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// Copyright (c) 2010-2014 SharpDX - Alexandre Mutel
//
// 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.
// -----------------------------------------------------------------------------
// Original code from SlimMath project. http://code.google.com/p/slimmath/
// Greetings to SlimDX Group. Original code published with the following license:
// -----------------------------------------------------------------------------
/*
* Copyright (c) 2007-2011 SlimDX Group
*
* 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.
*/
using System;
using System.Globalization;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
using SharpDX.Mathematics.Interop;
namespace SharpDX
{
/// <summary>
/// Represents a three dimensional mathematical vector.
/// </summary>
[StructLayout(LayoutKind.Sequential, Pack = 4)]
public struct Vector3 : IEquatable<Vector3>, IFormattable
{
/// <summary>
/// The size of the <see cref="Vector3"/> type, in bytes.
/// </summary>
public static readonly int SizeInBytes = Utilities.SizeOf<Vector3>();
/// <summary>
/// A <see cref="Vector3"/> with all of its components set to zero.
/// </summary>
public static readonly Vector3 Zero = new Vector3();
/// <summary>
/// The X unit <see cref="Vector3"/> (1, 0, 0).
/// </summary>
public static readonly Vector3 UnitX = new Vector3(1.0f, 0.0f, 0.0f);
/// <summary>
/// The Y unit <see cref="Vector3"/> (0, 1, 0).
/// </summary>
public static readonly Vector3 UnitY = new Vector3(0.0f, 1.0f, 0.0f);
/// <summary>
/// The Z unit <see cref="Vector3"/> (0, 0, 1).
/// </summary>
public static readonly Vector3 UnitZ = new Vector3(0.0f, 0.0f, 1.0f);
/// <summary>
/// A <see cref="Vector3"/> with all of its components set to one.
/// </summary>
public static readonly Vector3 One = new Vector3(1.0f, 1.0f, 1.0f);
/// <summary>
/// A unit <see cref="Vector3"/> designating up (0, 1, 0).
/// </summary>
public static readonly Vector3 Up = new Vector3(0.0f, 1.0f, 0.0f);
/// <summary>
/// A unit <see cref="Vector3"/> designating down (0, -1, 0).
/// </summary>
public static readonly Vector3 Down = new Vector3(0.0f, -1.0f, 0.0f);
/// <summary>
/// A unit <see cref="Vector3"/> designating left (-1, 0, 0).
/// </summary>
public static readonly Vector3 Left = new Vector3(-1.0f, 0.0f, 0.0f);
/// <summary>
/// A unit <see cref="Vector3"/> designating right (1, 0, 0).
/// </summary>
public static readonly Vector3 Right = new Vector3(1.0f, 0.0f, 0.0f);
/// <summary>
/// A unit <see cref="Vector3"/> designating forward in a right-handed coordinate system (0, 0, -1).
/// </summary>
public static readonly Vector3 ForwardRH = new Vector3(0.0f, 0.0f, -1.0f);
/// <summary>
/// A unit <see cref="Vector3"/> designating forward in a left-handed coordinate system (0, 0, 1).
/// </summary>
public static readonly Vector3 ForwardLH = new Vector3(0.0f, 0.0f, 1.0f);
/// <summary>
/// A unit <see cref="Vector3"/> designating backward in a right-handed coordinate system (0, 0, 1).
/// </summary>
public static readonly Vector3 BackwardRH = new Vector3(0.0f, 0.0f, 1.0f);
/// <summary>
/// A unit <see cref="Vector3"/> designating backward in a left-handed coordinate system (0, 0, -1).
/// </summary>
public static readonly Vector3 BackwardLH = new Vector3(0.0f, 0.0f, -1.0f);
/// <summary>
/// The X component of the vector.
/// </summary>
public float X;
/// <summary>
/// The Y component of the vector.
/// </summary>
public float Y;
/// <summary>
/// The Z component of the vector.
/// </summary>
public float Z;
/// <summary>
/// Initializes a new instance of the <see cref="Vector3"/> struct.
/// </summary>
/// <param name="value">The value that will be assigned to all components.</param>
public Vector3(float value)
{
X = value;
Y = value;
Z = value;
}
/// <summary>
/// Initializes a new instance of the <see cref="Vector3"/> struct.
/// </summary>
/// <param name="x">Initial value for the X component of the vector.</param>
/// <param name="y">Initial value for the Y component of the vector.</param>
/// <param name="z">Initial value for the Z component of the vector.</param>
public Vector3(float x, float y, float z)
{
X = x;
Y = y;
Z = z;
}
/// <summary>
/// Initializes a new instance of the <see cref="Vector3"/> struct.
/// </summary>
/// <param name="value">A vector containing the values with which to initialize the X and Y components.</param>
/// <param name="z">Initial value for the Z component of the vector.</param>
public Vector3(Vector2 value, float z)
{
X = value.X;
Y = value.Y;
Z = z;
}
/// <summary>
/// Initializes a new instance of the <see cref="Vector3"/> struct.
/// </summary>
/// <param name="values">The values to assign to the X, Y, and Z components of the vector. This must be an array with three elements.</param>
/// <exception cref="ArgumentNullException">Thrown when <paramref name="values"/> is <c>null</c>.</exception>
/// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="values"/> contains more or less than three elements.</exception>
public Vector3(float[] values)
{
if (values == null)
throw new ArgumentNullException("values");
if (values.Length != 3)
throw new ArgumentOutOfRangeException("values", "There must be three and only three input values for Vector3.");
X = values[0];
Y = values[1];
Z = values[2];
}
/// <summary>
/// Gets a value indicting whether this instance is normalized.
/// </summary>
public bool IsNormalized
{
get { return MathUtil.IsOne((X * X) + (Y * Y) + (Z * Z)); }
}
/// <summary>
/// Gets a value indicting whether this vector is zero
/// </summary>
public bool IsZero
{
get { return X == 0 && Y == 0 && Z == 0; }
}
/// <summary>
/// Gets or sets the component at the specified index.
/// </summary>
/// <value>The value of the X, Y, or Z component, depending on the index.</value>
/// <param name="index">The index of the component to access. Use 0 for the X component, 1 for the Y component, and 2 for the Z component.</param>
/// <returns>The value of the component at the specified index.</returns>
/// <exception cref="System.ArgumentOutOfRangeException">Thrown when the <paramref name="index"/> is out of the range [0, 2].</exception>
public float this[int index]
{
get
{
switch (index)
{
case 0: return X;
case 1: return Y;
case 2: return Z;
}
throw new ArgumentOutOfRangeException("index", "Indices for Vector3 run from 0 to 2, inclusive.");
}
set
{
switch (index)
{
case 0: X = value; break;
case 1: Y = value; break;
case 2: Z = value; break;
default: throw new ArgumentOutOfRangeException("index", "Indices for Vector3 run from 0 to 2, inclusive.");
}
}
}
/// <summary>
/// Calculates the length of the vector.
/// </summary>
/// <returns>The length of the vector.</returns>
/// <remarks>
/// <see cref="Vector3.LengthSquared"/> may be preferred when only the relative length is needed
/// and speed is of the essence.
/// </remarks>
public float Length()
{
return (float)Math.Sqrt((X * X) + (Y * Y) + (Z * Z));
}
/// <summary>
/// Calculates the squared length of the vector.
/// </summary>
/// <returns>The squared length of the vector.</returns>
/// <remarks>
/// This method may be preferred to <see cref="Vector3.Length"/> when only a relative length is needed
/// and speed is of the essence.
/// </remarks>
public float LengthSquared()
{
return (X * X) + (Y * Y) + (Z * Z);
}
/// <summary>
/// Converts the vector into a unit vector.
/// </summary>
public void Normalize()
{
float length = Length();
if (!MathUtil.IsZero(length))
{
float inv = 1.0f / length;
X *= inv;
Y *= inv;
Z *= inv;
}
}
/// <summary>
/// Creates an array containing the elements of the vector.
/// </summary>
/// <returns>A three-element array containing the components of the vector.</returns>
public float[] ToArray()
{
return new float[] { X, Y, Z };
}
/// <summary>
/// Adds two vectors.
/// </summary>
/// <param name="left">The first vector to add.</param>
/// <param name="right">The second vector to add.</param>
/// <param name="result">When the method completes, contains the sum of the two vectors.</param>
public static void Add(ref Vector3 left, ref Vector3 right, out Vector3 result)
{
result = new Vector3(left.X + right.X, left.Y + right.Y, left.Z + right.Z);
}
/// <summary>
/// Adds two vectors.
/// </summary>
/// <param name="left">The first vector to add.</param>
/// <param name="right">The second vector to add.</param>
/// <returns>The sum of the two vectors.</returns>
public static Vector3 Add(Vector3 left, Vector3 right)
{
return new Vector3(left.X + right.X, left.Y + right.Y, left.Z + right.Z);
}
/// <summary>
/// Perform a component-wise addition
/// </summary>
/// <param name="left">The input vector</param>
/// <param name="right">The scalar value to be added to elements</param>
/// <param name="result">The vector with added scalar for each element.</param>
public static void Add(ref Vector3 left, ref float right, out Vector3 result)
{
result = new Vector3(left.X + right, left.Y + right, left.Z + right);
}
/// <summary>
/// Perform a component-wise addition
/// </summary>
/// <param name="left">The input vector</param>
/// <param name="right">The scalar value to be added to elements</param>
/// <returns>The vector with added scalar for each element.</returns>
public static Vector3 Add(Vector3 left, float right)
{
return new Vector3(left.X + right, left.Y + right, left.Z + right);
}
/// <summary>
/// Subtracts two vectors.
