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/**
* @file m4math.h
* @brief LLMatrix3 class header file.
*
* $LicenseInfo:firstyear=2000&license=viewergpl$
*
* Copyright (c) 2000-2007, Linden Research, Inc.
*
* Second Life Viewer Source Code
* The source code in this file ("Source Code") is provided by Linden Lab
* to you under the terms of the GNU General Public License, version 2.0
* ("GPL"), unless you have obtained a separate licensing agreement
* ("Other License"), formally executed by you and Linden Lab. Terms of
* the GPL can be found in doc/GPL-license.txt in this distribution, or
* online at http://secondlife.com/developers/opensource/gplv2
*
* There are special exceptions to the terms and conditions of the GPL as
* it is applied to this Source Code. View the full text of the exception
* in the file doc/FLOSS-exception.txt in this software distribution, or
* online at http://secondlife.com/developers/opensource/flossexception
*
* By copying, modifying or distributing this software, you acknowledge
* that you have read and understood your obligations described above,
* and agree to abide by those obligations.
*
* ALL LINDEN LAB SOURCE CODE IS PROVIDED "AS IS." LINDEN LAB MAKES NO
* WARRANTIES, EXPRESS, IMPLIED OR OTHERWISE, REGARDING ITS ACCURACY,
* COMPLETENESS OR PERFORMANCE.
* $/LicenseInfo$
*/
#ifndef LL_M4MATH_H
#define LL_M4MATH_H
#include "v3math.h"
class LLVector4;
class LLMatrix3;
class LLQuaternion;
// NOTA BENE: Currently assuming a right-handed, x-forward, y-left, z-up universe
// Us versus OpenGL:
// Even though OpenGL uses column vectors and we use row vectors, we can plug our matrices
// directly into OpenGL. This is because OpenGL numbers its matrices going columnwise:
//
// OpenGL indexing: Our indexing:
// 0 4 8 12 [0][0] [0][1] [0][2] [0][3]
// 1 5 9 13 [1][0] [1][1] [1][2] [1][3]
// 2 6 10 14 [2][0] [2][1] [2][2] [2][3]
// 3 7 11 15 [3][0] [3][1] [3][2] [3][3]
//
// So when you're looking at OpenGL related matrices online, our matrices will be
// "transposed". But our matrices can be plugged directly into OpenGL and work fine!
//
// We're using row vectors - [vx, vy, vz, vw]
//
// There are several different ways of thinking of matrices, if you mix them up, you'll get very confused.
//
// One way to think about it is a matrix that takes the origin frame A
// and rotates it into B': i.e. A*M = B
//
// Vectors:
// f - forward axis of B expressed in A
// l - left axis of B expressed in A
// u - up axis of B expressed in A
//
// | 0: fx 1: fy 2: fz 3:0 |
// M = | 4: lx 5: ly 6: lz 7:0 |
// | 8: ux 9: uy 10: uz 11:0 |
// | 12: 0 13: 0 14: 0 15:1 |
//
//
//
//
// Another way to think of matrices is matrix that takes a point p in frame A, and puts it into frame B:
// This is used most commonly for the modelview matrix.
//
// so p*M = p'
//
// Vectors:
// f - forward of frame B in frame A
// l - left of frame B in frame A
// u - up of frame B in frame A
// o - origin of frame frame B in frame A
//
// | 0: fx 1: lx 2: ux 3:0 |
// M = | 4: fy 5: ly 6: uy 7:0 |
// | 8: fz 9: lz 10: uz 11:0 |
// | 12:-of 13:-ol 14:-ou 15:1 |
//
// of, ol, and ou mean the component of the "global" origin o in the f axis, l axis, and u axis.
//
static const U32 NUM_VALUES_IN_MAT4 = 4;
class LLMatrix4
{
public:
F32 mMatrix[NUM_VALUES_IN_MAT4][NUM_VALUES_IN_MAT4];
LLMatrix4(); // Initializes Matrix to identity matrix
explicit LLMatrix4(const F32 *mat); // Initializes Matrix to values in mat
explicit LLMatrix4(const LLMatrix3 &mat); // Initializes Matrix to valuee in mat and sets position to (0,0,0)
explicit LLMatrix4(const LLQuaternion &q); // Initializes Matrix with rotation q and sets position to (0,0,0)
LLMatrix4(const LLMatrix3 &mat, const LLVector4 &pos); // Initializes Matrix to values in mat and pos
// These are really, really, inefficient as implemented! - djs
LLMatrix4(const LLQuaternion &q, const LLVector4 &pos); // Initializes Matrix with rotation q and position pos
LLMatrix4(F32 angle,
const LLVector4 &vec,
const LLVector4 &pos); // Initializes Matrix with axis-angle and position
LLMatrix4(F32 angle, const LLVector4 &vec); // Initializes Matrix with axis-angle and sets position to (0,0,0)
LLMatrix4(const F32 roll, const F32 pitch, const F32 yaw,
const LLVector4 &pos); // Initializes Matrix with Euler angles
LLMatrix4(const F32 roll, const F32 pitch, const F32 yaw); // Initializes Matrix with Euler angles
~LLMatrix4(void); // Destructor
//////////////////////////////
//
// Matrix initializers - these replace any existing values in the matrix
//
void initRows(const LLVector4 &row0,
const LLVector4 &row1,
const LLVector4 &row2,
const LLVector4 &row3);
// various useful matrix functions
const LLMatrix4& identity(); // Load identity matrix
const LLMatrix4& zero(); // Clears matrix to all zeros.
