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+/**
+ * @file m3math.cpp
+ * @brief LLMatrix3 class implementation.
+ *
+ * Copyright (c) 2000-$CurrentYear$, Linden Research, Inc.
+ * $License$
+ */
+
+#include "linden_common.h"
+
+//#include "vmath.h"
+#include "v3math.h"
+#include "v3dmath.h"
+#include "v4math.h"
+#include "m4math.h"
+#include "m3math.h"
+#include "llquaternion.h"
+
+// LLMatrix3
+
+// 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
+
+
+// Constructors
+
+
+LLMatrix3::LLMatrix3(const LLQuaternion &q)
+{
+ *this = q.getMatrix3();
+}
+
+
+LLMatrix3::LLMatrix3(const F32 angle, const LLVector3 &vec)
+{
+ LLQuaternion quat(angle, vec);
+ *this = setRot(quat);
+}
+
+LLMatrix3::LLMatrix3(const F32 angle, const LLVector3d &vec)
+{
+ LLVector3 vec_f;
+ vec_f.setVec(vec);
+ LLQuaternion quat(angle, vec_f);
+ *this = setRot(quat);
+}
+
+LLMatrix3::LLMatrix3(const F32 angle, const LLVector4 &vec)
+{
+ LLQuaternion quat(angle, vec);
+ *this = setRot(quat);
+}
+
+LLMatrix3::LLMatrix3(const F32 angle, const F32 x, const F32 y, const F32 z)
+{
+ LLVector3 vec(x, y, z);
+ LLQuaternion quat(angle, vec);
+ *this = setRot(quat);
+}
+
+LLMatrix3::LLMatrix3(const F32 roll, const F32 pitch, const F32 yaw)
+{
+ // Rotates RH about x-axis by 'roll' then
+ // rotates RH about the old y-axis by 'pitch' then
+ // rotates RH about the original z-axis by 'yaw'.
+ // .
+ // /|\ yaw axis
+ // | __.
+ // ._ ___| /| pitch axis
+ // _||\ \\ |-. /
+ // \|| \_______\_|__\_/_______
+ // | _ _ o o o_o_o_o o /_\_ ________\ roll axis
+ // // /_______/ /__________> /
+ // /_,-' // /
+ // /__,-'
+
+ F32 cx, sx, cy, sy, cz, sz;
+ F32 cxsy, sxsy;
+
+ cx = (F32)cos(roll); //A
+ sx = (F32)sin(roll); //B
+ cy = (F32)cos(pitch); //C
+ sy = (F32)sin(pitch); //D
+ cz = (F32)cos(yaw); //E
+ sz = (F32)sin(yaw); //F
+
+ cxsy = cx * sy; //AD
+ sxsy = sx * sy; //BD
+
+ mMatrix[0][0] = cy * cz;
+ mMatrix[1][0] = -cy * sz;
+ mMatrix[2][0] = sy;
+ mMatrix[0][1] = sxsy * cz + cx * sz;
+ mMatrix[1][1] = -sxsy * sz + cx * cz;
+ mMatrix[2][1] = -sx * cy;
+ mMatrix[0][2] = -cxsy * cz + sx * sz;
+ mMatrix[1][2] = cxsy * sz + sx * cz;
+ mMatrix[2][2] = cx * cy;
+}
+
+// From Matrix and Quaternion FAQ
+void LLMatrix3::getEulerAngles(F32 *roll, F32 *pitch, F32 *yaw) const
+{
+ F64 angle_x, angle_y, angle_z;
+ F64 cx, cy, cz; // cosine of angle_x, angle_y, angle_z
+ F64 sx, sz; // sine of angle_x, angle_y, angle_z
+
+ angle_y = asin(llclamp(mMatrix[2][0], -1.f, 1.f));
