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/** KempoApi: The Turloc Toolkit *****************************/
/** * * **/
/** ** ** Filename: arcball.h **/
/** ** Version: Common **/
/** ** **/
/** **/
/** Arcball class for mouse manipulation. **/
/** **/
/** **/
/** **/
/** **/
/** (C) 1999-2003 Tatewake.com **/
/** History: **/
/** 08/17/2003 - (TJG) - Creation **/
/** 09/23/2003 - (TJG) - Bug fix and optimization **/
/** 09/25/2003 - (TJG) - Version for NeHe Basecode users **/
/** **/
/*************************************************************/
/*
MIT License:
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.
*/
#ifndef _ArcBall_h
#define _ArcBall_h
#ifdef _MSC_VER // Visual C++ compiler
# pragma comment( lib, "opengl32.lib" ) // Search For OpenGL32.lib While Linking
# pragma comment( lib, "glu32.lib" ) // Search For GLu32.lib While Linking
#endif
// 8<--Snip here if you have your own math types/funcs-->8
//Only support assertions in debug builds
#ifdef _DEBUG
# include "assert.h"
#else
#ifndef assert
# define assert(x) { }
#endif
#endif
//Math types derived from the KempoApi tMath library
typedef union Tuple2f_t
{
struct
{
GLfloat X, Y;
} s;
GLfloat T[2];
} Tuple2fT; //A generic 2-element tuple that is represented by single-precision floating point x,y coordinates.
typedef union Tuple3f_t
{
struct
{
GLfloat X, Y, Z;
} s;
GLfloat T[3];
} Tuple3fT; //A generic 3-element tuple that is represented by single precision-floating point x,y,z coordinates.
typedef union Tuple4f_t
{
struct
{
GLfloat X, Y, Z, W;
} s;
GLfloat T[4];
} Tuple4fT; //A 4-element tuple represented by single-precision floating point x,y,z,w coordinates.
typedef union Matrix3f_t
{
struct
{
//column major
union { GLfloat M00; GLfloat XX; GLfloat SX; }; //XAxis.X and Scale X
union { GLfloat M10; GLfloat XY; }; //XAxis.Y
union { GLfloat M20; GLfloat XZ; }; //XAxis.Z
union { GLfloat M01; GLfloat YX; }; //YAxis.X
union { GLfloat M11; GLfloat YY; GLfloat SY; }; //YAxis.Y and Scale Y
union { GLfloat M21; GLfloat YZ; }; //YAxis.Z
union { GLfloat M02; GLfloat ZX; }; //ZAxis.X
union { GLfloat M12; GLfloat ZY; }; //ZAxis.Y
union { GLfloat M22; GLfloat ZZ; GLfloat SZ; }; //ZAxis.Z and Scale Z
} s;
GLfloat M[9];
} Matrix3fT; //A single precision floating point 3 by 3 matrix.
typedef union Matrix4f_t
{
struct
{
//column major
union { GLfloat M00; GLfloat XX; GLfloat SX; }; //XAxis.X and Scale X
union { GLfloat M10; GLfloat XY; }; //XAxis.Y
union { GLfloat M20; GLfloat XZ; }; //XAxis.Z
union { GLfloat M30; GLfloat XW; }; //XAxis.W
union { GLfloat M01; GLfloat YX; }; //YAxis.X
union { GLfloat M11; GLfloat YY; GLfloat SY; }; //YAxis.Y and Scale Y
union { GLfloat M21; GLfloat YZ; }; //YAxis.Z
union { GLfloat M31; GLfloat YW; }; //YAxis.W
union { GLfloat M02; GLfloat ZX; }; //ZAxis.X
union { GLfloat M12; GLfloat ZY; }; //ZAxis.Y
union { GLfloat M22; GLfloat ZZ; GLfloat SZ; }; //ZAxis.Z and Scale Z
union { GLfloat M32; GLfloat ZW; }; //ZAxis.W
union { GLfloat M03; GLfloat TX; }; //Trans.X
union { GLfloat M13; GLfloat TY; }; //Trans.Y
union { GLfloat M23; GLfloat TZ; }; //Trans.Z
union { GLfloat M33; GLfloat TW; GLfloat SW; }; //Trans.W and Scale W
} s;
GLfloat M[16];
} Matrix4fT; //A single precision floating point 4 by 4 matrix.