/// </summary>
/// <param name="left">The first vector to subtract.</param>
/// <param name="right">The second vector to subtract.</param>
/// <param name="result">When the method completes, contains the difference of the two vectors.</param>
public static void Subtract(ref Vector3 left, ref Vector3 right, out Vector3 result)
{
result = new Vector3(left.X - right.X, left.Y - right.Y, left.Z - right.Z);
}
/// <summary>
/// Subtracts two vectors.
/// </summary>
/// <param name="left">The first vector to subtract.</param>
/// <param name="right">The second vector to subtract.</param>
/// <returns>The difference of the two vectors.</returns>
public static Vector3 Subtract(Vector3 left, Vector3 right)
{
return new Vector3(left.X - right.X, left.Y - right.Y, left.Z - right.Z);
}
/// <summary>
/// Perform a component-wise subtraction
/// </summary>
/// <param name="left">The input vector</param>
/// <param name="right">The scalar value to be subtraced from elements</param>
/// <param name="result">The vector with subtracted scalar for each element.</param>
public static void Subtract(ref Vector3 left, ref float right, out Vector3 result)
{
result = new Vector3(left.X - right, left.Y - right, left.Z - right);
}
/// <summary>
/// Perform a component-wise subtraction
/// </summary>
/// <param name="left">The input vector</param>
/// <param name="right">The scalar value to be subtraced from elements</param>
/// <returns>The vector with subtracted scalar for each element.</returns>
public static Vector3 Subtract(Vector3 left, float right)
{
return new Vector3(left.X - right, left.Y - right, left.Z - right);
}
/// <summary>
/// Perform a component-wise subtraction
/// </summary>
/// <param name="left">The scalar value to be subtraced from elements</param>
/// <param name="right">The input vector.</param>
/// <param name="result">The vector with subtracted scalar for each element.</param>
public static void Subtract(ref float left, ref Vector3 right, out Vector3 result)
{
result = new Vector3(left - right.X, left - right.Y, left - right.Z);
}
/// <summary>
/// Perform a component-wise subtraction
/// </summary>
/// <param name="left">The scalar value to be subtraced from elements</param>
/// <param name="right">The input vector.</param>
/// <returns>The vector with subtracted scalar for each element.</returns>
public static Vector3 Subtract(float left, Vector3 right)
{
return new Vector3(left - right.X, left - right.Y, left - right.Z);
}
/// <summary>
/// Scales a vector by the given value.
/// </summary>
/// <param name="value">The vector to scale.</param>
/// <param name="scale">The amount by which to scale the vector.</param>
/// <param name="result">When the method completes, contains the scaled vector.</param>
public static void Multiply(ref Vector3 value, float scale, out Vector3 result)
{
result = new Vector3(value.X * scale, value.Y * scale, value.Z * scale);
}
/// <summary>
/// Scales a vector by the given value.
/// </summary>
/// <param name="value">The vector to scale.</param>
/// <param name="scale">The amount by which to scale the vector.</param>
/// <returns>The scaled vector.</returns>
public static Vector3 Multiply(Vector3 value, float scale)
{
return new Vector3(value.X * scale, value.Y * scale, value.Z * scale);
}
/// <summary>
/// Multiply a vector with another by performing component-wise multiplication.
/// </summary>
/// <param name="left">The first vector to multiply.</param>
/// <param name="right">The second vector to multiply.</param>
/// <param name="result">When the method completes, contains the multiplied vector.</param>
public static void Multiply(ref Vector3 left, ref Vector3 right, out Vector3 result)
{
result = new Vector3(left.X * right.X, left.Y * right.Y, left.Z * right.Z);
}
/// <summary>
/// Multiply a vector with another by performing component-wise multiplication.
/// </summary>
/// <param name="left">The first vector to Multiply.</param>
/// <param name="right">The second vector to multiply.</param>
/// <returns>The multiplied vector.</returns>
public static Vector3 Multiply(Vector3 left, Vector3 right)
{
return new Vector3(left.X * right.X, left.Y * right.Y, left.Z * right.Z);
}
/// <summary>
/// Scales a vector by the given value.
/// </summary>
/// <param name="value">The vector to scale.</param>
/// <param name="scale">The amount by which to scale the vector.</param>
/// <param name="result">When the method completes, contains the scaled vector.</param>
public static void Divide(ref Vector3 value, float scale, out Vector3 result)
{
result = new Vector3(value.X / scale, value.Y / scale, value.Z / scale);
}
/// <summary>
/// Scales a vector by the given value.
/// </summary>
/// <param name="value">The vector to scale.</param>
/// <param name="scale">The amount by which to scale the vector.</param>
/// <returns>The scaled vector.</returns>
public static Vector3 Divide(Vector3 value, float scale)
{
return new Vector3(value.X / scale, value.Y / scale, value.Z / scale);
}
/// <summary>
/// Scales a vector by the given value.
/// </summary>
/// <param name="scale">The amount by which to scale the vector.</param>
/// <param name="value">The vector to scale.</param>
/// <param name="result">When the method completes, contains the scaled vector.</param>
public static void Divide(float scale, ref Vector3 value, out Vector3 result)
{
result = new Vector3(scale / value.X, scale / value.Y, scale / value.Z);
}
/// <summary>
/// Scales a vector by the given value.
/// </summary>
/// <param name="value">The vector to scale.</param>
/// <param name="scale">The amount by which to scale the vector.</param>
/// <returns>The scaled vector.</returns>
public static Vector3 Divide(float scale, Vector3 value)
{
return new Vector3(scale / value.X, scale / value.Y, scale / value.Z);
}
/// <summary>
/// Reverses the direction of a given vector.
/// </summary>
/// <param name="value">The vector to negate.</param>
/// <param name="result">When the method completes, contains a vector facing in the opposite direction.</param>
public static void Negate(ref Vector3 value, out Vector3 result)
{
result = new Vector3(-value.X, -value.Y, -value.Z);
}
/// <summary>
/// Reverses the direction of a given vector.
/// </summary>
/// <param name="value">The vector to negate.</param>
/// <returns>A vector facing in the opposite direction.</returns>
public static Vector3 Negate(Vector3 value)
{
return new Vector3(-value.X, -value.Y, -value.Z);
}
/// <summary>
/// Returns per component absolute value of a vector
/// </summary>
/// <param name="value">Input vector</param>
/// <param name="result">When the method completes, contains a vector with each component being the absolute value of the input component</param>
public static void Abs(ref Vector3 value, out Vector3 result)
{
result = new Vector3(value.X > 0.0f ? value.X : -value.X,
value.Y > 0.0f ? value.Y : -value.Y,
value.Z > 0.0f ? value.Z : -value.Z);
}
/// <summary>
/// Returns per component absolute value of a vector
/// </summary>
/// <param name="value">Input vector</param>
/// <returns>A vector with each component being the absolute value of the input component</returns>
public static Vector3 Abs(Vector3 value)
{
return new Vector3(
value.X > 0.0f ? value.X : -value.X,
value.Y > 0.0f ? value.Y : -value.Y,
value.Z > 0.0f ? value.Z : -value.Z);
}
/// <summary>
/// Returns a <see cref="Vector3"/> containing the 3D Cartesian coordinates of a point specified in Barycentric coordinates relative to a 3D triangle.
/// </summary>
/// <param name="value1">A <see cref="Vector3"/> containing the 3D Cartesian coordinates of vertex 1 of the triangle.</param>
/// <param name="value2">A <see cref="Vector3"/> containing the 3D Cartesian coordinates of vertex 2 of the triangle.</param>
/// <param name="value3">A <see cref="Vector3"/> containing the 3D Cartesian coordinates of vertex 3 of the triangle.</param>
/// <param name="amount1">Barycentric coordinate b2, which expresses the weighting factor toward vertex 2 (specified in <paramref name="value2"/>).</param>
/// <param name="amount2">Barycentric coordinate b3, which expresses the weighting factor toward vertex 3 (specified in <paramref name="value3"/>).</param>
/// <param name="result">When the method completes, contains the 3D Cartesian coordinates of the specified point.</param>
public static void Barycentric(ref Vector3 value1, ref Vector3 value2, ref Vector3 value3, float amount1, float amount2, out Vector3 result)
{
result = new Vector3((value1.X + (amount1 * (value2.X - value1.X))) + (amount2 * (value3.X - value1.X)),
(value1.Y + (amount1 * (value2.Y - value1.Y))) + (amount2 * (value3.Y - value1.Y)),
(value1.Z + (amount1 * (value2.Z - value1.Z))) + (amount2 * (value3.Z - value1.Z)));
}
/// <summary>
/// Returns a <see cref="Vector3"/> containing the 3D Cartesian coordinates of a point specified in Barycentric coordinates relative to a 3D triangle.
