nm02;
        dest.m10 = m10;
        dest.m11 = nm11;
        dest.m12 = nm12;
        dest.m20 = m20;
        dest.m21 = nm21;
        dest.m22 = nm22;
        return dest;
    }

    /**
     * Pre-multiply a rotation to this matrix by rotating the given amount of radians about the X axis.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
     * then the new matrix will be <code>R * M</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>R * M * v</code>, the
     * rotation will be applied last!
     * <p>
     * In order to set the matrix to a rotation matrix without pre-multiplying the rotation
     * transformation, use {@link #rotationX(float) rotationX()}.
     * <p>
     * Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle">http://en.wikipedia.org</a>
     * 
     * @see #rotationX(float)
     * 
     * @param ang
     *            the angle in radians to rotate about the X axis
     * @return this
     */
    public Matrix3f rotateLocalX(float ang) {
        return rotateLocalX(ang, this);
    }

    /**
     * Pre-multiply a rotation around the Y axis to this matrix by rotating the given amount of radians
     * about the Y axis and store the result in <code>dest</code>.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
     * then the new matrix will be <code>R * M</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>R * M * v</code>, the
     * rotation will be applied last!
     * <p>
     * In order to set the matrix to a rotation matrix without pre-multiplying the rotation
     * transformation, use {@link #rotationY(float) rotationY()}.
     * <p>
     * Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle">http://en.wikipedia.org</a>
     * 
     * @see #rotationY(float)
     * 
     * @param ang
     *            the angle in radians to rotate about the Y axis
     * @param dest
     *            will hold the result
     * @return dest
     */
    public Matrix3f rotateLocalY(float ang, Matrix3f dest) {
        float sin = (float) Math.sin(ang);
        float cos = (float) Math.cosFromSin(sin, ang);
        float nm00 =  cos * m00 + sin * m02;
        float nm02 = -sin * m00 + cos * m02;
        float nm10 =  cos * m10 + sin * m12;
        float nm12 = -sin * m10 + cos * m12;
        float nm20 =  cos * m20 + sin * m22;
        float nm22 = -sin * m20 + cos * m22;
        dest.m00 = nm00;
        dest.m01 = m01;
        dest.m02 = nm02;
        dest.m10 = nm10;
        dest.m11 = m11;
        dest.m12 = nm12;
        dest.m20 = nm20;
        dest.m21 = m21;
        dest.m22 = nm22;
        return dest;
    }

    /**
     * Pre-multiply a rotation to this matrix by rotating the given amount of radians about the Y axis.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
     * then the new matrix will be <code>R * M</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>R * M * v</code>, the
     * rotation will be applied last!
     * <p>
     * In order to set the matrix to a rotation matrix without pre-multiplying the rotation
     * transformation, use {@link #rotationY(float) rotationY()}.
     * <p>
     * Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle">http://en.wikipedia.org</a>
     * 
     * @see #rotationY(float)
     * 
     * @param ang
     *            the angle in radians to rotate about the Y axis
     * @return this
     */
    public Matrix3f rotateLocalY(float ang) {
        return rotateLocalY(ang, this);
    }

    /**
     * Pre-multiply a rotation around the Z axis to this matrix by rotating the given amount of radians
     * about the Z axis and store the result in <code>dest</code>.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
     * then the new matrix will be <code>R * M</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>R * M * v</code>, the
     * rotation will be applied last!
     * <p>
     * In order to set the matrix to a rotation matrix without pre-multiplying the rotation
     * transformation, use {@link #rotationZ(float) rotationZ()}.
     * <p>
     * Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle">http://en.wikipedia.org</a>
     * 
     * @see #rotationZ(float)
     * 
     * @param ang
     *            the angle in radians to rotate about the Z axis
     * @param dest
     *            will hold the result
     * @return dest
     */
    public Matrix3f rotateLocalZ(float ang, Matrix3f dest) {
        float sin = (float) Math.sin(ang);
        float cos = (float) Math.cosFromSin(sin, ang);
        float nm00 = cos * m00 - sin * m01;
        float nm01 = sin * m00 + cos * m01;
        float nm10 = cos * m10 - sin * m11;
        float nm11 = sin * m10 + cos * m11;
        float nm20 = cos * m20 - sin * m21;
        float nm21 = sin * m20 + cos * m21;
        dest.m00 = nm00;
        dest.m01 = nm01;
        dest.m02 = m02;
        dest.m10 = nm10;
        dest.m11 = nm11;
        dest.m12 = m12;
        dest.m20 = nm20;
        dest.m21 = nm21;
        dest.m22 = m22;
        return dest;
    }

    /**
     * Pre-multiply a rotation to this matrix by rotating the given amount of radians about the Z axis.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
     * then the new matrix will be <code>R * M</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>R * M * v</code>, the
     * rotation will be applied last!
     * <p>
     * In order to set the matrix to a rotation matrix without pre-multiplying the rotation
     * transformation, use {@link #rotationZ(float) rotationY()}.
     * <p>
     * Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle">http://en.wikipedia.org</a>
     * 
     * @see #rotationY(float)
     * 
     * @param ang
     *            the angle in radians to rotate about the Z axis
     * @return this
     */
    public Matrix3f rotateLocalZ(float ang) {
        return rotateLocalZ(ang, this);
    }

    /**
     * Apply the rotation - and possibly scaling - transformation of the given {@link Quaternionfc} to this matrix.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>Q</code> the rotation matrix obtained from the given quaternion,
     * then the new matrix will be <code>M * Q</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * Q * v</code>,
     * the quaternion rotation will be applied first!
     * <p>
     * In order to set the matrix to a rotation transformation without post-multiplying,
     * use {@link #rotation(Quaternionfc)}.
     * <p>
     * Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Quaternion">http://en.wikipedia.org</a>
     * 
     * @see #rotation(Quaternionfc)
     * 
     * @param quat
     *          the {@link Quaternionfc}
     * @return this
     */
    public Matrix3f rotate(Quaternionfc quat) {
        return rotate(quat, this);
    }