+ cy = cos(angle_y);
+
+ if (fabs(cy) > 0.005) // non-zero
+ {
+ // no gimbal lock
+ cx = mMatrix[2][2] / cy;
+ sx = - mMatrix[2][1] / cy;
+
+ angle_x = (F32) atan2(sx, cx);
+
+ cz = mMatrix[0][0] / cy;
+ sz = - mMatrix[1][0] / cy;
+
+ angle_z = (F32) atan2(sz, cz);
+ }
+ else
+ {
+ // yup, gimbal lock
+ angle_x = 0;
+
+ // some tricky math thereby avoided, see article
+
+ cz = mMatrix[1][1];
+ sz = mMatrix[0][1];
+
+ angle_z = atan2(sz, cz);
+ }
+
+ *roll = (F32)angle_x;
+ *pitch = (F32)angle_y;
+ *yaw = (F32)angle_z;
+}
+
+
+// Clear and Assignment Functions
+
+const LLMatrix3& LLMatrix3::identity()
+{
+ 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;
+ return (*this);
+}
+
+const LLMatrix3& LLMatrix3::zero()
+{
+ mMatrix[0][0] = 0.f;
+ mMatrix[0][1] = 0.f;
+ mMatrix[0][2] = 0.f;
+
+ mMatrix[1][0] = 0.f;
+ mMatrix[1][1] = 0.f;
+ mMatrix[1][2] = 0.f;
+
+ mMatrix[2][0] = 0.f;
+ mMatrix[2][1] = 0.f;
+ mMatrix[2][2] = 0.f;
+ return (*this);
+}
+
+// various useful mMatrix functions
+
+const LLMatrix3& LLMatrix3::transpose()
+{
+ // transpose the matrix
+ F32 temp;
+ temp = mMatrix[VX][VY]; mMatrix[VX][VY] = mMatrix[VY][VX]; mMatrix[VY][VX] = temp;
+ temp = mMatrix[VX][VZ]; mMatrix[VX][VZ] = mMatrix[VZ][VX]; mMatrix[VZ][VX] = temp;
+ temp = mMatrix[VY][VZ]; mMatrix[VY][VZ] = mMatrix[VZ][VY]; mMatrix[VZ][VY] = temp;
+ return *this;
+}
+
+
+F32 LLMatrix3::determinant() const
+{
+ // Is this a useful method when we assume the matrices are valid rotation
+ // matrices throughout this implementation?
+ return mMatrix[0][0] * (mMatrix[1][1] * mMatrix[2][2] - mMatrix[1][2] * mMatrix[2][1]) +
+ mMatrix[0][1] * (mMatrix[1][2] * mMatrix[2][0] - mMatrix[1][0] * mMatrix[2][2]) +
+ mMatrix[0][2] * (mMatrix[1][0] * mMatrix[2][1] - mMatrix[1][1] * mMatrix[2][0]);
+}
+
+// This is identical to the transMat3() method because we assume a rotation matrix
+const LLMatrix3& LLMatrix3::invert()
+{
+ // transpose the matrix
+ F32 temp;
+ temp = mMatrix[VX][VY]; mMatrix[VX][VY] = mMatrix[VY][VX]; mMatrix[VY][VX] = temp;
+ temp = mMatrix[VX][VZ]; mMatrix[VX][VZ] = mMatrix[VZ][VX]; mMatrix[VZ][VX] = temp;
+ temp = mMatrix[VY][VZ]; mMatrix[VY][VZ] = mMatrix[VZ][VY]; mMatrix[VZ][VY] = temp;
+ return *this;
+}
+
+// does not assume a rotation matrix, and does not divide by determinant, assuming results will be renormalized
+const LLMatrix3& LLMatrix3::adjointTranspose()
+{
+ LLMatrix3 adjoint_transpose;