/// </summary>
/// <param name="value1">A <see cref="Vector3"/> containing the 3D Cartesian coordinates of vertex 1 of the triangle.</param>
/// <param name="value2">A <see cref="Vector3"/> containing the 3D Cartesian coordinates of vertex 2 of the triangle.</param>
/// <param name="value3">A <see cref="Vector3"/> containing the 3D Cartesian coordinates of vertex 3 of the triangle.</param>
/// <param name="amount1">Barycentric coordinate b2, which expresses the weighting factor toward vertex 2 (specified in <paramref name="value2"/>).</param>
/// <param name="amount2">Barycentric coordinate b3, which expresses the weighting factor toward vertex 3 (specified in <paramref name="value3"/>).</param>
/// <returns>A new <see cref="Vector3"/> containing the 3D Cartesian coordinates of the specified point.</returns>
public static Vector3 Barycentric(Vector3 value1, Vector3 value2, Vector3 value3, float amount1, float amount2)
{
Vector3 result;
Barycentric(ref value1, ref value2, ref value3, amount1, amount2, out result);
return result;
}
/// <summary>
/// Restricts a value to be within a specified range.
/// </summary>
/// <param name="value">The value to clamp.</param>
/// <param name="min">The minimum value.</param>
/// <param name="max">The maximum value.</param>
/// <param name="result">When the method completes, contains the clamped value.</param>
public static void Clamp(ref Vector3 value, ref Vector3 min, ref Vector3 max, out Vector3 result)
{
float x = value.X;
x = (x > max.X) ? max.X : x;
x = (x < min.X) ? min.X : x;
float y = value.Y;
y = (y > max.Y) ? max.Y : y;
y = (y < min.Y) ? min.Y : y;
float z = value.Z;
z = (z > max.Z) ? max.Z : z;
z = (z < min.Z) ? min.Z : z;
result = new Vector3(x, y, z);
}
/// <summary>
/// Restricts a value to be within a specified range.
/// </summary>
/// <param name="value">The value to clamp.</param>
/// <param name="min">The minimum value.</param>
/// <param name="max">The maximum value.</param>
/// <returns>The clamped value.</returns>
public static Vector3 Clamp(Vector3 value, Vector3 min, Vector3 max)
{
Vector3 result;
Clamp(ref value, ref min, ref max, out result);
return result;
}
/// <summary>
/// Calculates the cross product of two vectors.
/// </summary>
/// <param name="left">First source vector.</param>
/// <param name="right">Second source vector.</param>
/// <param name="result">When the method completes, contains he cross product of the two vectors.</param>
public static void Cross(ref Vector3 left, ref Vector3 right, out Vector3 result)
{
result = new Vector3(
(left.Y * right.Z) - (left.Z * right.Y),
(left.Z * right.X) - (left.X * right.Z),
(left.X * right.Y) - (left.Y * right.X));
}
/// <summary>
/// Calculates the cross product of two vectors.
/// </summary>
/// <param name="left">First source vector.</param>
/// <param name="right">Second source vector.</param>
/// <returns>The cross product of the two vectors.</returns>
public static Vector3 Cross(Vector3 left, Vector3 right)
{
Vector3 result;
Cross(ref left, ref right, out result);
return result;
}
/// <summary>
/// Calculates the distance between two vectors.
/// </summary>
/// <param name="value1">The first vector.</param>
/// <param name="value2">The second vector.</param>
/// <param name="result">When the method completes, contains the distance between the two vectors.</param>
/// <remarks>
/// <see cref="Vector3.DistanceSquared(ref Vector3, ref Vector3, out float)"/> may be preferred when only the relative distance is needed
/// and speed is of the essence.
/// </remarks>
public static void Distance(ref Vector3 value1, ref Vector3 value2, out float result)
{
float x = value1.X - value2.X;
float y = value1.Y - value2.Y;
float z = value1.Z - value2.Z;
result = (float)Math.Sqrt((x * x) + (y * y) + (z * z));
}
/// <summary>
/// Calculates the distance between two vectors.
/// </summary>
/// <param name="value1">The first vector.</param>
/// <param name="value2">The second vector.</param>
/// <returns>The distance between the two vectors.</returns>
/// <remarks>
/// <see cref="Vector3.DistanceSquared(Vector3, Vector3)"/> may be preferred when only the relative distance is needed
/// and speed is of the essence.
/// </remarks>
public static float Distance(Vector3 value1, Vector3 value2)
{
float x = value1.X - value2.X;
float y = value1.Y - value2.Y;
float z = value1.Z - value2.Z;
return (float)Math.Sqrt((x * x) + (y * y) + (z * z));
}
/// <summary>
/// Calculates the squared distance between two vectors.
/// </summary>
/// <param name="value1">The first vector.</param>
/// <param name="value2">The second vector.</param>
/// <param name="result">When the method completes, contains the squared distance between the two vectors.</param>
/// <remarks>Distance squared is the value before taking the square root.
/// Distance squared can often be used in place of distance if relative comparisons are being made.
/// For example, consider three points A, B, and C. To determine whether B or C is further from A,
/// compare the distance between A and B to the distance between A and C. Calculating the two distances
/// involves two square roots, which are computationally expensive. However, using distance squared
/// provides the same information and avoids calculating two square roots.
/// </remarks>
public static void DistanceSquared(ref Vector3 value1, ref Vector3 value2, out float result)
{
float x = value1.X - value2.X;
float y = value1.Y - value2.Y;
float z = value1.Z - value2.Z;
result = (x * x) + (y * y) + (z * z);
}
/// <summary>
/// Calculates the squared distance between two vectors.
/// </summary>
/// <param name="value1">The first vector.</param>
/// <param name="value2">The second vector.</param>
/// <returns>The squared distance between the two vectors.</returns>
/// <remarks>Distance squared is the value before taking the square root.
/// Distance squared can often be used in place of distance if relative comparisons are being made.
/// For example, consider three points A, B, and C. To determine whether B or C is further from A,
/// compare the distance between A and B to the distance between A and C. Calculating the two distances
/// involves two square roots, which are computationally expensive. However, using distance squared
/// provides the same information and avoids calculating two square roots.
/// </remarks>
public static float DistanceSquared(Vector3 value1, Vector3 value2)
{
float x = value1.X - value2.X;
float y = value1.Y - value2.Y;
float z = value1.Z - value2.Z;
return (x * x) + (y * y) + (z * z);
}
/// <summary>
/// Tests whether one 3D vector is near another 3D vector.
/// </summary>
/// <param name="left">The left vector.</param>
/// <param name="right">The right vector.</param>
/// <param name="epsilon">The epsilon.</param>
/// <returns><c>true</c> if left and right are near another 3D, <c>false</c> otherwise</returns>
public static bool NearEqual(Vector3 left, Vector3 right, Vector3 epsilon)
{
return NearEqual(ref left, ref right, ref epsilon);
}
/// <summary>
/// Tests whether one 3D vector is near another 3D vector.
/// </summary>
/// <param name="left">The left vector.</param>
/// <param name="right">The right vector.</param>
/// <param name="epsilon">The epsilon.</param>
/// <returns><c>true</c> if left and right are near another 3D, <c>false</c> otherwise</returns>
public static bool NearEqual(ref Vector3 left, ref Vector3 right, ref Vector3 epsilon)
{
return MathUtil.WithinEpsilon(left.X, right.X, epsilon.X) &&
MathUtil.WithinEpsilon(left.Y, right.Y, epsilon.Y) &&
MathUtil.WithinEpsilon(left.Z, right.Z, epsilon.Z);
}
/// <summary>
/// Calculates the dot product of two vectors.
/// </summary>
/// <param name="left">First source vector.</param>
/// <param name="right">Second source vector.</param>
/// <param name="result">When the method completes, contains the dot product of the two vectors.</param>
public static void Dot(ref Vector3 left, ref Vector3 right, out float result)
{
result = (left.X * right.X) + (left.Y * right.Y) + (left.Z * right.Z);
}
/// <summary>
/// Calculates the dot product of two vectors.
/// </summary>
/// <param name="left">First source vector.</param>
/// <param name="right">Second source vector.</param>
/// <returns>The dot product of the two vectors.</returns>
public static float Dot(Vector3 left, Vector3 right)
{
return (left.X * right.X) + (left.Y * right.Y) + (left.Z * right.Z);
}
/// <summary>
/// Converts the vector into a unit vector.
/// </summary>
/// <param name="value">The vector to normalize.</param>
/// <param name="result">When the method completes, contains the normalized vector.</param>
public static void Normalize(ref Vector3 value, out Vector3 result)
{
result = value;
result.Normalize();
}
/// <summary>
/// Converts the vector into a unit vector.
/// </summary>
/// <param name="value">The vector to normalize.</param>
/// <returns>The normalized vector.</returns>
public static Vector3 Normalize(Vector3 value)
{
value.Normalize();
return value;
}
/// <summary>
/// Performs a linear interpolation between two vectors.