    /**
     * Apply the rotation - and possibly scaling - transformation of the given {@link Quaternionfc} to this matrix and store
     * the result in <code>dest</code>.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>Q</code> the rotation matrix obtained from the given quaternion,
     * then the new matrix will be <code>M * Q</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * Q * v</code>,
     * the quaternion rotation will be applied first!
     * <p>
     * In order to set the matrix to a rotation transformation without post-multiplying,
     * use {@link #rotation(Quaternionfc)}.
     * <p>
     * Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Quaternion">http://en.wikipedia.org</a>
     * 
     * @see #rotation(Quaternionfc)
     * 
     * @param quat
     *          the {@link Quaternionfc}
     * @param dest
     *          will hold the result
     * @return dest
     */
    public Matrix3f rotate(Quaternionfc quat, Matrix3f dest) {
        float w2 = quat.w() * quat.w();
        float x2 = quat.x() * quat.x();
        float y2 = quat.y() * quat.y();
        float z2 = quat.z() * quat.z();
        float zw = quat.z() * quat.w();
        float xy = quat.x() * quat.y();
        float xz = quat.x() * quat.z();
        float yw = quat.y() * quat.w();
        float yz = quat.y() * quat.z();
        float xw = quat.x() * quat.w();
        float rm00 = w2 + x2 - z2 - y2;
        float rm01 = xy + zw + zw + xy;
        float rm02 = xz - yw + xz - yw;
        float rm10 = -zw + xy - zw + xy;
        float rm11 = y2 - z2 + w2 - x2;
        float rm12 = yz + yz + xw + xw;
        float rm20 = yw + xz + xz + yw;
        float rm21 = yz + yz - xw - xw;
        float rm22 = z2 - y2 - x2 + w2;
        float nm00 = m00 * rm00 + m10 * rm01 + m20 * rm02;
        float nm01 = m01 * rm00 + m11 * rm01 + m21 * rm02;
        float nm02 = m02 * rm00 + m12 * rm01 + m22 * rm02;
        float nm10 = m00 * rm10 + m10 * rm11 + m20 * rm12;
        float nm11 = m01 * rm10 + m11 * rm11 + m21 * rm12;
        float nm12 = m02 * rm10 + m12 * rm11 + m22 * rm12;
        dest.m20 = m00 * rm20 + m10 * rm21 + m20 * rm22;
        dest.m21 = m01 * rm20 + m11 * rm21 + m21 * rm22;
        dest.m22 = m02 * rm20 + m12 * rm21 + m22 * rm22;
        dest.m00 = nm00;
        dest.m01 = nm01;
        dest.m02 = nm02;
        dest.m10 = nm10;
        dest.m11 = nm11;
        dest.m12 = nm12;
        return dest;
    }

    /**
     * Pre-multiply the rotation - and possibly scaling - transformation of the given {@link Quaternionfc} to this matrix and store
     * the result in <code>dest</code>.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>Q</code> the rotation matrix obtained from the given quaternion,
     * then the new matrix will be <code>Q * M</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>Q * M * v</code>,
     * the quaternion rotation will be applied last!
     * <p>
     * In order to set the matrix to a rotation transformation without pre-multiplying,
     * use {@link #rotation(Quaternionfc)}.
     * <p>
     * Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Quaternion">http://en.wikipedia.org</a>
     * 
     * @see #rotation(Quaternionfc)
     * 
     * @param quat
     *          the {@link Quaternionfc}
     * @param dest
     *          will hold the result
     * @return dest
     */
    public Matrix3f rotateLocal(Quaternionfc quat, Matrix3f dest) {
        float w2 = quat.w() * quat.w();
        float x2 = quat.x() * quat.x();
        float y2 = quat.y() * quat.y();
        float z2 = quat.z() * quat.z();
        float zw = quat.z() * quat.w();
        float xy = quat.x() * quat.y();
        float xz = quat.x() * quat.z();
        float yw = quat.y() * quat.w();
        float yz = quat.y() * quat.z();
        float xw = quat.x() * quat.w();
        float lm00 = w2 + x2 - z2 - y2;
        float lm01 = xy + zw + zw + xy;
        float lm02 = xz - yw + xz - yw;
        float lm10 = -zw + xy - zw + xy;
        float lm11 = y2 - z2 + w2 - x2;
        float lm12 = yz + yz + xw + xw;
        float lm20 = yw + xz + xz + yw;
        float lm21 = yz + yz - xw - xw;
        float lm22 = z2 - y2 - x2 + w2;
        float nm00 = lm00 * m00 + lm10 * m01 + lm20 * m02;
        float nm01 = lm01 * m00 + lm11 * m01 + lm21 * m02;
        float nm02 = lm02 * m00 + lm12 * m01 + lm22 * m02;
        float nm10 = lm00 * m10 + lm10 * m11 + lm20 * m12;
        float nm11 = lm01 * m10 + lm11 * m11 + lm21 * m12;
        float nm12 = lm02 * m10 + lm12 * m11 + lm22 * m12;
        float nm20 = lm00 * m20 + lm10 * m21 + lm20 * m22;
        float nm21 = lm01 * m20 + lm11 * m21 + lm21 * m22;
        float nm22 = lm02 * m20 + lm12 * m21 + lm22 * m22;
        dest.m00 = nm00;
        dest.m01 = nm01;
        dest.m02 = nm02;
        dest.m10 = nm10;
        dest.m11 = nm11;
        dest.m12 = nm12;
        dest.m20 = nm20;
        dest.m21 = nm21;
        dest.m22 = nm22;
        return dest;
    }

    /**
     * Pre-multiply the rotation - and possibly scaling - transformation of the given {@link Quaternionfc} to this matrix.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>Q</code> the rotation matrix obtained from the given quaternion,
     * then the new matrix will be <code>Q * M</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>Q * M * v</code>,
     * the quaternion rotation will be applied last!
     * <p>
     * In order to set the matrix to a rotation transformation without pre-multiplying,
     * use {@link #rotation(Quaternionfc)}.
     * <p>
     * Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Quaternion">http://en.wikipedia.org</a>
     * 
     * @see #rotation(Quaternionfc)
     * 
     * @param quat
     *          the {@link Quaternionfc}
     * @return this
     */
    public Matrix3f rotateLocal(Quaternionfc quat) {
        return rotateLocal(quat, this);
    }

    /**
     * Apply a rotation transformation, rotating about the given {@link AxisAngle4f}, to this matrix.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>A</code> the rotation matrix obtained from the given {@link AxisAngle4f},
     * then the new matrix will be <code>M * A</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * A * v</code>,
     * the {@link AxisAngle4f} rotation will be applied first!
     * <p>
     * In order to set the matrix to a rotation transformation without post-multiplying,
     * use {@link #rotation(AxisAngle4f)}.
     * <p>
     * Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Axis_and_angle">http://en.wikipedia.org</a>
     * 
     * @see #rotate(float, float, float, float)
     * @see #rotation(AxisAngle4f)
     * 
     * @param axisAngle
     *          the {@link AxisAngle4f} (needs to be {@link AxisAngle4f#normalize() normalized})
     * @return this
     */
    public Matrix3f rotate(AxisAngle4f axisAngle) {
        return rotate(axisAngle.angle, axisAngle.x, axisAngle.y, axisAngle.z);
    }

    /**
     * Apply a rotation transformation, rotating about the given {@link AxisAngle4f} and store the result in <code>dest</code>.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>A</code> the rotation matrix obtained from the given {@link AxisAngle4f},
     * then the new matrix will be <code>M * A</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * A * v</code>,
     * the {@link AxisAngle4f} rotation will be applied first!
     * <p>
     * In order to set the matrix to a rotation transformation without post-multiplying,
     * use {@link #rotation(AxisAngle4f)}.
     * <p>
     * Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Axis_and_angle">http://en.wikipedia.org</a>
     * 
     * @see #rotate(float, float, float, float)
     * @see #rotation(AxisAngle4f)
     * 
     * @param axisAngle
     *          the {@link AxisAngle4f} (needs to be {@link AxisAngle4f#normalize() normalized})
     * @param dest
     *          will hold the result
     * @return dest
     */
    public Matrix3f rotate(AxisAngle4f axisAngle, Matrix3f dest) {
        return rotate(axisAngle.angle, axisAngle.x, axisAngle.y, axisAngle.z, dest);
    }