typedef union Matrix4d_t
{
struct
{
//column major
union { GLdouble M00; GLdouble XX; GLdouble SX; }; //XAxis.X and Scale X
union { GLdouble M10; GLdouble XY; }; //XAxis.Y
union { GLdouble M20; GLdouble XZ; }; //XAxis.Z
union { GLdouble M30; GLdouble XW; }; //XAxis.W
union { GLdouble M01; GLdouble YX; }; //YAxis.X
union { GLdouble M11; GLdouble YY; GLdouble SY; }; //YAxis.Y and Scale Y
union { GLdouble M21; GLdouble YZ; }; //YAxis.Z
union { GLdouble M31; GLdouble YW; }; //YAxis.W
union { GLdouble M02; GLdouble ZX; }; //ZAxis.X
union { GLdouble M12; GLdouble ZY; }; //ZAxis.Y
union { GLdouble M22; GLdouble ZZ; GLdouble SZ; }; //ZAxis.Z and Scale Z
union { GLdouble M32; GLdouble ZW; }; //ZAxis.W
union { GLdouble M03; GLdouble TX; }; //Trans.X
union { GLdouble M13; GLdouble TY; }; //Trans.Y
union { GLdouble M23; GLdouble TZ; }; //Trans.Z
union { GLdouble M33; GLdouble TW; GLdouble SW; }; //Trans.W and Scale W
} s;
GLdouble M[16];
} Matrix4dT; //A double precision floating point 4 by 4 matrix.
//"Inherited" types
#define Point2fT Tuple2fT //A 2 element point that is represented by single precision floating point x,y coordinates.
#define Quat4fT Tuple4fT //A 4 element unit quaternion represented by single precision floating point x,y,z,w coordinates.
#define Vector2fT Tuple2fT //A 2-element vector that is represented by single-precision floating point x,y coordinates.
#define Vector3fT Tuple3fT //A 3-element vector that is represented by single-precision floating point x,y,z coordinates.
//Custom math, or speed overrides
#define FuncSqrt sqrtf
//Math functions
/**
* Sets the value of this tuple to the vector sum of itself and tuple t1.
* @param t1 the other tuple
*/
inline
static void Point2fAdd(Point2fT* NewObj, const Tuple2fT* t1)
{
assert(NewObj && t1);
NewObj->s.X += t1->s.X;
NewObj->s.Y += t1->s.Y;
}
/**
* Sets the value of this tuple to the vector difference of itself and tuple t1 (this = this - t1).
* @param t1 the other tuple
*/
inline
static void Point2fSub(Point2fT* NewObj, const Tuple2fT* t1)
{
assert(NewObj && t1);
NewObj->s.X -= t1->s.X;
NewObj->s.Y -= t1->s.Y;
}
/**
* Sets this vector to be the vector cross product of vectors v1 and v2.
* @param v1 the first vector
* @param v2 the second vector
*/
inline
static void Vector3fCross(Vector3fT* NewObj, const Vector3fT* v1, const Vector3fT* v2)
{
Vector3fT Result; //safe not to initialize
assert(NewObj && v1 && v2);
// store on stack once for aliasing-safty
// i.e. safe when a.cross(a, b)
Result.s.X = (v1->s.Y * v2->s.Z) - (v1->s.Z * v2->s.Y);
Result.s.Y = (v1->s.Z * v2->s.X) - (v1->s.X * v2->s.Z);
Result.s.Z = (v1->s.X * v2->s.Y) - (v1->s.Y * v2->s.X);
//copy result back
*NewObj = Result;
}
/**
* Computes the dot product of the this vector and vector v1.
* @param v1 the other vector
*/
inline
static GLfloat Vector3fDot(const Vector3fT* NewObj, const Vector3fT* v1)
{
assert(NewObj && v1);
return (NewObj->s.X * v1->s.X) +
(NewObj->s.Y * v1->s.Y) +
(NewObj->s.Z * v1->s.Z);
}
/**
* Returns the squared length of this vector.
* @return the squared length of this vector
*/
inline
static GLfloat Vector3fLengthSquared(const Vector3fT* NewObj)
{
assert(NewObj);
return (NewObj->s.X * NewObj->s.X) +
(NewObj->s.Y * NewObj->s.Y) +
(NewObj->s.Z * NewObj->s.Z);
}
/**
* Returns the length of this vector.