/// </summary>
/// <param name="start">Start vector.</param>
/// <param name="end">End vector.</param>
/// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end"/>.</param>
/// <param name="result">When the method completes, contains the linear interpolation of the two vectors.</param>
/// <remarks>
/// Passing <paramref name="amount"/> a value of 0 will cause <paramref name="start"/> to be returned; a value of 1 will cause <paramref name="end"/> to be returned.
/// </remarks>
public static void Lerp(ref Vector3 start, ref Vector3 end, float amount, out Vector3 result)
{
result.X = MathUtil.Lerp(start.X, end.X, amount);
result.Y = MathUtil.Lerp(start.Y, end.Y, amount);
result.Z = MathUtil.Lerp(start.Z, end.Z, amount);
}
/// <summary>
/// Performs a linear interpolation between two vectors.
/// </summary>
/// <param name="start">Start vector.</param>
/// <param name="end">End vector.</param>
/// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end"/>.</param>
/// <returns>The linear interpolation of the two vectors.</returns>
/// <remarks>
/// Passing <paramref name="amount"/> a value of 0 will cause <paramref name="start"/> to be returned; a value of 1 will cause <paramref name="end"/> to be returned.
/// </remarks>
public static Vector3 Lerp(Vector3 start, Vector3 end, float amount)
{
Vector3 result;
Lerp(ref start, ref end, amount, out result);
return result;
}
/// <summary>
/// Performs a cubic interpolation between two vectors.
/// </summary>
/// <param name="start">Start vector.</param>
/// <param name="end">End vector.</param>
/// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end"/>.</param>
/// <param name="result">When the method completes, contains the cubic interpolation of the two vectors.</param>
public static void SmoothStep(ref Vector3 start, ref Vector3 end, float amount, out Vector3 result)
{
amount = MathUtil.SmoothStep(amount);
Lerp(ref start, ref end, amount, out result);
}
/// <summary>
/// Performs a cubic interpolation between two vectors.
/// </summary>
/// <param name="start">Start vector.</param>
/// <param name="end">End vector.</param>
/// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end"/>.</param>
/// <returns>The cubic interpolation of the two vectors.</returns>
public static Vector3 SmoothStep(Vector3 start, Vector3 end, float amount)
{
Vector3 result;
SmoothStep(ref start, ref end, amount, out result);
return result;
}
/// <summary>
/// Performs a Hermite spline interpolation.
/// </summary>
/// <param name="value1">First source position vector.</param>
/// <param name="tangent1">First source tangent vector.</param>
/// <param name="value2">Second source position vector.</param>
/// <param name="tangent2">Second source tangent vector.</param>
/// <param name="amount">Weighting factor.</param>
/// <param name="result">When the method completes, contains the result of the Hermite spline interpolation.</param>
public static void Hermite(ref Vector3 value1, ref Vector3 tangent1, ref Vector3 value2, ref Vector3 tangent2, float amount, out Vector3 result)
{
float squared = amount * amount;
float cubed = amount * squared;
float part1 = ((2.0f * cubed) - (3.0f * squared)) + 1.0f;
float part2 = (-2.0f * cubed) + (3.0f * squared);
float part3 = (cubed - (2.0f * squared)) + amount;
float part4 = cubed - squared;
result.X = (((value1.X * part1) + (value2.X * part2)) + (tangent1.X * part3)) + (tangent2.X * part4);
result.Y = (((value1.Y * part1) + (value2.Y * part2)) + (tangent1.Y * part3)) + (tangent2.Y * part4);
result.Z = (((value1.Z * part1) + (value2.Z * part2)) + (tangent1.Z * part3)) + (tangent2.Z * part4);
}
/// <summary>
/// Performs a Hermite spline interpolation.
/// </summary>
/// <param name="value1">First source position vector.</param>
/// <param name="tangent1">First source tangent vector.</param>
/// <param name="value2">Second source position vector.</param>
/// <param name="tangent2">Second source tangent vector.</param>
/// <param name="amount">Weighting factor.</param>
/// <returns>The result of the Hermite spline interpolation.</returns>
public static Vector3 Hermite(Vector3 value1, Vector3 tangent1, Vector3 value2, Vector3 tangent2, float amount)
{
Vector3 result;
Hermite(ref value1, ref tangent1, ref value2, ref tangent2, amount, out result);
return result;
}
/// <summary>
/// Performs a Catmull-Rom interpolation using the specified positions.
/// </summary>
/// <param name="value1">The first position in the interpolation.</param>
/// <param name="value2">The second position in the interpolation.</param>
/// <param name="value3">The third position in the interpolation.</param>
/// <param name="value4">The fourth position in the interpolation.</param>
/// <param name="amount">Weighting factor.</param>
/// <param name="result">When the method completes, contains the result of the Catmull-Rom interpolation.</param>
public static void CatmullRom(ref Vector3 value1, ref Vector3 value2, ref Vector3 value3, ref Vector3 value4, float amount, out Vector3 result)
{
float squared = amount * amount;
float cubed = amount * squared;
result.X = 0.5f * ((((2.0f * value2.X) + ((-value1.X + value3.X) * amount)) +
(((((2.0f * value1.X) - (5.0f * value2.X)) + (4.0f * value3.X)) - value4.X) * squared)) +
((((-value1.X + (3.0f * value2.X)) - (3.0f * value3.X)) + value4.X) * cubed));
result.Y = 0.5f * ((((2.0f * value2.Y) + ((-value1.Y + value3.Y) * amount)) +
(((((2.0f * value1.Y) - (5.0f * value2.Y)) + (4.0f * value3.Y)) - value4.Y) * squared)) +
((((-value1.Y + (3.0f * value2.Y)) - (3.0f * value3.Y)) + value4.Y) * cubed));
result.Z = 0.5f * ((((2.0f * value2.Z) + ((-value1.Z + value3.Z) * amount)) +
(((((2.0f * value1.Z) - (5.0f * value2.Z)) + (4.0f * value3.Z)) - value4.Z) * squared)) +
((((-value1.Z + (3.0f * value2.Z)) - (3.0f * value3.Z)) + value4.Z) * cubed));
}
/// <summary>
/// Performs a Catmull-Rom interpolation using the specified positions.
/// </summary>
/// <param name="value1">The first position in the interpolation.</param>
/// <param name="value2">The second position in the interpolation.</param>
/// <param name="value3">The third position in the interpolation.</param>
/// <param name="value4">The fourth position in the interpolation.</param>
/// <param name="amount">Weighting factor.</param>
/// <returns>A vector that is the result of the Catmull-Rom interpolation.</returns>
public static Vector3 CatmullRom(Vector3 value1, Vector3 value2, Vector3 value3, Vector3 value4, float amount)
{
Vector3 result;
CatmullRom(ref value1, ref value2, ref value3, ref value4, amount, out result);
return result;
}
/// <summary>
/// Returns a vector containing the largest components of the specified vectors.
/// </summary>
/// <param name="left">The first source vector.</param>
/// <param name="right">The second source vector.</param>
/// <param name="result">When the method completes, contains an new vector composed of the largest components of the source vectors.</param>
public static void Max(ref Vector3 left, ref Vector3 right, out Vector3 result)
{
result.X = (left.X > right.X) ? left.X : right.X;
result.Y = (left.Y > right.Y) ? left.Y : right.Y;
result.Z = (left.Z > right.Z) ? left.Z : right.Z;
}
/// <summary>
/// Returns a vector containing the largest components of the specified vectors.
/// </summary>
/// <param name="left">The first source vector.</param>
/// <param name="right">The second source vector.</param>
/// <returns>A vector containing the largest components of the source vectors.</returns>
public static Vector3 Max(Vector3 left, Vector3 right)
{
Vector3 result;
Max(ref left, ref right, out result);
return result;
}
/// <summary>
/// Returns a vector containing the smallest components of the specified vectors.
/// </summary>
/// <param name="left">The first source vector.</param>
/// <param name="right">The second source vector.</param>
/// <param name="result">When the method completes, contains an new vector composed of the smallest components of the source vectors.</param>
public static void Min(ref Vector3 left, ref Vector3 right, out Vector3 result)
{
result.X = (left.X < right.X) ? left.X : right.X;
result.Y = (left.Y < right.Y) ? left.Y : right.Y;
result.Z = (left.Z < right.Z) ? left.Z : right.Z;
}
/// <summary>
/// Returns a vector containing the smallest components of the specified vectors.
/// </summary>
/// <param name="left">The first source vector.</param>
/// <param name="right">The second source vector.</param>
/// <returns>A vector containing the smallest components of the source vectors.</returns>
public static Vector3 Min(Vector3 left, Vector3 right)
{
Vector3 result;
Min(ref left, ref right, out result);
return result;
}
/// <summary>
/// Projects a 3D vector from object space into screen space.