    /**
     * Apply a rotation transformation, rotating the given radians about the specified axis, to this matrix.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>A</code> the rotation matrix obtained from the given angle and axis,
     * then the new matrix will be <code>M * A</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * A * v</code>,
     * the axis-angle rotation will be applied first!
     * <p>
     * In order to set the matrix to a rotation transformation without post-multiplying,
     * use {@link #rotation(float, Vector3fc)}.
     * <p>
     * Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Axis_and_angle">http://en.wikipedia.org</a>
     * 
     * @see #rotate(float, float, float, float)
     * @see #rotation(float, Vector3fc)
     * 
     * @param angle
     *          the angle in radians
     * @param axis
     *          the rotation axis (needs to be {@link Vector3f#normalize() normalized})
     * @return this
     */
    public Matrix3f rotate(float angle, Vector3fc axis) {
        return rotate(angle, axis.x(), axis.y(), axis.z());
    }

    /**
     * Apply a rotation transformation, rotating the given radians about the specified axis and store the result in <code>dest</code>.
     * <p>
     * When used with a right-handed coordinate system, the produced rotation will rotate a vector 
     * counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin.
     * When used with a left-handed coordinate system, the rotation is clockwise.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>A</code> the rotation matrix obtained from the given angle and axis,
     * then the new matrix will be <code>M * A</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * A * v</code>,
     * the axis-angle rotation will be applied first!
     * <p>
     * In order to set the matrix to a rotation transformation without post-multiplying,
     * use {@link #rotation(float, Vector3fc)}.
     * <p>
     * Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Axis_and_angle">http://en.wikipedia.org</a>
     * 
     * @see #rotate(float, float, float, float)
     * @see #rotation(float, Vector3fc)
     * 
     * @param angle
     *          the angle in radians
     * @param axis
     *          the rotation axis (needs to be {@link Vector3f#normalize() normalized})
     * @param dest
     *          will hold the result
     * @return dest
     */
    public Matrix3f rotate(float angle, Vector3fc axis, Matrix3f dest) {
        return rotate(angle, axis.x(), axis.y(), axis.z(), dest);
    }

    /**
     * Apply a rotation transformation to this matrix to make <code>-z</code> point along <code>dir</code>. 
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>L</code> the lookalong rotation matrix,
     * then the new matrix will be <code>M * L</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * L * v</code>, the
     * lookalong rotation transformation will be applied first!
     * <p>
     * In order to set the matrix to a lookalong transformation without post-multiplying it,
     * use {@link #setLookAlong(Vector3fc, Vector3fc) setLookAlong()}.
     * 
     * @see #lookAlong(float, float, float, float, float, float)
     * @see #setLookAlong(Vector3fc, Vector3fc)
     * 
     * @param dir
     *            the direction in space to look along
     * @param up
     *            the direction of 'up'
     * @return this
     */
    public Matrix3f lookAlong(Vector3fc dir, Vector3fc up) {
        return lookAlong(dir.x(), dir.y(), dir.z(), up.x(), up.y(), up.z(), this);
    }

    /**
     * Apply a rotation transformation to this matrix to make <code>-z</code> point along <code>dir</code>
     * and store the result in <code>dest</code>. 
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>L</code> the lookalong rotation matrix,
     * then the new matrix will be <code>M * L</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * L * v</code>, the
     * lookalong rotation transformation will be applied first!
     * <p>
     * In order to set the matrix to a lookalong transformation without post-multiplying it,
     * use {@link #setLookAlong(Vector3fc, Vector3fc) setLookAlong()}.
     * 
     * @see #lookAlong(float, float, float, float, float, float)
     * @see #setLookAlong(Vector3fc, Vector3fc)
     * 
     * @param dir
     *            the direction in space to look along
     * @param up
     *            the direction of 'up'
     * @param dest
     *            will hold the result
     * @return dest
     */
    public Matrix3f lookAlong(Vector3fc dir, Vector3fc up, Matrix3f dest) {
        return lookAlong(dir.x(), dir.y(), dir.z(), up.x(), up.y(), up.z(), dest);
    }

    /**
     * Apply a rotation transformation to this matrix to make <code>-z</code> point along <code>dir</code>
     * and store the result in <code>dest</code>. 
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>L</code> the lookalong rotation matrix,
     * then the new matrix will be <code>M * L</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * L * v</code>, the
     * lookalong rotation transformation will be applied first!
     * <p>
     * In order to set the matrix to a lookalong transformation without post-multiplying it,
     * use {@link #setLookAlong(float, float, float, float, float, float) setLookAlong()}
     * 
     * @see #setLookAlong(float, float, float, float, float, float)
     * 
     * @param dirX
     *              the x-coordinate of the direction to look along
     * @param dirY
     *              the y-coordinate of the direction to look along
     * @param dirZ
     *              the z-coordinate of the direction to look along
     * @param upX
     *              the x-coordinate of the up vector
     * @param upY
     *              the y-coordinate of the up vector
     * @param upZ
     *              the z-coordinate of the up vector
     * @param dest
     *              will hold the result
     * @return dest
     */
    public Matrix3f lookAlong(float dirX, float dirY, float dirZ,
                              float upX, float upY, float upZ, Matrix3f dest) {
        // Normalize direction
        float invDirLength = 1.0f / (float) Math.sqrt(dirX * dirX + dirY * dirY + dirZ * dirZ);
        dirX *= -invDirLength;
        dirY *= -invDirLength;
        dirZ *= -invDirLength;
        // left = up x direction
        float leftX, leftY, leftZ;
        leftX = upY * dirZ - upZ * dirY;
        leftY = upZ * dirX - upX * dirZ;
        leftZ = upX * dirY - upY * dirX;
        // normalize left
        float invLeftLength = 1.0f / (float) Math.sqrt(leftX * leftX + leftY * leftY + leftZ * leftZ);
        leftX *= invLeftLength;
        leftY *= invLeftLength;
        leftZ *= invLeftLength;
        // up = direction x left
        float upnX = dirY * leftZ - dirZ * leftY;
        float upnY = dirZ * leftX - dirX * leftZ;
        float upnZ = dirX * leftY - dirY * leftX;

        // calculate right matrix elements
        float rm00 = leftX;
        float rm01 = upnX;
        float rm02 = dirX;
        float rm10 = leftY;
        float rm11 = upnY;
        float rm12 = dirY;
        float rm20 = leftZ;
        float rm21 = upnZ;
        float rm22 = dirZ;

