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/**
* @file m3math.h
* @brief LLMatrix3 class header file.
*
* Copyright (c) 2000-$CurrentYear$, Linden Research, Inc.
* $License$
*/
#ifndef LL_M3MATH_H
#define LL_M3MATH_H
#include "llerror.h"
class LLVector4;
class LLVector3;
class LLVector3d;
class LLQuaternion;
// NOTA BENE: Currently assuming a right-handed, z-up universe
// ji
// LLMatrix3 = | 00 01 02 |
// | 10 11 12 |
// | 20 21 22 |
// LLMatrix3 = | fx fy fz | forward-axis
// | lx ly lz | left-axis
// | ux uy uz | up-axis
// NOTE: The world of computer graphics uses column-vectors and matricies that
// "operate to the left".
static const U32 NUM_VALUES_IN_MAT3 = 3;
class LLMatrix3
{
public:
F32 mMatrix[NUM_VALUES_IN_MAT3][NUM_VALUES_IN_MAT3];
LLMatrix3(void); // Initializes Matrix to identity matrix
explicit LLMatrix3(const F32 *mat); // Initializes Matrix to values in mat
explicit LLMatrix3(const LLQuaternion &q); // Initializes Matrix with rotation q
LLMatrix3(const F32 angle, const F32 x, const F32 y, const F32 z); // Initializes Matrix with axis angle
LLMatrix3(const F32 angle, const LLVector3 &vec); // Initializes Matrix with axis angle
LLMatrix3(const F32 angle, const LLVector3d &vec); // Initializes Matrix with axis angle
LLMatrix3(const F32 angle, const LLVector4 &vec); // Initializes Matrix with axis angle
LLMatrix3(const F32 roll, const F32 pitch, const F32 yaw); // Initializes Matrix with Euler angles
//////////////////////////////
//
// Matrix initializers - these replace any existing values in the matrix
//
// various useful matrix functions
const LLMatrix3& identity(); // Load identity matrix
const LLMatrix3& zero(); // Clears Matrix to zero
///////////////////////////
//
// Matrix setters - set some properties without modifying others
//
// These functions take Rotation arguments
const LLMatrix3& setRot(const F32 angle, const F32 x, const F32 y, const F32 z); // Calculate rotation matrix for rotating angle radians about (x, y, z)
const LLMatrix3& setRot(const F32 angle, const LLVector3 &vec); // Calculate rotation matrix for rotating angle radians about vec
const LLMatrix3& setRot(const F32 roll, const F32 pitch, const F32 yaw); // Calculate rotation matrix from Euler angles
const LLMatrix3& setRot(const LLQuaternion &q); // Transform matrix by Euler angles and translating by pos
const LLMatrix3& setRows(const LLVector3 &x_axis, const LLVector3 &y_axis, const LLVector3 &z_axis);
///////////////////////////
//
// Get properties of a matrix
//
LLQuaternion quaternion() const; // Returns quaternion from mat
void getEulerAngles(F32 *roll, F32 *pitch, F32 *yaw) const; // Returns Euler angles, in radians
// Axis extraction routines
LLVector3 getFwdRow() const;
LLVector3 getLeftRow() const;
LLVector3 getUpRow() const;
F32 determinant() const; // Return determinant
///////////////////////////
//
// Operations on an existing matrix
//
const LLMatrix3& transpose(); // Transpose MAT4
const LLMatrix3& invert(); // Invert MAT4
const LLMatrix3& orthogonalize(); // Orthogonalizes X, then Y, then Z
const LLMatrix3& adjointTranspose(); // returns transpose of matrix adjoint, for multiplying normals
// Rotate existing matrix
// Note: the two lines below are equivalent:
// foo.rotate(bar)
// foo = foo * bar
// That is, foo.rotMat3(bar) multiplies foo by bar FROM THE RIGHT
const LLMatrix3& rotate(const F32 angle, const F32 x, const F32 y, const F32 z); // Rotate matrix by rotating angle radians about (x, y, z)
const LLMatrix3& rotate(const F32 angle, const LLVector3 &vec); // Rotate matrix by rotating angle radians about vec
const LLMatrix3& rotate(const F32 roll, const F32 pitch, const F32 yaw); // Rotate matrix by roll (about x), pitch (about y), and yaw (about z)
const LLMatrix3& rotate(const LLQuaternion &q); // Transform matrix by Euler angles and translating by pos
// This operator is misleading as to operation direction
// friend LLVector3 operator*(const LLMatrix3 &a, const LLVector3 &b); // Apply rotation a to vector b
friend LLVector3 operator*(const LLVector3 &a, const LLMatrix3 &b); // Apply rotation b to vector a
friend LLVector3d operator*(const LLVector3d &a, const LLMatrix3 &b); // Apply rotation b to vector a
friend LLMatrix3 operator*(const LLMatrix3 &a, const LLMatrix3 &b); // Return a * b
friend bool operator==(const LLMatrix3 &a, const LLMatrix3 &b); // Return a == b
friend bool operator!=(const LLMatrix3 &a, const LLMatrix3 &b); // Return a != b
friend const LLMatrix3& operator*=(LLMatrix3 &a, const LLMatrix3 &b); // Return a * b
friend std::ostream& operator<<(std::ostream& s, const LLMatrix3 &a); // Stream a
};
inline LLMatrix3::LLMatrix3(void)
{
mMatrix[0][0] = 1.f;
mMatrix[0][1] = 0.f;
mMatrix[0][2] = 0.f;
mMatrix[1][0] = 0.f;
mMatrix[1][1] = 1.f;
mMatrix[1][2] = 0.f;
mMatrix[2][0] = 0.f;
mMatrix[2][1] = 0.f;
mMatrix[2][2] = 1.f;
}
inline LLMatrix3::LLMatrix3(const F32 *mat)
{
mMatrix[0][0] = mat[0];
mMatrix[0][1] = mat[1];
mMatrix[0][2] = mat[2];
mMatrix[1][0] = mat[3];
mMatrix[1][1] = mat[4];
mMatrix[1][2] = mat[5];
mMatrix[2][0] = mat[6];
mMatrix[2][1] = mat[7];
mMatrix[2][2] = mat[8];
}
#endif
// Rotation matrix hints...
// Inverse of Rotation Matrices
// ----------------------------
// If R is a rotation matrix that rotate vectors from Frame-A to Frame-B,
// then the transpose of R will rotate vectors from Frame-B to Frame-A.
// Creating Rotation Matricies From Object Axes
// --------------------------------------------
// Suppose you know the three axes of some object in some "absolute-frame".
// If you take those three vectors and throw them into the rows of
// a rotation matrix what do you get?
//
// R = | X0 X1 X2 |
// | Y0 Y1 Y2 |
// | Z0 Z1 Z2 |
//
// Yeah, but what does it mean?
//
// Transpose the matrix and have it operate on a vector...
//
// V * R_transpose = [ V0 V1 V2 ] * | X0 Y0 Z0 |
// | X1 Y1 Z1 |
// | X2 Y2 Z2 |
//
// = [ V*X V*Y V*Z ]
//
// = components of V that are parallel to the three object axes
//
// = transformation of V into object frame
//
// Since the transformation of a rotation matrix is its inverse, then
// R must rotate vectors from the object-frame into the absolute-frame.
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