/// </summary>
/// <param name="vector">The vector to project.</param>
/// <param name="x">The X position of the viewport.</param>
/// <param name="y">The Y position of the viewport.</param>
/// <param name="width">The width of the viewport.</param>
/// <param name="height">The height of the viewport.</param>
/// <param name="minZ">The minimum depth of the viewport.</param>
/// <param name="maxZ">The maximum depth of the viewport.</param>
/// <param name="worldViewProjection">The combined world-view-projection matrix.</param>
/// <param name="result">When the method completes, contains the vector in screen space.</param>
public static void Project(ref Vector3 vector, float x, float y, float width, float height, float minZ, float maxZ, ref Matrix worldViewProjection, out Vector3 result)
{
Vector3 v = new Vector3();
TransformCoordinate(ref vector, ref worldViewProjection, out v);
result = new Vector3(((1.0f + v.X) * 0.5f * width) + x, ((1.0f - v.Y) * 0.5f * height) + y, (v.Z * (maxZ - minZ)) + minZ);
}
/// <summary>
/// Projects a 3D vector from object space into screen space.
/// </summary>
/// <param name="vector">The vector to project.</param>
/// <param name="x">The X position of the viewport.</param>
/// <param name="y">The Y position of the viewport.</param>
/// <param name="width">The width of the viewport.</param>
/// <param name="height">The height of the viewport.</param>
/// <param name="minZ">The minimum depth of the viewport.</param>
/// <param name="maxZ">The maximum depth of the viewport.</param>
/// <param name="worldViewProjection">The combined world-view-projection matrix.</param>
/// <returns>The vector in screen space.</returns>
public static Vector3 Project(Vector3 vector, float x, float y, float width, float height, float minZ, float maxZ, Matrix worldViewProjection)
{
Vector3 result;
Project(ref vector, x, y, width, height, minZ, maxZ, ref worldViewProjection, out result);
return result;
}
/// <summary>
/// Projects a 3D vector from screen space into object space.
/// </summary>
/// <param name="vector">The vector to project.</param>
/// <param name="x">The X position of the viewport.</param>
/// <param name="y">The Y position of the viewport.</param>
/// <param name="width">The width of the viewport.</param>
/// <param name="height">The height of the viewport.</param>
/// <param name="minZ">The minimum depth of the viewport.</param>
/// <param name="maxZ">The maximum depth of the viewport.</param>
/// <param name="worldViewProjection">The combined world-view-projection matrix.</param>
/// <param name="result">When the method completes, contains the vector in object space.</param>
public static void Unproject(ref Vector3 vector, float x, float y, float width, float height, float minZ, float maxZ, ref Matrix worldViewProjection, out Vector3 result)
{
Vector3 v = new Vector3();
Matrix matrix = new Matrix();
Matrix.Invert(ref worldViewProjection, out matrix);
v.X = (((vector.X - x) / width) * 2.0f) - 1.0f;
v.Y = -((((vector.Y - y) / height) * 2.0f) - 1.0f);
v.Z = (vector.Z - minZ) / (maxZ - minZ);
TransformCoordinate(ref v, ref matrix, out result);
}
/// <summary>
/// Projects a 3D vector from screen space into object space.
/// </summary>
/// <param name="vector">The vector to project.</param>
/// <param name="x">The X position of the viewport.</param>
/// <param name="y">The Y position of the viewport.</param>
/// <param name="width">The width of the viewport.</param>
/// <param name="height">The height of the viewport.</param>
/// <param name="minZ">The minimum depth of the viewport.</param>
/// <param name="maxZ">The maximum depth of the viewport.</param>
/// <param name="worldViewProjection">The combined world-view-projection matrix.</param>
/// <returns>The vector in object space.</returns>
public static Vector3 Unproject(Vector3 vector, float x, float y, float width, float height, float minZ, float maxZ, Matrix worldViewProjection)
{
Vector3 result;
Unproject(ref vector, x, y, width, height, minZ, maxZ, ref worldViewProjection, out result);
return result;
}
/// <summary>
/// Returns the reflection of a vector off a surface that has the specified normal.
/// </summary>
/// <param name="vector">The source vector.</param>
/// <param name="normal">Normal of the surface.</param>
/// <param name="result">When the method completes, contains the reflected vector.</param>
/// <remarks>Reflect only gives the direction of a reflection off a surface, it does not determine
/// whether the original vector was close enough to the surface to hit it.</remarks>
public static void Reflect(ref Vector3 vector, ref Vector3 normal, out Vector3 result)
{
float dot = (vector.X * normal.X) + (vector.Y * normal.Y) + (vector.Z * normal.Z);
result.X = vector.X - ((2.0f * dot) * normal.X);
result.Y = vector.Y - ((2.0f * dot) * normal.Y);
result.Z = vector.Z - ((2.0f * dot) * normal.Z);
}
/// <summary>
/// Returns the reflection of a vector off a surface that has the specified normal.
/// </summary>
/// <param name="vector">The source vector.</param>
/// <param name="normal">Normal of the surface.</param>
/// <returns>The reflected vector.</returns>
/// <remarks>Reflect only gives the direction of a reflection off a surface, it does not determine
/// whether the original vector was close enough to the surface to hit it.</remarks>
public static Vector3 Reflect(Vector3 vector, Vector3 normal)
{
Vector3 result;
Reflect(ref vector, ref normal, out result);
return result;
}
/// <summary>
/// Orthogonalizes a list of vectors.
/// </summary>
/// <param name="destination">The list of orthogonalized vectors.</param>
/// <param name="source">The list of vectors to orthogonalize.</param>
/// <remarks>
/// <para>Orthogonalization is the process of making all vectors orthogonal to each other. This
/// means that any given vector in the list will be orthogonal to any other given vector in the
/// list.</para>
/// <para>Because this method uses the modified Gram-Schmidt process, the resulting vectors
/// tend to be numerically unstable. The numeric stability decreases according to the vectors
/// position in the list so that the first vector is the most stable and the last vector is the
/// least stable.</para>
/// </remarks>
/// <exception cref="ArgumentNullException">Thrown when <paramref name="source"/> or <paramref name="destination"/> is <c>null</c>.</exception>
/// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="destination"/> is shorter in length than <paramref name="source"/>.</exception>
public static void Orthogonalize(Vector3[] destination, params Vector3[] source)
{
//Uses the modified Gram-Schmidt process.
//q1 = m1
//q2 = m2 - ((q1 ⋅ m2) / (q1 ⋅ q1)) * q1
//q3 = m3 - ((q1 ⋅ m3) / (q1 ⋅ q1)) * q1 - ((q2 ⋅ m3) / (q2 ⋅ q2)) * q2
//q4 = m4 - ((q1 ⋅ m4) / (q1 ⋅ q1)) * q1 - ((q2 ⋅ m4) / (q2 ⋅ q2)) * q2 - ((q3 ⋅ m4) / (q3 ⋅ q3)) * q3
//q5 = ...
if (source == null)
throw new ArgumentNullException("source");
if (destination == null)
throw new ArgumentNullException("destination");
if (destination.Length < source.Length)
throw new ArgumentOutOfRangeException("destination", "The destination array must be of same length or larger length than the source array.");
for (int i = 0; i < source.Length; ++i)
{
Vector3 newvector = source[i];
for (int r = 0; r < i; ++r)
{
newvector -= (Vector3.Dot(destination[r], newvector) / Vector3.Dot(destination[r], destination[r])) * destination[r];
}
destination[i] = newvector;
}
}
/// <summary>
/// Orthonormalizes a list of vectors.
/// </summary>
/// <param name="destination">The list of orthonormalized vectors.</param>
/// <param name="source">The list of vectors to orthonormalize.</param>
/// <remarks>
/// <para>Orthonormalization is the process of making all vectors orthogonal to each
/// other and making all vectors of unit length. This means that any given vector will
/// be orthogonal to any other given vector in the list.</para>
/// <para>Because this method uses the modified Gram-Schmidt process, the resulting vectors
/// tend to be numerically unstable. The numeric stability decreases according to the vectors
/// position in the list so that the first vector is the most stable and the last vector is the
/// least stable.</para>
/// </remarks>
/// <exception cref="ArgumentNullException">Thrown when <paramref name="source"/> or <paramref name="destination"/> is <c>null</c>.</exception>
/// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="destination"/> is shorter in length than <paramref name="source"/>.</exception>
public static void Orthonormalize(Vector3[] destination, params Vector3[] source)
{
//Uses the modified Gram-Schmidt process.
//Because we are making unit vectors, we can optimize the math for orthogonalization
//and simplify the projection operation to remove the division.
//q1 = m1 / |m1|
//q2 = (m2 - (q1 ⋅ m2) * q1) / |m2 - (q1 ⋅ m2) * q1|
//q3 = (m3 - (q1 ⋅ m3) * q1 - (q2 ⋅ m3) * q2) / |m3 - (q1 ⋅ m3) * q1 - (q2 ⋅ m3) * q2|
//q4 = (m4 - (q1 ⋅ m4) * q1 - (q2 ⋅ m4) * q2 - (q3 ⋅ m4) * q3) / |m4 - (q1 ⋅ m4) * q1 - (q2 ⋅ m4) * q2 - (q3 ⋅ m4) * q3|
//q5 = ...
if (source == null)
throw new ArgumentNullException("source");
if (destination == null)
throw new ArgumentNullException("destination");
if (destination.Length < source.Length)
throw new ArgumentOutOfRangeException("destination", "The destination array must be of same length or larger length than the source array.");
for (int i = 0; i < source.Length; ++i)
{
Vector3 newvector = source[i];
for (int r = 0; r < i; ++r)
{
newvector -= Vector3.Dot(destination[r], newvector) * destination[r];
}
newvector.Normalize();
destination[i] = newvector;
}
}
/// <summary>
/// Transforms a 3D vector by the given <see cref="Quaternion"/> rotation.