        // perform optimized matrix multiplication
        // introduce temporaries for dependent results
        float nm00 = m00 * rm00 + m10 * rm01 + m20 * rm02;
        float nm01 = m01 * rm00 + m11 * rm01 + m21 * rm02;
        float nm02 = m02 * rm00 + m12 * rm01 + m22 * rm02;
        float nm10 = m00 * rm10 + m10 * rm11 + m20 * rm12;
        float nm11 = m01 * rm10 + m11 * rm11 + m21 * rm12;
        float nm12 = m02 * rm10 + m12 * rm11 + m22 * rm12;
        dest.m20 = m00 * rm20 + m10 * rm21 + m20 * rm22;
        dest.m21 = m01 * rm20 + m11 * rm21 + m21 * rm22;
        dest.m22 = m02 * rm20 + m12 * rm21 + m22 * rm22;
        // set the rest of the matrix elements
        dest.m00 = nm00;
        dest.m01 = nm01;
        dest.m02 = nm02;
        dest.m10 = nm10;
        dest.m11 = nm11;
        dest.m12 = nm12;

        return dest;
    }

    /**
     * Apply a rotation transformation to this matrix to make <code>-z</code> point along <code>dir</code>. 
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>L</code> the lookalong rotation matrix,
     * then the new matrix will be <code>M * L</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * L * v</code>, the
     * lookalong rotation transformation will be applied first!
     * <p>
     * In order to set the matrix to a lookalong transformation without post-multiplying it,
     * use {@link #setLookAlong(float, float, float, float, float, float) setLookAlong()}
     * 
     * @see #setLookAlong(float, float, float, float, float, float)
     * 
     * @param dirX
     *              the x-coordinate of the direction to look along
     * @param dirY
     *              the y-coordinate of the direction to look along
     * @param dirZ
     *              the z-coordinate of the direction to look along
     * @param upX
     *              the x-coordinate of the up vector
     * @param upY
     *              the y-coordinate of the up vector
     * @param upZ
     *              the z-coordinate of the up vector
     * @return this
     */
    public Matrix3f lookAlong(float dirX, float dirY, float dirZ,
                              float upX, float upY, float upZ) {
        return lookAlong(dirX, dirY, dirZ, upX, upY, upZ, this);
    }

    /**
     * Set this matrix to a rotation transformation to make <code>-z</code>
     * point along <code>dir</code>.
     * <p>
     * In order to apply the lookalong transformation to any previous existing transformation,
     * use {@link #lookAlong(Vector3fc, Vector3fc)}.
     * 
     * @see #setLookAlong(Vector3fc, Vector3fc)
     * @see #lookAlong(Vector3fc, Vector3fc)
     * 
     * @param dir
     *            the direction in space to look along
     * @param up
     *            the direction of 'up'
     * @return this
     */
    public Matrix3f setLookAlong(Vector3fc dir, Vector3fc up) {
        return setLookAlong(dir.x(), dir.y(), dir.z(), up.x(), up.y(), up.z());
    }

    /**
     * Set this matrix to a rotation transformation to make <code>-z</code>
     * point along <code>dir</code>.
     * <p>
     * In order to apply the lookalong transformation to any previous existing transformation,
     * use {@link #lookAlong(float, float, float, float, float, float) lookAlong()}
     * 
     * @see #setLookAlong(float, float, float, float, float, float)
     * @see #lookAlong(float, float, float, float, float, float)
     * 
     * @param dirX
     *              the x-coordinate of the direction to look along
     * @param dirY
     *              the y-coordinate of the direction to look along
     * @param dirZ
     *              the z-coordinate of the direction to look along
     * @param upX
     *              the x-coordinate of the up vector
     * @param upY
     *              the y-coordinate of the up vector
     * @param upZ
     *              the z-coordinate of the up vector
     * @return this
     */
    public Matrix3f setLookAlong(float dirX, float dirY, float dirZ,
                                 float upX, float upY, float upZ) {
        // Normalize direction
        float invDirLength = 1.0f / (float) Math.sqrt(dirX * dirX + dirY * dirY + dirZ * dirZ);
        dirX *= -invDirLength;
        dirY *= -invDirLength;
        dirZ *= -invDirLength;
        // left = up x direction
        float leftX, leftY, leftZ;
        leftX = upY * dirZ - upZ * dirY;
        leftY = upZ * dirX - upX * dirZ;
        leftZ = upX * dirY - upY * dirX;
        // normalize left
        float invLeftLength = 1.0f / (float) Math.sqrt(leftX * leftX + leftY * leftY + leftZ * leftZ);
        leftX *= invLeftLength;
        leftY *= invLeftLength;
        leftZ *= invLeftLength;
        // up = direction x left
        float upnX = dirY * leftZ - dirZ * leftY;
        float upnY = dirZ * leftX - dirX * leftZ;
        float upnZ = dirX * leftY - dirY * leftX;

        m00 = leftX;
        m01 = upnX;
        m02 = dirX;
        m10 = leftY;
        m11 = upnY;
        m12 = dirY;
        m20 = leftZ;
        m21 = upnZ;
        m22 = dirZ;

        return this;
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#getRow(int, org.joml.Vector3f)
     */
    public Vector3f getRow(int row, Vector3f dest) throws IndexOutOfBoundsException {
        switch (row) {
        case 0:
            dest.x = m00;
            dest.y = m10;
            dest.z = m20;
            break;
        case 1:
            dest.x = m01;
            dest.y = m11;
            dest.z = m21;
            break;
        case 2:
            dest.x = m02;
            dest.y = m12;
            dest.z = m22;
            break;
        default:
            throw new IndexOutOfBoundsException();
        }
        
        return dest;
    }

    /**
     * Set the row at the given <code>row</code> index, starting with <code>0</code>.
     * 
     * @param row
     *          the row index in <tt>[0..2]</tt>
     * @param src
     *          the row components to set
     * @return this
     * @throws IndexOutOfBoundsException if <code>row</code> is not in <tt>[0..2]</tt>
     */
    public Matrix3f setRow(int row, Vector3fc src) throws IndexOutOfBoundsException {
        return setRow(row, src.x(), src.y(), src.z());
    }

    /**
     * Set the row at the given <code>row</code> index, starting with <code>0</code>.
     * 
     * @param row
     *          the row index in <tt>[0..2]</tt>
     * @param x
     *          the first element in the row
     * @param y
     *          the second element in the row
     * @param z
     *          the third element in the row
     * @return this
     * @throws IndexOutOfBoundsException if <code>row</code> is not in <tt>[0..2]</tt>
     */
    public Matrix3f setRow(int row, float x, float y, float z) throws IndexOutOfBoundsException {
        switch (row) {
        case 0:
            this.m00 = x;
            this.m01 = y;
            this.m02 = z;
            break;
        case 1:
            this.m10 = x;
            this.m11 = y;
            this.m12 = z;
            break;
        case 2:
            this.m20 = x;
            this.m21 = y;
            this.m22 = z;
            break;
        default:
            throw new IndexOutOfBoundsException();
        }
        return this;
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#getColumn(int, org.joml.Vector3f)
     */
    public Vector3f getColumn(int column, Vector3f dest) throws IndexOutOfBoundsException {
        switch (column) {
        case 0:
            dest.x = m00;
            dest.y = m01;
            dest.z = m02;
            break;
        case 1:
            dest.x = m10;
            dest.y = m11;
            dest.z = m12;
            break;
        case 2:
            dest.x = m20;
            dest.y = m21;
            dest.z = m22;
            break;
        default:
            throw new IndexOutOfBoundsException();
        }
        return dest;
    }