* @return the length of this vector
*/
inline
static GLfloat Vector3fLength(const Vector3fT* NewObj)
{
assert(NewObj);
return FuncSqrt(Vector3fLengthSquared(NewObj));
}
inline
static void Matrix3fSetZero(Matrix3fT* NewObj)
{
NewObj->s.M00 = NewObj->s.M01 = NewObj->s.M02 =
NewObj->s.M10 = NewObj->s.M11 = NewObj->s.M12 =
NewObj->s.M20 = NewObj->s.M21 = NewObj->s.M22 = 0.0f;
}
/**
* Sets this Matrix3 to identity.
*/
inline
static void Matrix3fSetIdentity(Matrix3fT* NewObj)
{
Matrix3fSetZero(NewObj);
//then set diagonal as 1
NewObj->s.M00 =
NewObj->s.M11 =
NewObj->s.M22 = 1.0f;
}
/**
* Sets the value of this matrix to the matrix conversion of the
* quaternion argument.
* @param q1 the quaternion to be converted
*/
//$hack this can be optimized some(if s == 0)
inline
static void Matrix3fSetRotationFromQuat4f(Matrix3fT* NewObj, const Quat4fT* q1)
{
GLfloat n, s;
GLfloat xs, ys, zs;
GLfloat wx, wy, wz;
GLfloat xx, xy, xz;
GLfloat yy, yz, zz;
assert(NewObj && q1);
n = (q1->s.X * q1->s.X) + (q1->s.Y * q1->s.Y) + (q1->s.Z * q1->s.Z) + (q1->s.W * q1->s.W);
s = (n > 0.0f) ? (2.0f / n) : 0.0f;
xs = q1->s.X * s; ys = q1->s.Y * s; zs = q1->s.Z * s;
wx = q1->s.W * xs; wy = q1->s.W * ys; wz = q1->s.W * zs;
xx = q1->s.X * xs; xy = q1->s.X * ys; xz = q1->s.X * zs;
yy = q1->s.Y * ys; yz = q1->s.Y * zs; zz = q1->s.Z * zs;
NewObj->s.XX = 1.0f - (yy + zz); NewObj->s.YX = xy - wz; NewObj->s.ZX = xz + wy;
NewObj->s.XY = xy + wz; NewObj->s.YY = 1.0f - (xx + zz); NewObj->s.ZY = yz - wx;
NewObj->s.XZ = xz - wy; NewObj->s.YZ = yz + wx; NewObj->s.ZZ = 1.0f - (xx + yy);
}
inline
static void Matrix4fSetRotationScaleFromMatrix4f(Matrix4fT* NewObj, const Matrix4fT* m1)
{
assert(NewObj && m1);
NewObj->s.XX = m1->s.XX; NewObj->s.YX = m1->s.YX; NewObj->s.ZX = m1->s.ZX;
NewObj->s.XY = m1->s.XY; NewObj->s.YY = m1->s.YY; NewObj->s.ZY = m1->s.ZY;
NewObj->s.XZ = m1->s.XZ; NewObj->s.YZ = m1->s.YZ; NewObj->s.ZZ = m1->s.ZZ;
}
/**
* Performs SVD on this matrix and gets scale and rotation.
* Rotation is placed into rot3, and rot4.
* @param rot3 the rotation factor(Matrix3d). if null, ignored
* @param rot4 the rotation factor(Matrix4) only upper 3x3 elements are changed. if null, ignored
* @return scale factor
*/
inline
static GLfloat Matrix4fSVD(const Matrix4fT* NewObj, Matrix3fT* rot3, Matrix4fT* rot4)
{
GLfloat s, n;
assert(NewObj);
// this is a simple svd.
// Not complete but fast and reasonable.