/// </summary>
/// <param name="vector">The vector to rotate.</param>
/// <param name="rotation">The <see cref="Quaternion"/> rotation to apply.</param>
/// <param name="result">When the method completes, contains the transformed <see cref="Vector4"/>.</param>
public static void Transform(ref Vector3 vector, ref Quaternion rotation, out Vector3 result)
{
float x = rotation.X + rotation.X;
float y = rotation.Y + rotation.Y;
float z = rotation.Z + rotation.Z;
float wx = rotation.W * x;
float wy = rotation.W * y;
float wz = rotation.W * z;
float xx = rotation.X * x;
float xy = rotation.X * y;
float xz = rotation.X * z;
float yy = rotation.Y * y;
float yz = rotation.Y * z;
float zz = rotation.Z * z;
result = new Vector3(
((vector.X * ((1.0f - yy) - zz)) + (vector.Y * (xy - wz))) + (vector.Z * (xz + wy)),
((vector.X * (xy + wz)) + (vector.Y * ((1.0f - xx) - zz))) + (vector.Z * (yz - wx)),
((vector.X * (xz - wy)) + (vector.Y * (yz + wx))) + (vector.Z * ((1.0f - xx) - yy)));
}
/// <summary>
/// Transforms a 3D vector by the given <see cref="Quaternion"/> rotation.
/// </summary>
/// <param name="vector">The vector to rotate.</param>
/// <param name="rotation">The <see cref="Quaternion"/> rotation to apply.</param>
/// <returns>The transformed <see cref="Vector4"/>.</returns>
public static Vector3 Transform(Vector3 vector, Quaternion rotation)
{
Vector3 result;
Transform(ref vector, ref rotation, out result);
return result;
}
/// <summary>
/// Transforms an array of vectors by the given <see cref="Quaternion"/> rotation.
/// </summary>
/// <param name="source">The array of vectors to transform.</param>
/// <param name="rotation">The <see cref="Quaternion"/> rotation to apply.</param>
/// <param name="destination">The array for which the transformed vectors are stored.
/// This array may be the same array as <paramref name="source"/>.</param>
/// <exception cref="ArgumentNullException">Thrown when <paramref name="source"/> or <paramref name="destination"/> is <c>null</c>.</exception>
/// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="destination"/> is shorter in length than <paramref name="source"/>.</exception>
public static void Transform(Vector3[] source, ref Quaternion rotation, Vector3[] destination)
{
if (source == null)
throw new ArgumentNullException("source");
if (destination == null)
throw new ArgumentNullException("destination");
if (destination.Length < source.Length)
throw new ArgumentOutOfRangeException("destination", "The destination array must be of same length or larger length than the source array.");
float x = rotation.X + rotation.X;
float y = rotation.Y + rotation.Y;
float z = rotation.Z + rotation.Z;
float wx = rotation.W * x;
float wy = rotation.W * y;
float wz = rotation.W * z;
float xx = rotation.X * x;
float xy = rotation.X * y;
float xz = rotation.X * z;
float yy = rotation.Y * y;
float yz = rotation.Y * z;
float zz = rotation.Z * z;
float num1 = ((1.0f - yy) - zz);
float num2 = (xy - wz);
float num3 = (xz + wy);
float num4 = (xy + wz);
float num5 = ((1.0f - xx) - zz);
float num6 = (yz - wx);
float num7 = (xz - wy);
float num8 = (yz + wx);
float num9 = ((1.0f - xx) - yy);
for (int i = 0; i < source.Length; ++i)
{
destination[i] = new Vector3(
((source[i].X * num1) + (source[i].Y * num2)) + (source[i].Z * num3),
((source[i].X * num4) + (source[i].Y * num5)) + (source[i].Z * num6),
((source[i].X * num7) + (source[i].Y * num8)) + (source[i].Z * num9));
}
}
/// <summary>
/// Transforms a 3D vector by the given <see cref="Matrix3x3"/>.
/// </summary>
/// <param name="vector">The source vector.</param>
/// <param name="transform">The transformation <see cref="Matrix3x3"/>.</param>
/// <param name="result">When the method completes, contains the transformed <see cref="Vector3"/>.</param>
public static void Transform(ref Vector3 vector, ref Matrix3x3 transform, out Vector3 result)
{
result = new Vector3( (vector.X * transform.M11) + (vector.Y * transform.M21) + (vector.Z * transform.M31),
(vector.X * transform.M12) + (vector.Y * transform.M22) + (vector.Z * transform.M32),
(vector.X * transform.M13) + (vector.Y * transform.M23) + (vector.Z * transform.M33)
);
}
/// <summary>
/// Transforms a 3D vector by the given <see cref="Matrix3x3"/>.
/// </summary>
/// <param name="vector">The source vector.</param>
/// <param name="transform">The transformation <see cref="Matrix3x3"/>.</param>
/// <returns>The transformed <see cref="Vector3"/>.</returns>
public static Vector3 Transform(Vector3 vector, Matrix3x3 transform)
{
Vector3 result;
Transform(ref vector, ref transform, out result);
return result;
}
/// <summary>
/// Transforms a 3D vector by the given <see cref="Matrix"/>.
/// </summary>
/// <param name="vector">The source vector.</param>
/// <param name="transform">The transformation <see cref="Matrix"/>.</param>
/// <param name="result">When the method completes, contains the transformed <see cref="Vector3"/>.</param>
public static void Transform(ref Vector3 vector, ref Matrix transform, out Vector3 result)
{
Vector4 intermediate;
Transform(ref vector, ref transform, out intermediate);
result = (Vector3)intermediate;
}
/// <summary>
/// Transforms a 3D vector by the given <see cref="Matrix"/>.
/// </summary>
/// <param name="vector">The source vector.</param>
/// <param name="transform">The transformation <see cref="Matrix"/>.</param>
/// <param name="result">When the method completes, contains the transformed <see cref="Vector4"/>.</param>
public static void Transform(ref Vector3 vector, ref Matrix transform, out Vector4 result)
{
result = new Vector4(
(vector.X * transform.M11) + (vector.Y * transform.M21) + (vector.Z * transform.M31) + transform.M41,
(vector.X * transform.M12) + (vector.Y * transform.M22) + (vector.Z * transform.M32) + transform.M42,
(vector.X * transform.M13) + (vector.Y * transform.M23) + (vector.Z * transform.M33) + transform.M43,
(vector.X * transform.M14) + (vector.Y * transform.M24) + (vector.Z * transform.M34) + transform.M44);
}
/// <summary>
/// Transforms a 3D vector by the given <see cref="Matrix"/>.
/// </summary>
/// <param name="vector">The source vector.</param>
/// <param name="transform">The transformation <see cref="Matrix"/>.</param>
/// <returns>The transformed <see cref="Vector4"/>.</returns>
public static Vector4 Transform(Vector3 vector, Matrix transform)
{
Vector4 result;
Transform(ref vector, ref transform, out result);
return result;
}
/// <summary>
/// Transforms an array of 3D vectors by the given <see cref="Matrix"/>.
/// </summary>
/// <param name="source">The array of vectors to transform.</param>
/// <param name="transform">The transformation <see cref="Matrix"/>.</param>
/// <param name="destination">The array for which the transformed vectors are stored.</param>
/// <exception cref="ArgumentNullException">Thrown when <paramref name="source"/> or <paramref name="destination"/> is <c>null</c>.</exception>
/// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="destination"/> is shorter in length than <paramref name="source"/>.</exception>
public static void Transform(Vector3[] source, ref Matrix transform, Vector4[] destination)
{
if (source == null)
throw new ArgumentNullException("source");
if (destination == null)
throw new ArgumentNullException("destination");
if (destination.Length < source.Length)
throw new ArgumentOutOfRangeException("destination", "The destination array must be of same length or larger length than the source array.");
for (int i = 0; i < source.Length; ++i)
{
Transform(ref source[i], ref transform, out destination[i]);
}
}
/// <summary>
/// Performs a coordinate transformation using the given <see cref="Matrix"/>.
/// </summary>
/// <param name="coordinate">The coordinate vector to transform.</param>
/// <param name="transform">The transformation <see cref="Matrix"/>.</param>
/// <param name="result">When the method completes, contains the transformed coordinates.</param>
/// <remarks>
/// A coordinate transform performs the transformation with the assumption that the w component
/// is one. The four dimensional vector obtained from the transformation operation has each
/// component in the vector divided by the w component. This forces the w component to be one and
/// therefore makes the vector homogeneous. The homogeneous vector is often preferred when working
/// with coordinates as the w component can safely be ignored.