    /**
     * Set the column at the given <code>column</code> index, starting with <code>0</code>.
     * 
     * @param column
     *          the column index in <tt>[0..2]</tt>
     * @param src
     *          the column components to set
     * @return this
     * @throws IndexOutOfBoundsException if <code>column</code> is not in <tt>[0..2]</tt>
     */
    public Matrix3f setColumn(int column, Vector3fc src) throws IndexOutOfBoundsException {
        return setColumn(column, src.x(), src.y(), src.z());
    }

    /**
     * Set the column at the given <code>column</code> index, starting with <code>0</code>.
     * 
     * @param column
     *          the column index in <tt>[0..2]</tt>
     * @param x
     *          the first element in the column
     * @param y
     *          the second element in the column
     * @param z
     *          the third element in the column
     * @return this
     * @throws IndexOutOfBoundsException if <code>column</code> is not in <tt>[0..2]</tt>
     */
    public Matrix3f setColumn(int column, float x, float y, float z) throws IndexOutOfBoundsException {
        switch (column) {
        case 0:
            this.m00 = x;
            this.m01 = y;
            this.m02 = z;
            break;
        case 1:
            this.m10 = x;
            this.m11 = y;
            this.m12 = z;
            break;
        case 2:
            this.m20 = x;
            this.m21 = y;
            this.m22 = z;
            break;
        default:
            throw new IndexOutOfBoundsException();
        }
        return this;
    }

    /*
     * (non-Javadoc)
     * @see org.joml.Matrix3fc#get(int, int)
     */
    public float get(int column, int row) {
        switch (column) {
        case 0:
            switch (row) {
            case 0:
                return m00;
            case 1:
                return m01;
            case 2:
                return m02;
            default:
                break;
            }
            break;
        case 1:
            switch (row) {
            case 0:
                return m10;
            case 1:
                return m11;
            case 2:
                return m12;
            default:
                break;
            }
            break;
        case 2:
            switch (row) {
            case 0:
                return m20;
            case 1:
                return m21;
            case 2:
                return m22;
            default:
                break;
            }
            break;
        default:
            break;
        }
        throw new IllegalArgumentException();
    }

    /**
     * Set the matrix element at the given column and row to the specified value.
     * 
     * @param column
     *          the colum index in <tt>[0..2]</tt>
     * @param row
     *          the row index in <tt>[0..2]</tt>
     * @param value
     *          the value
     * @return this
     */
    public Matrix3f set(int column, int row, float value) {
        switch (column) {
        case 0:
            switch (row) {
            case 0:
                this.m00 = value;
                return this;
            case 1:
                this.m01 = value;
                return this;
            case 2:
                this.m02 = value;
                return this;
            default:
                break;
            }
            break;
        case 1:
            switch (row) {
            case 0:
                this.m10 = value;
                return this;
            case 1:
                this.m11 = value;
                return this;
            case 2:
                this.m12 = value;
                return this;
            default:
                break;
            }
            break;
        case 2:
            switch (row) {
            case 0:
                this.m20 = value;
                return this;
            case 1:
                this.m21 = value;
                return this;
            case 2:
                this.m22 = value;
                return this;
            default:
                break;
            }
            break;
        default:
            break;
        }
        throw new IllegalArgumentException();
    }

    /**
     * Set <code>this</code> matrix to its own normal matrix.
     * <p>
     * Please note that, if <code>this</code> is an orthogonal matrix or a matrix whose columns are orthogonal vectors, 
     * then this method <i>need not</i> be invoked, since in that case <code>this</code> itself is its normal matrix.
     * In this case, use {@link #set(Matrix3fc)} to set a given Matrix3f to this matrix.
     * 
     * @see #set(Matrix3fc)
     * 
     * @return this
     */
    public Matrix3f normal() {
        return normal(this);
    }

    /**
     * Compute a normal matrix from <code>this</code> matrix and store it into <code>dest</code>.
     * <p>
     * Please note that, if <code>this</code> is an orthogonal matrix or a matrix whose columns are orthogonal vectors, 
     * then this method <i>need not</i> be invoked, since in that case <code>this</code> itself is its normal matrix.
     * In this case, use {@link #set(Matrix3fc)} to set a given Matrix3f to this matrix.
     * 
     * @see #set(Matrix3fc)
     * 
     * @param dest
     *             will hold the result
     * @return dest
     */
    public Matrix3f normal(Matrix3f dest) {
        float m00m11 = m00 * m11;
        float m01m10 = m01 * m10;
        float m02m10 = m02 * m10;
        float m00m12 = m00 * m12;
        float m01m12 = m01 * m12;
        float m02m11 = m02 * m11;
        float det = (m00m11 - m01m10) * m22 + (m02m10 - m00m12) * m21 + (m01m12 - m02m11) * m20;
        float s = 1.0f / det;
        /* Invert and transpose in one go */
        float nm00 = (m11 * m22 - m21 * m12) * s;
        float nm01 = (m20 * m12 - m10 * m22) * s;
        float nm02 = (m10 * m21 - m20 * m11) * s;
        float nm10 = (m21 * m02 - m01 * m22) * s;
        float nm11 = (m00 * m22 - m20 * m02) * s;
        float nm12 = (m20 * m01 - m00 * m21) * s;
        float nm20 = (m01m12 - m02m11) * s;
        float nm21 = (m02m10 - m00m12) * s;
        float nm22 = (m00m11 - m01m10) * s;
        dest.m00 = nm00;
        dest.m01 = nm01;
        dest.m02 = nm02;
        dest.m10 = nm10;
        dest.m11 = nm11;
        dest.m12 = nm12;
        dest.m20 = nm20;
        dest.m21 = nm21;
        dest.m22 = nm22;
        return dest;
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#getScale(org.joml.Vector3f)
     */
    public Vector3f getScale(Vector3f dest) {
        dest.x = (float) Math.sqrt(m00 * m00 + m01 * m01 + m02 * m02);
        dest.y = (float) Math.sqrt(m10 * m10 + m11 * m11 + m12 * m12);
        dest.z = (float) Math.sqrt(m20 * m20 + m21 * m21 + m22 * m22);
        return dest;
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#positiveZ(org.joml.Vector3f)
     */
    public Vector3f positiveZ(Vector3f dir) {
        dir.x = m10 * m21 - m11 * m20;
        dir.y = m20 * m01 - m21 * m00;
        dir.z = m00 * m11 - m01 * m10;
        dir.normalize();
        return dir;
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#normalizedPositiveZ(org.joml.Vector3f)
     */
    public Vector3f normalizedPositiveZ(Vector3f dir) {
        dir.x = m02;
        dir.y = m12;
        dir.z = m22;
        return dir;
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#positiveX(org.joml.Vector3f)
     */
    public Vector3f positiveX(Vector3f dir) {
        dir.x = m11 * m22 - m12 * m21;
        dir.y = m02 * m21 - m01 * m22;
        dir.z = m01 * m12 - m02 * m11;
        dir.normalize();
        return dir;
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#normalizedPositiveX(org.joml.Vector3f)
     */
    public Vector3f normalizedPositiveX(Vector3f dir) {
        dir.x = m00;
        dir.y = m10;
        dir.z = m20;
        return dir;
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#positiveY(org.joml.Vector3f)
     */
    public Vector3f positiveY(Vector3f dir) {
        dir.x = m12 * m20 - m10 * m22;
        dir.y = m00 * m22 - m02 * m20;
        dir.z = m02 * m10 - m00 * m12;
        dir.normalize();
        return dir;
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#normalizedPositiveY(org.joml.Vector3f)
     */
    public Vector3f normalizedPositiveY(Vector3f dir) {
        dir.x = m01;
        dir.y = m11;
        dir.z = m21;
        return dir;
    }