const LLMatrix4& initRotation(const F32 angle, const F32 x, const F32 y, const F32 z); // Calculate rotation matrix by rotating angle radians about (x, y, z)
const LLMatrix4& initRotation(const F32 angle, const LLVector4 &axis); // Calculate rotation matrix for rotating angle radians about vec
const LLMatrix4& initRotation(const F32 roll, const F32 pitch, const F32 yaw); // Calculate rotation matrix from Euler angles
const LLMatrix4& initRotation(const LLQuaternion &q); // Set with Quaternion and position
// Position Only
const LLMatrix4& initMatrix(const LLMatrix3 &mat); //
const LLMatrix4& initMatrix(const LLMatrix3 &mat, const LLVector4 &translation);
// These operation create a matrix that will rotate and translate by the
// specified amounts.
const LLMatrix4& initRotTrans(const F32 angle,
const F32 rx, const F32 ry, const F32 rz,
const F32 px, const F32 py, const F32 pz);
const LLMatrix4& initRotTrans(const F32 angle, const LLVector3 &axis, const LLVector3 &translation); // Rotation from axis angle + translation
const LLMatrix4& initRotTrans(const F32 roll, const F32 pitch, const F32 yaw, const LLVector4 &pos); // Rotation from Euler + translation
const LLMatrix4& initRotTrans(const LLQuaternion &q, const LLVector4 &pos); // Set with Quaternion and position
// Set all
const LLMatrix4& initAll(const LLVector3 &scale, const LLQuaternion &q, const LLVector3 &pos);
///////////////////////////
//
// Matrix setters - set some properties without modifying others
//
const LLMatrix4& setTranslation(const F32 x, const F32 y, const F32 z); // Sets matrix to translate by (x,y,z)
void setFwdRow(const LLVector3 &row);
void setLeftRow(const LLVector3 &row);
void setUpRow(const LLVector3 &row);
void setFwdCol(const LLVector3 &col);
void setLeftCol(const LLVector3 &col);
void setUpCol(const LLVector3 &col);
const LLMatrix4& setTranslation(const LLVector4 &translation);
const LLMatrix4& setTranslation(const LLVector3 &translation);
///////////////////////////
//
// Get properties of a matrix
//
F32 determinant(void) const; // Return determinant
LLQuaternion quaternion(void) const; // Returns quaternion
LLVector4 getFwdRow4() const;
LLVector4 getLeftRow4() const;
LLVector4 getUpRow4() const;
LLMatrix3 getMat3() const;
const LLVector3& getTranslation() const { return *(LLVector3*)&mMatrix[3][0]; }
///////////////////////////
//
// Operations on an existing matrix
//
const LLMatrix4& transpose(); // Transpose LLMatrix4
const LLMatrix4& invert(); // Invert LLMatrix4
// Rotate existing matrix
// These are really, really, inefficient as implemented! - djs
const LLMatrix4& rotate(const F32 angle, const F32 x, const F32 y, const F32 z); // Rotate matrix by rotating angle radians about (x, y, z)
const LLMatrix4& rotate(const F32 angle, const LLVector4 &vec); // Rotate matrix by rotating angle radians about vec
const LLMatrix4& rotate(const F32 roll, const F32 pitch, const F32 yaw); // Rotate matrix by Euler angles
const LLMatrix4& rotate(const LLQuaternion &q); // Rotate matrix by Quaternion
// Translate existing matrix
const LLMatrix4& translate(const LLVector3 &vec); // Translate matrix by (vec[VX], vec[VY], vec[VZ])
///////////////////////
//
// Operators
//