// See comment in Matrix3d.
s = FuncSqrt(
( (NewObj->s.XX * NewObj->s.XX) + (NewObj->s.XY * NewObj->s.XY) + (NewObj->s.XZ * NewObj->s.XZ) +
(NewObj->s.YX * NewObj->s.YX) + (NewObj->s.YY * NewObj->s.YY) + (NewObj->s.YZ * NewObj->s.YZ) +
(NewObj->s.ZX * NewObj->s.ZX) + (NewObj->s.ZY * NewObj->s.ZY) + (NewObj->s.ZZ * NewObj->s.ZZ) ) / 3.0f );
if (rot3) //if pointer not null
{
//this->getRotationScale(rot3);
rot3->s.XX = NewObj->s.XX; rot3->s.XY = NewObj->s.XY; rot3->s.XZ = NewObj->s.XZ;
rot3->s.YX = NewObj->s.YX; rot3->s.YY = NewObj->s.YY; rot3->s.YZ = NewObj->s.YZ;
rot3->s.ZX = NewObj->s.ZX; rot3->s.ZY = NewObj->s.ZY; rot3->s.ZZ = NewObj->s.ZZ;
// zero-div may occur.
n = 1.0f / FuncSqrt( (NewObj->s.XX * NewObj->s.XX) +
(NewObj->s.XY * NewObj->s.XY) +
(NewObj->s.XZ * NewObj->s.XZ) );
rot3->s.XX *= n;
rot3->s.XY *= n;
rot3->s.XZ *= n;
n = 1.0f / FuncSqrt( (NewObj->s.YX * NewObj->s.YX) +
(NewObj->s.YY * NewObj->s.YY) +
(NewObj->s.YZ * NewObj->s.YZ) );
rot3->s.YX *= n;
rot3->s.YY *= n;
rot3->s.YZ *= n;
n = 1.0f / FuncSqrt( (NewObj->s.ZX * NewObj->s.ZX) +
(NewObj->s.ZY * NewObj->s.ZY) +
(NewObj->s.ZZ * NewObj->s.ZZ) );
rot3->s.ZX *= n;
rot3->s.ZY *= n;
rot3->s.ZZ *= n;
}
if (rot4) //if pointer not null
{
if (rot4 != NewObj)
{
Matrix4fSetRotationScaleFromMatrix4f(rot4, NewObj); // private method
}
// zero-div may occur.
n = 1.0f / FuncSqrt( (NewObj->s.XX * NewObj->s.XX) +
(NewObj->s.XY * NewObj->s.XY) +
(NewObj->s.XZ * NewObj->s.XZ) );
rot4->s.XX *= n;
rot4->s.XY *= n;
rot4->s.XZ *= n;
n = 1.0f / FuncSqrt( (NewObj->s.YX * NewObj->s.YX) +
(NewObj->s.YY * NewObj->s.YY) +
(NewObj->s.YZ * NewObj->s.YZ) );
rot4->s.YX *= n;
rot4->s.YY *= n;
rot4->s.YZ *= n;
n = 1.0f / FuncSqrt( (NewObj->s.ZX * NewObj->s.ZX) +
(NewObj->s.ZY * NewObj->s.ZY) +
(NewObj->s.ZZ * NewObj->s.ZZ) );
rot4->s.ZX *= n;
rot4->s.ZY *= n;
rot4->s.ZZ *= n;
}
return s;
}
inline
static void Matrix4fSetRotationScaleFromMatrix3f(Matrix4fT* NewObj, const Matrix3fT* m1)
{
assert(NewObj && m1);
NewObj->s.XX = m1->s.XX; NewObj->s.YX = m1->s.YX; NewObj->s.ZX = m1->s.ZX;
NewObj->s.XY = m1->s.XY; NewObj->s.YY = m1->s.YY; NewObj->s.ZY = m1->s.ZY;
NewObj->s.XZ = m1->s.XZ; NewObj->s.YZ = m1->s.YZ; NewObj->s.ZZ = m1->s.ZZ;
}
inline
static void Matrix4fMulRotationScale(Matrix4fT* NewObj, GLfloat scale)
{
assert(NewObj);
NewObj->s.XX *= scale; NewObj->s.YX *= scale; NewObj->s.ZX *= scale;
NewObj->s.XY *= scale; NewObj->s.YY *= scale; NewObj->s.ZY *= scale;
NewObj->s.XZ *= scale; NewObj->s.YZ *= scale; NewObj->s.ZZ *= scale;
}
/**
* Sets the rotational component (upper 3x3) of this matrix to the matrix
* values in the T precision Matrix3d argument; the other elements of
* this matrix are unchanged; a singular value decomposition is performed
* on this object's upper 3x3 matrix to factor out the scale, then this
* object's upper 3x3 matrix components are replaced by the passed rotation
* components, and then the scale is reapplied to the rotational
* components.