    public int hashCode() {
        final int prime = 31;
        int result = 1;
        result = prime * result + Float.floatToIntBits(m00);
        result = prime * result + Float.floatToIntBits(m01);
        result = prime * result + Float.floatToIntBits(m02);
        result = prime * result + Float.floatToIntBits(m10);
        result = prime * result + Float.floatToIntBits(m11);
        result = prime * result + Float.floatToIntBits(m12);
        result = prime * result + Float.floatToIntBits(m20);
        result = prime * result + Float.floatToIntBits(m21);
        result = prime * result + Float.floatToIntBits(m22);
        return result;
    }

    public boolean equals(Object obj) {
        if (this == obj)
            return true;
        if (obj == null)
            return false;
        if (getClass() != obj.getClass())
            return false;
        Matrix3f other = (Matrix3f) obj;
        if (Float.floatToIntBits(m00) != Float.floatToIntBits(other.m00))
            return false;
        if (Float.floatToIntBits(m01) != Float.floatToIntBits(other.m01))
            return false;
        if (Float.floatToIntBits(m02) != Float.floatToIntBits(other.m02))
            return false;
        if (Float.floatToIntBits(m10) != Float.floatToIntBits(other.m10))
            return false;
        if (Float.floatToIntBits(m11) != Float.floatToIntBits(other.m11))
            return false;
        if (Float.floatToIntBits(m12) != Float.floatToIntBits(other.m12))
            return false;
        if (Float.floatToIntBits(m20) != Float.floatToIntBits(other.m20))
            return false;
        if (Float.floatToIntBits(m21) != Float.floatToIntBits(other.m21))
            return false;
        if (Float.floatToIntBits(m22) != Float.floatToIntBits(other.m22))
            return false;
        return true;
    }

    /**
     * Exchange the values of <code>this</code> matrix with the given <code>other</code> matrix.
     * 
     * @param other
     *          the other matrix to exchange the values with
     * @return this
     */
    public Matrix3f swap(Matrix3f other) {
        MemUtil.INSTANCE.swap(this, other);
        return this;
    }

    /**
     * Component-wise add <code>this</code> and <code>other</code>.
     * 
     * @param other
     *          the other addend 
     * @return this
     */
    public Matrix3f add(Matrix3fc other) {
        return add(other, this);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#add(org.joml.Matrix3fc, org.joml.Matrix3f)
     */
    public Matrix3f add(Matrix3fc other, Matrix3f dest) {
        dest.m00 = m00 + other.m00();
        dest.m01 = m01 + other.m01();
        dest.m02 = m02 + other.m02();
        dest.m10 = m10 + other.m10();
        dest.m11 = m11 + other.m11();
        dest.m12 = m12 + other.m12();
        dest.m20 = m20 + other.m20();
        dest.m21 = m21 + other.m21();
        dest.m22 = m22 + other.m22();
        return dest;
    }

    /**
     * Component-wise subtract <code>subtrahend</code> from <code>this</code>.
     * 
     * @param subtrahend
     *          the subtrahend
     * @return this
     */
    public Matrix3f sub(Matrix3fc subtrahend) {
        return sub(subtrahend, this);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#sub(org.joml.Matrix3fc, org.joml.Matrix3f)
     */
    public Matrix3f sub(Matrix3fc subtrahend, Matrix3f dest) {
        dest.m00 = m00 - subtrahend.m00();
        dest.m01 = m01 - subtrahend.m01();
        dest.m02 = m02 - subtrahend.m02();
        dest.m10 = m10 - subtrahend.m10();
        dest.m11 = m11 - subtrahend.m11();
        dest.m12 = m12 - subtrahend.m12();
        dest.m20 = m20 - subtrahend.m20();
        dest.m21 = m21 - subtrahend.m21();
        dest.m22 = m22 - subtrahend.m22();
        return dest;
    }

    /**
     * Component-wise multiply <code>this</code> by <code>other</code>.
     * 
     * @param other
     *          the other matrix
     * @return this
     */
    public Matrix3f mulComponentWise(Matrix3fc other) {
        return mulComponentWise(other, this);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#mulComponentWise(org.joml.Matrix3fc, org.joml.Matrix3f)
     */
    public Matrix3f mulComponentWise(Matrix3fc other, Matrix3f dest) {
        dest.m00 = m00 * other.m00();
        dest.m01 = m01 * other.m01();
        dest.m02 = m02 * other.m02();
        dest.m10 = m10 * other.m10();
        dest.m11 = m11 * other.m11();
        dest.m12 = m12 * other.m12();
        dest.m20 = m20 * other.m20();
        dest.m21 = m21 * other.m21();
        dest.m22 = m22 * other.m22();
        return dest;
    }

    /**
     * Set this matrix to a skew-symmetric matrix using the following layout:
     * <pre>
     *  0,  a, -b
     * -a,  0,  c
     *  b, -c,  0
     * </pre>
     * 
     * Reference: <a href="https://en.wikipedia.org/wiki/Skew-symmetric_matrix">https://en.wikipedia.org</a>
     * 
     * @param a
     *          the value used for the matrix elements m01 and m10
     * @param b
     *          the value used for the matrix elements m02 and m20
     * @param c
     *          the value used for the matrix elements m12 and m21
     * @return this
     */
    public Matrix3f setSkewSymmetric(float a, float b, float c) {
        m00 = m11 = m22 = 0;
        m01 = -a;
        m02 = b;
        m10 = a;
        m12 = -c;
        m20 = -b;
        m21 = c;
        return this;
    }