+ adjoint_transpose.mMatrix[VX][VX] = mMatrix[VY][VY] * mMatrix[VZ][VZ] - mMatrix[VY][VZ] * mMatrix[VZ][VY] ;
+ adjoint_transpose.mMatrix[VY][VX] = mMatrix[VY][VZ] * mMatrix[VZ][VX] - mMatrix[VY][VX] * mMatrix[VZ][VZ] ;
+ adjoint_transpose.mMatrix[VZ][VX] = mMatrix[VY][VX] * mMatrix[VZ][VY] - mMatrix[VY][VY] * mMatrix[VZ][VX] ;
+ adjoint_transpose.mMatrix[VX][VY] = mMatrix[VZ][VY] * mMatrix[VX][VZ] - mMatrix[VZ][VZ] * mMatrix[VX][VY] ;
+ adjoint_transpose.mMatrix[VY][VY] = mMatrix[VZ][VZ] * mMatrix[VX][VX] - mMatrix[VZ][VX] * mMatrix[VX][VZ] ;
+ adjoint_transpose.mMatrix[VZ][VY] = mMatrix[VZ][VX] * mMatrix[VX][VY] - mMatrix[VZ][VY] * mMatrix[VX][VX] ;
+ adjoint_transpose.mMatrix[VX][VZ] = mMatrix[VX][VY] * mMatrix[VY][VZ] - mMatrix[VX][VZ] * mMatrix[VY][VY] ;
+ adjoint_transpose.mMatrix[VY][VZ] = mMatrix[VX][VZ] * mMatrix[VY][VX] - mMatrix[VX][VX] * mMatrix[VY][VZ] ;
+ adjoint_transpose.mMatrix[VZ][VZ] = mMatrix[VX][VX] * mMatrix[VY][VY] - mMatrix[VX][VY] * mMatrix[VY][VX] ;
+
+ *this = adjoint_transpose;
+ return *this;
+}
+
+// SJB: This code is correct for a logicly stored (non-transposed) matrix;
+// Our matrices are stored transposed, OpenGL style, so this generates the
+// INVERSE quaternion (-x, -y, -z, w)!
+// Because we use similar logic in LLQuaternion::getMatrix3,
+// we are internally consistant so everything works OK :)
+LLQuaternion LLMatrix3::quaternion() const
+{
+ LLQuaternion quat;
+ F32 tr, s, q[4];
+ U32 i, j, k;
+ U32 nxt[3] = {1, 2, 0};
+
+ tr = mMatrix[0][0] + mMatrix[1][1] + mMatrix[2][2];
+
+ // check the diagonal
+ if (tr > 0.f)
+ {
+ s = (F32)sqrt (tr + 1.f);
+ quat.mQ[VS] = s / 2.f;
+ s = 0.5f / s;
+ quat.mQ[VX] = (mMatrix[1][2] - mMatrix[2][1]) * s;
+ quat.mQ[VY] = (mMatrix[2][0] - mMatrix[0][2]) * s;
+ quat.mQ[VZ] = (mMatrix[0][1] - mMatrix[1][0]) * s;
+ }
+ else
+ {
+ // diagonal is negative
+ i = 0;
+ if (mMatrix[1][1] > mMatrix[0][0])
+ i = 1;
+ if (mMatrix[2][2] > mMatrix[i][i])
+ i = 2;
+
+ j = nxt[i];
+ k = nxt[j];
+
+
+ s = (F32)sqrt ((mMatrix[i][i] - (mMatrix[j][j] + mMatrix[k][k])) + 1.f);
+
+ q[i] = s * 0.5f;
+
+ if (s != 0.f)
+ s = 0.5f / s;
+
+ q[3] = (mMatrix[j][k] - mMatrix[k][j]) * s;
+ q[j] = (mMatrix[i][j] + mMatrix[j][i]) * s;
+ q[k] = (mMatrix[i][k] + mMatrix[k][i]) * s;
+
+ quat.setQuat(q);
+ }
+ return quat;
+}
+
+
+// These functions take Rotation arguments
+const LLMatrix3& LLMatrix3::setRot(const F32 angle, const F32 x, const F32 y, const F32 z)
+{
+ LLMatrix3 mat(angle, x, y, z);