* @param m1 T precision 3x3 matrix
*/
inline
static void Matrix4fSetRotationFromMatrix3f(Matrix4fT* NewObj, const Matrix3fT* m1)
{
GLfloat scale;
assert(NewObj && m1);
scale = Matrix4fSVD(NewObj, NULL, NULL);
Matrix4fSetRotationScaleFromMatrix3f(NewObj, m1);
Matrix4fMulRotationScale(NewObj, scale);
}
inline
static void Matrix3fMulMatrix3f(Matrix3fT* NewObj, const Matrix3fT* m1)
{
Matrix3fT Result; //safe not to initialize
assert(NewObj && m1);
// alias-safe way.
Result.s.M00 = (NewObj->s.M00 * m1->s.M00) + (NewObj->s.M01 * m1->s.M10) + (NewObj->s.M02 * m1->s.M20);
Result.s.M01 = (NewObj->s.M00 * m1->s.M01) + (NewObj->s.M01 * m1->s.M11) + (NewObj->s.M02 * m1->s.M21);
Result.s.M02 = (NewObj->s.M00 * m1->s.M02) + (NewObj->s.M01 * m1->s.M12) + (NewObj->s.M02 * m1->s.M22);
Result.s.M10 = (NewObj->s.M10 * m1->s.M00) + (NewObj->s.M11 * m1->s.M10) + (NewObj->s.M12 * m1->s.M20);
Result.s.M11 = (NewObj->s.M10 * m1->s.M01) + (NewObj->s.M11 * m1->s.M11) + (NewObj->s.M12 * m1->s.M21);
Result.s.M12 = (NewObj->s.M10 * m1->s.M02) + (NewObj->s.M11 * m1->s.M12) + (NewObj->s.M12 * m1->s.M22);
Result.s.M20 = (NewObj->s.M20 * m1->s.M00) + (NewObj->s.M21 * m1->s.M10) + (NewObj->s.M22 * m1->s.M20);
Result.s.M21 = (NewObj->s.M20 * m1->s.M01) + (NewObj->s.M21 * m1->s.M11) + (NewObj->s.M22 * m1->s.M21);
Result.s.M22 = (NewObj->s.M20 * m1->s.M02) + (NewObj->s.M21 * m1->s.M12) + (NewObj->s.M22 * m1->s.M22);
//copy result back to this
*NewObj = Result;
}
/* Apply the Matrix3f rotation to the existing values in NewObj */
inline
static void Matrix4fMulRotationFromMatrix3f(Matrix4fT* NewObj, const Matrix3fT* m1)
{
Matrix3fT tmp, tmp2;
GLfloat scale;
assert(NewObj && m1);
scale = Matrix4fSVD(NewObj, &tmp, NULL);
tmp2 = *m1;
Matrix3fMulMatrix3f(&tmp2, &tmp);
Matrix4fSetRotationScaleFromMatrix3f(NewObj, &tmp2);
Matrix4fMulRotationScale(NewObj, scale);
}
// 8<--Snip here if you have your own math types/funcs-->8
class ArcBall
{
protected:
inline
void _mapToSphere(const Point2fT* NewPt, Vector3fT* NewVec) const;
public:
//Create/Destroy
ArcBall(GLfloat NewWidth = 2.0, GLfloat NewHeight = 2.0);
~ArcBall() { /* nothing to do */ };
//Set new bounds
inline
void setBounds(GLfloat NewWidth, GLfloat NewHeight)
{
assert((NewWidth > 1.0f) && (NewHeight > 1.0f));
//Set adjustment factor for width/height
this->AdjustWidth = 1.0f / ((NewWidth - 1.0f) * 0.5f);
this->AdjustHeight = 1.0f / ((NewHeight - 1.0f) * 0.5f);
}
//Mouse down
void click(GLfloat x, GLfloat y, Matrix4fT *startTransform);
//Mouse drag, calculate rotation
void drag(GLfloat x, GLfloat y, Quat4fT* NewRot);
void dragAccumulate(GLfloat x, GLfloat y, Matrix4fT *transform);
protected:
Vector3fT StVec; //Saved click vector
Matrix4fT StTransform; //Reference start transform
Vector3fT EnVec; //Saved drag vector
GLfloat AdjustWidth; //Mouse bounds width
GLfloat AdjustHeight; //Mouse bounds height
};
#endif
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