    /**
     * Linearly interpolate <code>this</code> and <code>other</code> using the given interpolation factor <code>t</code>
     * and store the result in <code>this</code>.
     * <p>
     * If <code>t</code> is <tt>0.0</tt> then the result is <code>this</code>. If the interpolation factor is <code>1.0</code>
     * then the result is <code>other</code>.
     *
     * @param other
     *          the other matrix
     * @param t
     *          the interpolation factor between 0.0 and 1.0
     * @return this
     */
    public Matrix3f lerp(Matrix3fc other, float t) {
        return lerp(other, t, this);
    }

    /* (non-Javadoc)
     * @see org.joml.Matrix3fc#lerp(org.joml.Matrix3fc, float, org.joml.Matrix3f)
     */
    public Matrix3f lerp(Matrix3fc other, float t, Matrix3f dest) {
        dest.m00 = m00 + (other.m00() - m00) * t;
        dest.m01 = m01 + (other.m01() - m01) * t;
        dest.m02 = m02 + (other.m02() - m02) * t;
        dest.m10 = m10 + (other.m10() - m10) * t;
        dest.m11 = m11 + (other.m11() - m11) * t;
        dest.m12 = m12 + (other.m12() - m12) * t;
        dest.m20 = m20 + (other.m20() - m20) * t;
        dest.m21 = m21 + (other.m21() - m21) * t;
        dest.m22 = m22 + (other.m22() - m22) * t;
        return dest;
    }

    /**
     * Apply a model transformation to this matrix for a right-handed coordinate system, 
     * that aligns the local <code>+Z</code> axis with <code>direction</code>
     * and store the result in <code>dest</code>.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>L</code> the lookat matrix,
     * then the new matrix will be <code>M * L</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * L * v</code>,
     * the lookat transformation will be applied first!
     * <p>
     * In order to set the matrix to a rotation transformation without post-multiplying it,
     * use {@link #rotationTowards(Vector3fc, Vector3fc) rotationTowards()}.
     * <p>
     * This method is equivalent to calling: <tt>mul(new Matrix3f().lookAlong(new Vector3f(dir).negate(), up).invert(), dest)</tt>
     * 
     * @see #rotateTowards(float, float, float, float, float, float, Matrix3f)
     * @see #rotationTowards(Vector3fc, Vector3fc)
     * 
     * @param direction
     *              the direction to rotate towards
     * @param up
     *              the model's up vector
     * @param dest
     *              will hold the result
     * @return dest
     */
    public Matrix3f rotateTowards(Vector3fc direction, Vector3fc up, Matrix3f dest) {
        return rotateTowards(direction.x(), direction.y(), direction.z(), up.x(), up.y(), up.z(), dest);
    }

    /**
     * Apply a model transformation to this matrix for a right-handed coordinate system, 
     * that aligns the local <code>+Z</code> axis with <code>direction</code>.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>L</code> the lookat matrix,
     * then the new matrix will be <code>M * L</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * L * v</code>,
     * the lookat transformation will be applied first!
     * <p>
     * In order to set the matrix to a rotation transformation without post-multiplying it,
     * use {@link #rotationTowards(Vector3fc, Vector3fc) rotationTowards()}.
     * <p>
     * This method is equivalent to calling: <tt>mul(new Matrix3f().lookAlong(new Vector3f(dir).negate(), up).invert())</tt>
     * 
     * @see #rotateTowards(float, float, float, float, float, float)
     * @see #rotationTowards(Vector3fc, Vector3fc)
     * 
     * @param direction
     *              the direction to orient towards
     * @param up
     *              the up vector
     * @return this
     */
    public Matrix3f rotateTowards(Vector3fc direction, Vector3fc up) {
        return rotateTowards(direction.x(), direction.y(), direction.z(), up.x(), up.y(), up.z(), this);
    }

    /**
     * Apply a model transformation to this matrix for a right-handed coordinate system, 
     * that aligns the local <code>+Z</code> axis with <code>direction</code>.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>L</code> the lookat matrix,
     * then the new matrix will be <code>M * L</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * L * v</code>,
     * the lookat transformation will be applied first!
     * <p>
     * In order to set the matrix to a rotation transformation without post-multiplying it,
     * use {@link #rotationTowards(float, float, float, float, float, float) rotationTowards()}.
     * <p>
     * This method is equivalent to calling: <tt>mul(new Matrix3f().lookAlong(-dirX, -dirY, -dirZ, upX, upY, upZ).invert())</tt>
     * 
     * @see #rotateTowards(Vector3fc, Vector3fc)
     * @see #rotationTowards(float, float, float, float, float, float)
     * 
     * @param dirX
     *              the x-coordinate of the direction to rotate towards
     * @param dirY
     *              the y-coordinate of the direction to rotate towards
     * @param dirZ
     *              the z-coordinate of the direction to rotate towards
     * @param upX
     *              the x-coordinate of the up vector
     * @param upY
     *              the y-coordinate of the up vector
     * @param upZ
     *              the z-coordinate of the up vector
     * @return this
     */
    public Matrix3f rotateTowards(float dirX, float dirY, float dirZ, float upX, float upY, float upZ) {
        return rotateTowards(dirX, dirY, dirZ, upX, upY, upZ, this);
    }