+ *this = mat;
+ return *this;
+}
+
+const LLMatrix3& LLMatrix3::setRot(const F32 angle, const LLVector3 &vec)
+{
+ LLMatrix3 mat(angle, vec);
+ *this = mat;
+ return *this;
+}
+
+const LLMatrix3& LLMatrix3::setRot(const F32 roll, const F32 pitch, const F32 yaw)
+{
+ LLMatrix3 mat(roll, pitch, yaw);
+ *this = mat;
+ return *this;
+}
+
+
+const LLMatrix3& LLMatrix3::setRot(const LLQuaternion &q)
+{
+ LLMatrix3 mat(q);
+ *this = mat;
+ return *this;
+}
+
+
+const LLMatrix3& LLMatrix3::setRows(const LLVector3 &fwd, const LLVector3 &left, const LLVector3 &up)
+{
+ mMatrix[0][0] = fwd.mV[0];
+ mMatrix[0][1] = fwd.mV[1];
+ mMatrix[0][2] = fwd.mV[2];
+
+ mMatrix[1][0] = left.mV[0];
+ mMatrix[1][1] = left.mV[1];
+ mMatrix[1][2] = left.mV[2];
+
+ mMatrix[2][0] = up.mV[0];
+ mMatrix[2][1] = up.mV[1];
+ mMatrix[2][2] = up.mV[2];
+
+ return *this;
+}
+
+
+// Rotate exisitng mMatrix
+const LLMatrix3& LLMatrix3::rotate(const F32 angle, const F32 x, const F32 y, const F32 z)
+{
+ LLMatrix3 mat(angle, x, y, z);
+ *this *= mat;
+ return *this;
+}
+
+
+const LLMatrix3& LLMatrix3::rotate(const F32 angle, const LLVector3 &vec)
+{
+ LLMatrix3 mat(angle, vec);
+ *this *= mat;
+ return *this;
+}
+
+
+const LLMatrix3& LLMatrix3::rotate(const F32 roll, const F32 pitch, const F32 yaw)
+{
+ LLMatrix3 mat(roll, pitch, yaw);
+ *this *= mat;
+ return *this;
+}
+
+
+const LLMatrix3& LLMatrix3::rotate(const LLQuaternion &q)
+{
+ LLMatrix3 mat(q);
+ *this *= mat;
+ return *this;
+}
+
+
+LLVector3 LLMatrix3::getFwdRow() const
+{
+ return LLVector3(mMatrix[VX]);
+}
+
+LLVector3 LLMatrix3::getLeftRow() const
+{
+ return LLVector3(mMatrix[VY]);
+}
+
+LLVector3 LLMatrix3::getUpRow() const
+{
+ return LLVector3(mMatrix[VZ]);
+}
+
+
+
+const LLMatrix3& LLMatrix3::orthogonalize()
+{
+ LLVector3 x_axis(mMatrix[VX]);
+ LLVector3 y_axis(mMatrix[VY]);
+ LLVector3 z_axis(mMatrix[VZ]);
+
+ x_axis.normVec();
+ y_axis -= x_axis * (x_axis * y_axis);
+ y_axis.normVec();
+ z_axis = x_axis % y_axis;
+ setRows(x_axis, y_axis, z_axis);
+ return (*this);
+}
+
+
+// LLMatrix3 Operators
+
+LLMatrix3 operator*(const LLMatrix3 &a, const LLMatrix3 &b)
+{
+ U32 i, j;
+ LLMatrix3 mat;
+ for (i = 0; i < NUM_VALUES_IN_MAT3; i++)
+ {
+ for (j = 0; j < NUM_VALUES_IN_MAT3; 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];
+ }
+ }
+ return mat;
+}
+
+/* Not implemented to help enforce code consistency with the syntax of
+ row-major notation. This is a Good Thing.