/// </remarks>
public static void TransformCoordinate(ref Vector3 coordinate, ref Matrix transform, out Vector3 result)
{
Vector4 vector = new Vector4();
vector.X = (coordinate.X * transform.M11) + (coordinate.Y * transform.M21) + (coordinate.Z * transform.M31) + transform.M41;
vector.Y = (coordinate.X * transform.M12) + (coordinate.Y * transform.M22) + (coordinate.Z * transform.M32) + transform.M42;
vector.Z = (coordinate.X * transform.M13) + (coordinate.Y * transform.M23) + (coordinate.Z * transform.M33) + transform.M43;
vector.W = 1f / ((coordinate.X * transform.M14) + (coordinate.Y * transform.M24) + (coordinate.Z * transform.M34) + transform.M44);
result = new Vector3(vector.X * vector.W, vector.Y * vector.W, vector.Z * vector.W);
}
/// <summary>
/// Performs a coordinate transformation using the given <see cref="Matrix"/>.
/// </summary>
/// <param name="coordinate">The coordinate vector to transform.</param>
/// <param name="transform">The transformation <see cref="Matrix"/>.</param>
/// <returns>The transformed coordinates.</returns>
/// <remarks>
/// A coordinate transform performs the transformation with the assumption that the w component
/// is one. The four dimensional vector obtained from the transformation operation has each
/// component in the vector divided by the w component. This forces the w component to be one and
/// therefore makes the vector homogeneous. The homogeneous vector is often preferred when working
/// with coordinates as the w component can safely be ignored.
/// </remarks>
public static Vector3 TransformCoordinate(Vector3 coordinate, Matrix transform)
{
Vector3 result;
TransformCoordinate(ref coordinate, ref transform, out result);
return result;
}
/// <summary>
/// Performs a coordinate transformation on an array of vectors using the given <see cref="Matrix"/>.
/// </summary>
/// <param name="source">The array of coordinate vectors to transform.</param>
/// <param name="transform">The transformation <see cref="Matrix"/>.</param>
/// <param name="destination">The array for which the transformed vectors are stored.
/// This array may be the same array as <paramref name="source"/>.</param>
/// <exception cref="ArgumentNullException">Thrown when <paramref name="source"/> or <paramref name="destination"/> is <c>null</c>.</exception>
/// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="destination"/> is shorter in length than <paramref name="source"/>.</exception>
/// <remarks>
/// A coordinate transform performs the transformation with the assumption that the w component
/// is one. The four dimensional vector obtained from the transformation operation has each
/// component in the vector divided by the w component. This forces the w component to be one and
/// therefore makes the vector homogeneous. The homogeneous vector is often preferred when working
/// with coordinates as the w component can safely be ignored.
/// </remarks>
public static void TransformCoordinate(Vector3[] source, ref Matrix transform, Vector3[] destination)
{
if (source == null)
throw new ArgumentNullException("source");
if (destination == null)
throw new ArgumentNullException("destination");
if (destination.Length < source.Length)
throw new ArgumentOutOfRangeException("destination", "The destination array must be of same length or larger length than the source array.");
for (int i = 0; i < source.Length; ++i)
{
TransformCoordinate(ref source[i], ref transform, out destination[i]);
}
}
/// <summary>
/// Performs a normal transformation using the given <see cref="Matrix"/>.
/// </summary>
/// <param name="normal">The normal vector to transform.</param>
/// <param name="transform">The transformation <see cref="Matrix"/>.</param>
/// <param name="result">When the method completes, contains the transformed normal.</param>
/// <remarks>
/// A normal transform performs the transformation with the assumption that the w component
/// is zero. This causes the fourth row and fourth column of the matrix to be unused. The
/// end result is a vector that is not translated, but all other transformation properties
/// apply. This is often preferred for normal vectors as normals purely represent direction
/// rather than location because normal vectors should not be translated.
/// </remarks>
public static void TransformNormal(ref Vector3 normal, ref Matrix transform, out Vector3 result)
{
result = new Vector3(
(normal.X * transform.M11) + (normal.Y * transform.M21) + (normal.Z * transform.M31),
(normal.X * transform.M12) + (normal.Y * transform.M22) + (normal.Z * transform.M32),
(normal.X * transform.M13) + (normal.Y * transform.M23) + (normal.Z * transform.M33));
}
/// <summary>
/// Performs a normal transformation using the given <see cref="Matrix"/>.
/// </summary>
/// <param name="normal">The normal vector to transform.</param>
/// <param name="transform">The transformation <see cref="Matrix"/>.</param>
/// <returns>The transformed normal.</returns>
/// <remarks>
/// A normal transform performs the transformation with the assumption that the w component
/// is zero. This causes the fourth row and fourth column of the matrix to be unused. The
/// end result is a vector that is not translated, but all other transformation properties
/// apply. This is often preferred for normal vectors as normals purely represent direction
/// rather than location because normal vectors should not be translated.
/// </remarks>
public static Vector3 TransformNormal(Vector3 normal, Matrix transform)
{
Vector3 result;
TransformNormal(ref normal, ref transform, out result);
return result;
}
/// <summary>
/// Performs a normal transformation on an array of vectors using the given <see cref="Matrix"/>.
/// </summary>
/// <param name="source">The array of normal vectors to transform.</param>
/// <param name="transform">The transformation <see cref="Matrix"/>.</param>
/// <param name="destination">The array for which the transformed vectors are stored.
/// This array may be the same array as <paramref name="source"/>.</param>
/// <exception cref="ArgumentNullException">Thrown when <paramref name="source"/> or <paramref name="destination"/> is <c>null</c>.</exception>
/// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="destination"/> is shorter in length than <paramref name="source"/>.</exception>
/// <remarks>
/// A normal transform performs the transformation with the assumption that the w component
/// is zero. This causes the fourth row and fourth column of the matrix to be unused. The
/// end result is a vector that is not translated, but all other transformation properties
/// apply. This is often preferred for normal vectors as normals purely represent direction
/// rather than location because normal vectors should not be translated.
/// </remarks>
public static void TransformNormal(Vector3[] source, ref Matrix transform, Vector3[] destination)
{
if (source == null)
throw new ArgumentNullException("source");
if (destination == null)
throw new ArgumentNullException("destination");
if (destination.Length < source.Length)
throw new ArgumentOutOfRangeException("destination", "The destination array must be of same length or larger length than the source array.");
for (int i = 0; i < source.Length; ++i)
{
TransformNormal(ref source[i], ref transform, out destination[i]);
}
}
/// <summary>
/// Adds two vectors.
/// </summary>
/// <param name="left">The first vector to add.</param>
/// <param name="right">The second vector to add.</param>
/// <returns>The sum of the two vectors.</returns>
public static Vector3 operator +(Vector3 left, Vector3 right)
{
return new Vector3(left.X + right.X, left.Y + right.Y, left.Z + right.Z);
}
/// <summary>
/// Multiplies a vector with another by performing component-wise multiplication equivalent to <see cref="Multiply(ref Vector3,ref Vector3,out Vector3)"/>.
/// </summary>
/// <param name="left">The first vector to multiply.</param>
/// <param name="right">The second vector to multiply.</param>
/// <returns>The multiplication of the two vectors.</returns>
public static Vector3 operator *(Vector3 left, Vector3 right)
{
return new Vector3(left.X * right.X, left.Y * right.Y, left.Z * right.Z);
}
/// <summary>
/// Assert a vector (return it unchanged).
/// </summary>
/// <param name="value">The vector to assert (unchanged).</param>
/// <returns>The asserted (unchanged) vector.</returns>
public static Vector3 operator +(Vector3 value)
{
return value;
}
/// <summary>
/// Subtracts two vectors.
/// </summary>
/// <param name="left">The first vector to subtract.</param>
/// <param name="right">The second vector to subtract.</param>
/// <returns>The difference of the two vectors.</returns>
public static Vector3 operator -(Vector3 left, Vector3 right)
{
return new Vector3(left.X - right.X, left.Y - right.Y, left.Z - right.Z);
}
/// <summary>
/// Reverses the direction of a given vector.
/// </summary>
/// <param name="value">The vector to negate.</param>
/// <returns>A vector facing in the opposite direction.</returns>
public static Vector3 operator -(Vector3 value)
{
return new Vector3(-value.X, -value.Y, -value.Z);
}
/// <summary>
/// Scales a vector by the given value.
/// </summary>
/// <param name="value">The vector to scale.</param>
/// <param name="scale">The amount by which to scale the vector.</param>
/// <returns>The scaled vector.</returns>
public static Vector3 operator *(float scale, Vector3 value)
{
return new Vector3(value.X * scale, value.Y * scale, value.Z * scale);
}
/// <summary>
/// Scales a vector by the given value.
/// </summary>
/// <param name="value">The vector to scale.</param>
/// <param name="scale">The amount by which to scale the vector.</param>
/// <returns>The scaled vector.</returns>
public static Vector3 operator *(Vector3 value, float scale)
{
return new Vector3(value.X * scale, value.Y * scale, value.Z * scale);
}
/// <summary>
/// Scales a vector by the given value.