    /**
     * Apply a model transformation to this matrix for a right-handed coordinate system, 
     * that aligns the local <code>+Z</code> axis with <code>dir</code>
     * and store the result in <code>dest</code>.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>L</code> the lookat matrix,
     * then the new matrix will be <code>M * L</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * L * v</code>,
     * the lookat transformation will be applied first!
     * <p>
     * In order to set the matrix to a rotation transformation without post-multiplying it,
     * use {@link #rotationTowards(float, float, float, float, float, float) rotationTowards()}.
     * <p>
     * This method is equivalent to calling: <tt>mul(new Matrix3f().lookAlong(-dirX, -dirY, -dirZ, upX, upY, upZ).invert(), dest)</tt>
     * 
     * @see #rotateTowards(Vector3fc, Vector3fc)
     * @see #rotationTowards(float, float, float, float, float, float)
     * 
     * @param dirX
     *              the x-coordinate of the direction to rotate towards
     * @param dirY
     *              the y-coordinate of the direction to rotate towards
     * @param dirZ
     *              the z-coordinate of the direction to rotate towards
     * @param upX
     *              the x-coordinate of the up vector
     * @param upY
     *              the y-coordinate of the up vector
     * @param upZ
     *              the z-coordinate of the up vector
     * @param dest
     *              will hold the result
     * @return dest
     */
    public Matrix3f rotateTowards(float dirX, float dirY, float dirZ, float upX, float upY, float upZ, Matrix3f dest) {
        // Normalize direction
        float invDirLength = 1.0f / (float) Math.sqrt(dirX * dirX + dirY * dirY + dirZ * dirZ);
        float ndirX = dirX * invDirLength;
        float ndirY = dirY * invDirLength;
        float ndirZ = dirZ * invDirLength;
        // left = up x direction
        float leftX, leftY, leftZ;
        leftX = upY * ndirZ - upZ * ndirY;
        leftY = upZ * ndirX - upX * ndirZ;
        leftZ = upX * ndirY - upY * ndirX;
        // normalize left
        float invLeftLength = 1.0f / (float) Math.sqrt(leftX * leftX + leftY * leftY + leftZ * leftZ);
        leftX *= invLeftLength;
        leftY *= invLeftLength;
        leftZ *= invLeftLength;
        // up = direction x left
        float upnX = ndirY * leftZ - ndirZ * leftY;
        float upnY = ndirZ * leftX - ndirX * leftZ;
        float upnZ = ndirX * leftY - ndirY * leftX;
        float rm00 = leftX;
        float rm01 = leftY;
        float rm02 = leftZ;
        float rm10 = upnX;
        float rm11 = upnY;
        float rm12 = upnZ;
        float rm20 = ndirX;
        float rm21 = ndirY;
        float rm22 = ndirZ;
        float nm00 = m00 * rm00 + m10 * rm01 + m20 * rm02;
        float nm01 = m01 * rm00 + m11 * rm01 + m21 * rm02;
        float nm02 = m02 * rm00 + m12 * rm01 + m22 * rm02;
        float nm10 = m00 * rm10 + m10 * rm11 + m20 * rm12;
        float nm11 = m01 * rm10 + m11 * rm11 + m21 * rm12;
        float nm12 = m02 * rm10 + m12 * rm11 + m22 * rm12;
        dest.m20 = m00 * rm20 + m10 * rm21 + m20 * rm22;
        dest.m21 = m01 * rm20 + m11 * rm21 + m21 * rm22;
        dest.m22 = m02 * rm20 + m12 * rm21 + m22 * rm22;
        dest.m00 = nm00;
        dest.m01 = nm01;
        dest.m02 = nm02;
        dest.m10 = nm10;
        dest.m11 = nm11;
        dest.m12 = nm12;
        return dest;
    }

    /**
     * Set this matrix to a model transformation for a right-handed coordinate system, 
     * that aligns the local <code>-z</code> axis with <code>center - eye</code>.
     * <p>
     * In order to apply the rotation transformation to a previous existing transformation,
     * use {@link #rotateTowards(float, float, float, float, float, float) rotateTowards}.
     * <p>
     * This method is equivalent to calling: <tt>setLookAlong(new Vector3f(dir).negate(), up).invert()</tt>
     * 
     * @see #rotationTowards(Vector3fc, Vector3fc)
     * @see #rotateTowards(float, float, float, float, float, float)
     * 
     * @param dir
     *              the direction to orient the local -z axis towards
     * @param up
     *              the up vector
     * @return this
     */
    public Matrix3f rotationTowards(Vector3fc dir, Vector3fc up) {
        return rotationTowards(dir.x(), dir.y(), dir.z(), up.x(), up.y(), up.z());
    }

    /**
     * Set this matrix to a model transformation for a right-handed coordinate system, 
     * that aligns the local <code>-z</code> axis with <code>center - eye</code>.
     * <p>
     * In order to apply the rotation transformation to a previous existing transformation,
     * use {@link #rotateTowards(float, float, float, float, float, float) rotateTowards}.
     * <p>
     * This method is equivalent to calling: <tt>setLookAlong(-dirX, -dirY, -dirZ, upX, upY, upZ).invert()</tt>
     * 
     * @see #rotateTowards(Vector3fc, Vector3fc)
     * @see #rotationTowards(float, float, float, float, float, float)
     * 
     * @param dirX
     *              the x-coordinate of the direction to rotate towards
     * @param dirY
     *              the y-coordinate of the direction to rotate towards
     * @param dirZ
     *              the z-coordinate of the direction to rotate towards
     * @param upX
     *              the x-coordinate of the up vector
     * @param upY
     *              the y-coordinate of the up vector
     * @param upZ
     *              the z-coordinate of the up vector
     * @return this
     */
    public Matrix3f rotationTowards(float dirX, float dirY, float dirZ, float upX, float upY, float upZ) {
        // Normalize direction
        float invDirLength = 1.0f / (float) Math.sqrt(dirX * dirX + dirY * dirY + dirZ * dirZ);
        float ndirX = dirX * invDirLength;
        float ndirY = dirY * invDirLength;
        float ndirZ = dirZ * invDirLength;
        // left = up x direction
        float leftX, leftY, leftZ;
        leftX = upY * ndirZ - upZ * ndirY;
        leftY = upZ * ndirX - upX * ndirZ;
        leftZ = upX * ndirY - upY * ndirX;
        // normalize left
        float invLeftLength = 1.0f / (float) Math.sqrt(leftX * leftX + leftY * leftY + leftZ * leftZ);
        leftX *= invLeftLength;
        leftY *= invLeftLength;
        leftZ *= invLeftLength;
        // up = direction x left
        float upnX = ndirY * leftZ - ndirZ * leftY;
        float upnY = ndirZ * leftX - ndirX * leftZ;
        float upnZ = ndirX * leftY - ndirY * leftX;
        this.m00 = leftX;
        this.m01 = leftY;
        this.m02 = leftZ;
        this.m10 = upnX;
        this.m11 = upnY;
        this.m12 = upnZ;
        this.m20 = ndirX;
        this.m21 = ndirY;
        this.m22 = ndirZ;
        return this;
    }

    /**
     * Extract the Euler angles from the rotation represented by <code>this</code> matrix and store the extracted Euler angles in <code>dest</code>.
     * <p>
     * This method assumes that <code>this</code> matrix only represents a rotation without scaling.
     * <p>
     * Note that the returned Euler angles must be applied in the order <tt>Z * Y * X</tt> to obtain the identical matrix.
     * This means that calling {@link Matrix3f#rotateZYX(float, float, float)} using the obtained Euler angles will yield
     * the same rotation as the original matrix from which the Euler angles were obtained, so in the below code the matrix
     * <tt>m2</tt> should be identical to <tt>m</tt> (disregarding possible floating-point inaccuracies).
     * <pre>
     * Matrix3f m = ...; // &lt;- matrix only representing rotation
     * Matrix3f n = new Matrix3f();
     * n.rotateZYX(m.getEulerAnglesZYX(new Vector3f()));
     * </pre>
     * <p>
     * Reference: <a href="http://nghiaho.com/?page_id=846">http://nghiaho.com/</a>
     * 
     * @param dest
     *          will hold the extracted Euler angles
     * @return dest
     */
    public Vector3f getEulerAnglesZYX(Vector3f dest) {
        dest.x = (float) Math.atan2(m12, m22);
        dest.y = (float) Math.atan2(-m02, (float) Math.sqrt(m12 * m12 + m22 * m22));
        dest.z = (float) Math.atan2(m01, m00);
        return dest;
    }

}