m4math.h
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- /**
- * @file m4math.h
- * @brief LLMatrix4 class header file.
- *
- * $LicenseInfo:firstyear=2000&license=viewergpl$
- *
- * Copyright (c) 2000-2010, 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://secondlifegrid.net/programs/open_source/licensing/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://secondlifegrid.net/programs/open_source/licensing/flossexception
- *
- * By copying, modifying or distributing this software, you acknowledge
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- * 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];
- // Initializes Matrix to identity matrix
- LLMatrix4()
- {
- setIdentity();
- }
- explicit LLMatrix4(const F32 *mat); // Initializes Matrix to values in mat
- explicit LLMatrix4(const LLMatrix3 &mat); // Initializes Matrix to values 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& setIdentity(); // Load identity matrix
- const LLMatrix4& setZero(); // 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 const 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 const LLMatrix4& LLMatrix4::setIdentity()
- {
- 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;
- }
- // Operates "to the left" on row-vector a
- //
- // When avatar vertex programs are off, this function is a hot spot in profiles
- // due to software skinning in LLViewerJointMesh::updateGeometry(). JC
- inline const LLVector3 operator*(const LLVector3 &a, const LLMatrix4 &b)
- {
- // This is better than making a temporary LLVector3. This eliminates an
- // unnecessary LLVector3() constructor and also helps the compiler to
- // realize that the output floats do not alias the input floats, hence
- // eliminating redundant loads of a.mV[0], etc. JC
- return LLVector3(a.mV[VX] * b.mMatrix[VX][VX] +
- a.mV[VY] * b.mMatrix[VY][VX] +
- a.mV[VZ] * b.mMatrix[VZ][VX] +
- b.mMatrix[VW][VX],
-
- a.mV[VX] * b.mMatrix[VX][VY] +
- a.mV[VY] * b.mMatrix[VY][VY] +
- a.mV[VZ] * b.mMatrix[VZ][VY] +
- b.mMatrix[VW][VY],
-
- a.mV[VX] * b.mMatrix[VX][VZ] +
- a.mV[VY] * b.mMatrix[VY][VZ] +
- a.mV[VZ] * b.mMatrix[VZ][VZ] +
- b.mMatrix[VW][VZ]);
- }
- #endif