+LLVector3 operator*(const LLMatrix3 &a, const LLVector3 &b)
+{
+ LLVector3 vec;
+ // matrix operates "from the left" on column vector
+ vec.mV[VX] = a.mMatrix[VX][VX] * b.mV[VX] +
+ a.mMatrix[VX][VY] * b.mV[VY] +
+ a.mMatrix[VX][VZ] * b.mV[VZ];
+
+ vec.mV[VY] = a.mMatrix[VY][VX] * b.mV[VX] +
+ a.mMatrix[VY][VY] * b.mV[VY] +
+ a.mMatrix[VY][VZ] * b.mV[VZ];
+
+ vec.mV[VZ] = a.mMatrix[VZ][VX] * b.mV[VX] +
+ a.mMatrix[VZ][VY] * b.mV[VY] +
+ a.mMatrix[VZ][VZ] * b.mV[VZ];
+ return vec;
+}
+*/
+
+
+LLVector3 operator*(const LLVector3 &a, const LLMatrix3 &b)
+{
+ // matrix operates "from the right" on row vector
+ return LLVector3(
+ a.mV[VX] * b.mMatrix[VX][VX] +
+ a.mV[VY] * b.mMatrix[VY][VX] +
+ a.mV[VZ] * b.mMatrix[VZ][VX],
+
+ a.mV[VX] * b.mMatrix[VX][VY] +
+ a.mV[VY] * b.mMatrix[VY][VY] +
+ a.mV[VZ] * b.mMatrix[VZ][VY],
+
+ a.mV[VX] * b.mMatrix[VX][VZ] +
+ a.mV[VY] * b.mMatrix[VY][VZ] +
+ a.mV[VZ] * b.mMatrix[VZ][VZ] );
+}
+
+LLVector3d operator*(const LLVector3d &a, const LLMatrix3 &b)
+{
+ // matrix operates "from the right" on row vector
+ return LLVector3d(
+ a.mdV[VX] * b.mMatrix[VX][VX] +
+ a.mdV[VY] * b.mMatrix[VY][VX] +
+ a.mdV[VZ] * b.mMatrix[VZ][VX],
+
+ a.mdV[VX] * b.mMatrix[VX][VY] +
+ a.mdV[VY] * b.mMatrix[VY][VY] +
+ a.mdV[VZ] * b.mMatrix[VZ][VY],
+
+ a.mdV[VX] * b.mMatrix[VX][VZ] +
+ a.mdV[VY] * b.mMatrix[VY][VZ] +
+ a.mdV[VZ] * b.mMatrix[VZ][VZ] );
+}
+
+bool operator==(const LLMatrix3 &a, const LLMatrix3 &b)
+{
+ U32 i, j;
+ for (i = 0; i < NUM_VALUES_IN_MAT3; i++)
+ {
+ for (j = 0; j < NUM_VALUES_IN_MAT3; j++)
+ {
+ if (a.mMatrix[j][i] != b.mMatrix[j][i])
+ return FALSE;
+ }
+ }
+ return TRUE;
+}
+
+bool operator!=(const LLMatrix3 &a, const LLMatrix3 &b)
+{
+ U32 i, j;
+ for (i = 0; i < NUM_VALUES_IN_MAT3; i++)
+ {
+ for (j = 0; j < NUM_VALUES_IN_MAT3; j++)
+ {
+ if (a.mMatrix[j][i] != b.mMatrix[j][i])
+ return TRUE;
+ }
+ }
+ return FALSE;
+}
+
+const LLMatrix3& operator*=(LLMatrix3 &a, const LLMatrix3 &b)
+{
+ U32 i, j;
+ LLMatrix3 mat;
+ for (i = 0; i < NUM_VALUES_IN_MAT3; i++)
+ {
+ for (j = 0; j < NUM_VALUES_IN_MAT3; 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 = mat;
+ return a;
+}
+
+std::ostream& operator<<(std::ostream& s, const LLMatrix3 &a)
+{
+ s << "{ "
+ << a.mMatrix[VX][VX] << ", " << a.mMatrix[VX][VY] << ", " << a.mMatrix[VX][VZ] << "; "
+ << a.mMatrix[VY][VX] << ", " << a.mMatrix[VY][VY] << ", " << a.mMatrix[VY][VZ] << "; "
+ << a.mMatrix[VZ][VX] << ", " << a.mMatrix[VZ][VY] << ", " << a.mMatrix[VZ][VZ]
+ << " }";
+ return s;
+}
+
generated by cgit v1.2.3 (git 2.25.1) at 2025-02-08 12:00:36 +0000