/// </summary>
/// <param name="value">The vector to scale.</param>
/// <param name="scale">The amount by which to scale the vector.</param>
/// <returns>The scaled vector.</returns>
public static Vector3 operator /(Vector3 value, float scale)
{
return new Vector3(value.X / scale, value.Y / scale, value.Z / scale);
}
/// <summary>
/// Scales a vector by the given value.
/// </summary>
/// <param name="scale">The amount by which to scale the vector.</param>
/// <param name="value">The vector to scale.</param>
/// <returns>The scaled vector.</returns>
public static Vector3 operator /(float scale, Vector3 value)
{
return new Vector3(scale / value.X, scale / value.Y, scale / value.Z);
}
/// <summary>
/// Scales a vector by the given value.
/// </summary>
/// <param name="value">The vector to scale.</param>
/// <param name="scale">The amount by which to scale the vector.</param>
/// <returns>The scaled vector.</returns>
public static Vector3 operator /(Vector3 value, Vector3 scale)
{
return new Vector3(value.X / scale.X, value.Y / scale.Y, value.Z / scale.Z);
}
/// <summary>
/// Perform a component-wise addition
/// </summary>
/// <param name="value">The input vector.</param>
/// <param name="scalar">The scalar value to be added on elements</param>
/// <returns>The vector with added scalar for each element.</returns>
public static Vector3 operator +(Vector3 value, float scalar)
{
return new Vector3(value.X + scalar, value.Y + scalar, value.Z + scalar);
}
/// <summary>
/// Perform a component-wise addition
/// </summary>
/// <param name="value">The input vector.</param>
/// <param name="scalar">The scalar value to be added on elements</param>
/// <returns>The vector with added scalar for each element.</returns>
public static Vector3 operator +(float scalar, Vector3 value)
{
return new Vector3(scalar + value.X, scalar + value.Y, scalar + value.Z);
}
/// <summary>
/// Perform a component-wise subtraction
/// </summary>
/// <param name="value">The input vector.</param>
/// <param name="scalar">The scalar value to be subtraced from elements</param>
/// <returns>The vector with added scalar from each element.</returns>
public static Vector3 operator -(Vector3 value, float scalar)
{
return new Vector3(value.X - scalar, value.Y - scalar, value.Z - scalar);
}
/// <summary>
/// Perform a component-wise subtraction
/// </summary>
/// <param name="value">The input vector.</param>
/// <param name="scalar">The scalar value to be subtraced from elements</param>
/// <returns>The vector with subtraced scalar from each element.</returns>
public static Vector3 operator -(float scalar, Vector3 value)
{
return new Vector3(scalar - value.X, scalar - value.Y, scalar - value.Z);
}
/// <summary>
/// Tests for equality between two objects.
/// </summary>
/// <param name="left">The first value to compare.</param>
/// <param name="right">The second value to compare.</param>
/// <returns><c>true</c> if <paramref name="left"/> has the same value as <paramref name="right"/>; otherwise, <c>false</c>.</returns>
[MethodImpl((MethodImplOptions)0x100)] // MethodImplOptions.AggressiveInlining
public static bool operator ==(Vector3 left, Vector3 right)
{
return left.Equals(ref right);
}
/// <summary>
/// Tests for inequality between two objects.
/// </summary>
/// <param name="left">The first value to compare.</param>
/// <param name="right">The second value to compare.</param>
/// <returns><c>true</c> if <paramref name="left"/> has a different value than <paramref name="right"/>; otherwise, <c>false</c>.</returns>
[MethodImpl((MethodImplOptions)0x100)] // MethodImplOptions.AggressiveInlining
public static bool operator !=(Vector3 left, Vector3 right)
{
return !left.Equals(ref right);
}
/// <summary>
/// Performs an explicit conversion from <see cref="Vector3"/> to <see cref="Vector2"/>.
/// </summary>
/// <param name="value">The value.</param>
/// <returns>The result of the conversion.</returns>
public static explicit operator Vector2(Vector3 value)
{
return new Vector2(value.X, value.Y);
}
/// <summary>
/// Performs an explicit conversion from <see cref="Vector3"/> to <see cref="Vector4"/>.
/// </summary>
/// <param name="value">The value.</param>
/// <returns>The result of the conversion.</returns>
public static explicit operator Vector4(Vector3 value)
{
return new Vector4(value, 0.0f);
}
/// <summary>
/// Returns a <see cref="System.String"/> that represents this instance.
/// </summary>
/// <returns>
/// A <see cref="System.String"/> that represents this instance.
/// </returns>
public override string ToString()
{
return string.Format(CultureInfo.CurrentCulture, "X:{0} Y:{1} Z:{2}", X, Y, Z);
}
/// <summary>
/// Returns a <see cref="System.String"/> that represents this instance.
/// </summary>
/// <param name="format">The format.</param>
/// <returns>
/// A <see cref="System.String"/> that represents this instance.
/// </returns>
public string ToString(string format)
{
if (format == null)
return ToString();
return string.Format(CultureInfo.CurrentCulture, "X:{0} Y:{1} Z:{2}", X.ToString(format, CultureInfo.CurrentCulture),
Y.ToString(format, CultureInfo.CurrentCulture), Z.ToString(format, CultureInfo.CurrentCulture));
}
/// <summary>
/// Returns a <see cref="System.String"/> that represents this instance.
/// </summary>
/// <param name="formatProvider">The format provider.</param>
/// <returns>
/// A <see cref="System.String"/> that represents this instance.
/// </returns>
public string ToString(IFormatProvider formatProvider)
{
return string.Format(formatProvider, "X:{0} Y:{1} Z:{2}", X, Y, Z);
}
/// <summary>
/// Returns a <see cref="System.String"/> that represents this instance.
/// </summary>
/// <param name="format">The format.</param>
/// <param name="formatProvider">The format provider.</param>
/// <returns>
/// A <see cref="System.String"/> that represents this instance.
/// </returns>
public string ToString(string format, IFormatProvider formatProvider)
{
if (format == null)
return ToString(formatProvider);
return string.Format(formatProvider, "X:{0} Y:{1} Z:{2}", X.ToString(format, formatProvider),
Y.ToString(format, formatProvider), Z.ToString(format, formatProvider));
}
/// <summary>
/// Returns a hash code for this instance.
/// </summary>
/// <returns>
/// A hash code for this instance, suitable for use in hashing algorithms and data structures like a hash table.
/// </returns>
public override int GetHashCode()
{
unchecked
{
var hashCode = X.GetHashCode();
hashCode = (hashCode * 397) ^ Y.GetHashCode();
hashCode = (hashCode * 397) ^ Z.GetHashCode();
return hashCode;
}
}
/// <summary>
/// Determines whether the specified <see cref="Vector3"/> is equal to this instance.
/// </summary>
/// <param name="other">The <see cref="Vector3"/> to compare with this instance.</param>
/// <returns>
/// <c>true</c> if the specified <see cref="Vector3"/> is equal to this instance; otherwise, <c>false</c>.
/// </returns>
[MethodImpl((MethodImplOptions)0x100)] // MethodImplOptions.AggressiveInlining
public bool Equals(ref Vector3 other)
{
return MathUtil.NearEqual(other.X, X) && MathUtil.NearEqual(other.Y, Y) && MathUtil.NearEqual(other.Z, Z);
}
/// <summary>
/// Determines whether the specified <see cref="Vector3"/> is equal to this instance.
/// </summary>
/// <param name="other">The <see cref="Vector3"/> to compare with this instance.</param>
/// <returns>
/// <c>true</c> if the specified <see cref="Vector3"/> is equal to this instance; otherwise, <c>false</c>.
/// </returns>
[MethodImpl((MethodImplOptions)0x100)] // MethodImplOptions.AggressiveInlining
public bool Equals(Vector3 other)
{
return Equals(ref other);
}
/// <summary>
/// Determines whether the specified <see cref="System.Object"/> is equal to this instance.
/// </summary>
/// <param name="value">The <see cref="System.Object"/> to compare with this instance.</param>
/// <returns>
/// <c>true</c> if the specified <see cref="System.Object"/> is equal to this instance; otherwise, <c>false</c>.
/// </returns>
public override bool Equals(object value)
{
if (!(value is Vector3))
return false;
var strongValue = (Vector3)value;
return Equals(ref strongValue);
}
/// <summary>
/// Performs an implicit conversion from <see cref="Vector3"/> to <see cref="RawVector3"/>.
/// </summary>
/// <param name="value">The value.</param>
/// <returns>The result of the conversion.</returns>
public unsafe static implicit operator RawVector3(Vector3 value)
{
return *(RawVector3*)&value;
}
/// <summary>
/// Performs an implicit conversion from <see cref="RawVector3"/> to <see cref="Vector3"/>.
/// </summary>
/// <param name="value">The value.</param>
/// <returns>The result of the conversion.</returns>
public unsafe static implicit operator Vector3(RawVector3 value)
{
return *(Vector3*)&value;
}
}
}