// Not implemented to enforce code that agrees with symbolic syntax
// friend LLVector4 operator*(const LLMatrix4 &a, const LLVector4 &b); // Apply rotation a to vector b
// friend inline LLMatrix4 operator*(const LLMatrix4 &a, const LLMatrix4 &b); // Return a * b
friend LLVector4 operator*(const LLVector4 &a, const LLMatrix4 &b); // Return transform of vector a by matrix b
friend LLVector3 operator*(const LLVector3 &a, const LLMatrix4 &b); // Return full transform of a by matrix b
friend LLVector4 rotate_vector(const LLVector4 &a, const LLMatrix4 &b); // Rotates a but does not translate
friend LLVector3 rotate_vector(const LLVector3 &a, const LLMatrix4 &b); // Rotates a but does not translate
friend bool operator==(const LLMatrix4 &a, const LLMatrix4 &b); // Return a == b
friend bool operator!=(const LLMatrix4 &a, const LLMatrix4 &b); // Return a != b
friend const LLMatrix4& operator+=(LLMatrix4 &a, const LLMatrix4 &b); // Return a + b
friend const LLMatrix4& operator-=(LLMatrix4 &a, const LLMatrix4 &b); // Return a - b
friend const LLMatrix4& operator*=(LLMatrix4 &a, const LLMatrix4 &b); // Return a * b
friend const LLMatrix4& operator*=(LLMatrix4 &a, const F32 &b); // Return a * b
friend std::ostream& operator<<(std::ostream& s, const LLMatrix4 &a); // Stream a
};
inline LLMatrix4::LLMatrix4()
{
identity();
}
inline const LLMatrix4& LLMatrix4::identity()
{
mMatrix[0][0] = 1.f;
mMatrix[0][1] = 0.f;
mMatrix[0][2] = 0.f;
mMatrix[0][3] = 0.f;
mMatrix[1][0] = 0.f;
mMatrix[1][1] = 1.f;
mMatrix[1][2] = 0.f;
mMatrix[1][3] = 0.f;
mMatrix[2][0] = 0.f;
mMatrix[2][1] = 0.f;
mMatrix[2][2] = 1.f;
mMatrix[2][3] = 0.f;
mMatrix[3][0] = 0.f;
mMatrix[3][1] = 0.f;
mMatrix[3][2] = 0.f;
mMatrix[3][3] = 1.f;
return (*this);
}
/*
inline LLMatrix4 operator*(const LLMatrix4 &a, const LLMatrix4 &b)
{
U32 i, j;
LLMatrix4 mat;
for (i = 0; i < NUM_VALUES_IN_MAT4; i++)
{
for (j = 0; j < NUM_VALUES_IN_MAT4; j++)
{
mat.mMatrix[j][i] = a.mMatrix[j][0] * b.mMatrix[0][i] +
a.mMatrix[j][1] * b.mMatrix[1][i] +
a.mMatrix[j][2] * b.mMatrix[2][i] +
a.mMatrix[j][3] * b.mMatrix[3][i];
}
}
return mat;
}
*/
inline const LLMatrix4& operator*=(LLMatrix4 &a, const LLMatrix4 &b)
{
U32 i, j;
LLMatrix4 mat;
for (i = 0; i < NUM_VALUES_IN_MAT4; i++)
{
for (j = 0; j < NUM_VALUES_IN_MAT4; j++)
{
mat.mMatrix[j][i] = a.mMatrix[j][0] * b.mMatrix[0][i] +
a.mMatrix[j][1] * b.mMatrix[1][i] +
a.mMatrix[j][2] * b.mMatrix[2][i] +
a.mMatrix[j][3] * b.mMatrix[3][i];
}
}
a = mat;
return a;
}
inline const LLMatrix4& operator*=(LLMatrix4 &a, const F32 &b)
{
U32 i, j;
LLMatrix4 mat;
for (i = 0; i < NUM_VALUES_IN_MAT4; i++)
{
for (j = 0; j < NUM_VALUES_IN_MAT4; j++)
{
mat.mMatrix[j][i] = a.mMatrix[j][i] * b;
}
}
a = mat;
return a;
}
inline const LLMatrix4& operator+=(LLMatrix4 &a, const LLMatrix4 &b)
{
LLMatrix4 mat;
U32 i, j;
for (i = 0; i < NUM_VALUES_IN_MAT4; i++)
{
for (j = 0; j < NUM_VALUES_IN_MAT4; j++)
{
mat.mMatrix[j][i] = a.mMatrix[j][i] + b.mMatrix[j][i];
}
}
a = mat;
return a;
}
inline const LLMatrix4& operator-=(LLMatrix4 &a, const LLMatrix4 &b)
{
LLMatrix4 mat;
U32 i, j;
for (i = 0; i < NUM_VALUES_IN_MAT4; i++)
{
for (j = 0; j < NUM_VALUES_IN_MAT4; j++)
{
mat.mMatrix[j][i] = a.mMatrix[j][i] - b.mMatrix[j][i];
}
}
a = mat;
return a;
}
#endif
|