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-rw-r--r--indra/llmath/llquaternion.cpp1921
1 files changed, 961 insertions, 960 deletions
diff --git a/indra/llmath/llquaternion.cpp b/indra/llmath/llquaternion.cpp
index fdcc19d657..efdc10e2c6 100644
--- a/indra/llmath/llquaternion.cpp
+++ b/indra/llmath/llquaternion.cpp
@@ -1,960 +1,961 @@
-/**
- * @file llquaternion.cpp
- * @brief LLQuaternion class implementation.
- *
- * $LicenseInfo:firstyear=2000&license=viewergpl$
- *
- * Copyright (c) 2000-2009, 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
- * 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.
- * $/LicenseInfo$
- */
-
-#include "linden_common.h"
-
-#include "llquaternion.h"
-
-#include "llmath.h" // for F_PI
-//#include "vmath.h"
-#include "v3math.h"
-#include "v3dmath.h"
-#include "v4math.h"
-#include "m4math.h"
-#include "m3math.h"
-#include "llquantize.h"
-
-// WARNING: Don't use this for global const definitions! using this
-// at the top of a *.cpp file might not give you what you think.
-const LLQuaternion LLQuaternion::DEFAULT;
-
-// Constructors
-
-LLQuaternion::LLQuaternion(const LLMatrix4 &mat)
-{
- *this = mat.quaternion();
- normalize();
-}
-
-LLQuaternion::LLQuaternion(const LLMatrix3 &mat)
-{
- *this = mat.quaternion();
- normalize();
-}
-
-LLQuaternion::LLQuaternion(F32 angle, const LLVector4 &vec)
-{
- LLVector3 v(vec.mV[VX], vec.mV[VY], vec.mV[VZ]);
- v.normalize();
-
- F32 c, s;
- c = cosf(angle*0.5f);
- s = sinf(angle*0.5f);
-
- mQ[VX] = v.mV[VX] * s;
- mQ[VY] = v.mV[VY] * s;
- mQ[VZ] = v.mV[VZ] * s;
- mQ[VW] = c;
- normalize();
-}
-
-LLQuaternion::LLQuaternion(F32 angle, const LLVector3 &vec)
-{
- LLVector3 v(vec);
- v.normalize();
-
- F32 c, s;
- c = cosf(angle*0.5f);
- s = sinf(angle*0.5f);
-
- mQ[VX] = v.mV[VX] * s;
- mQ[VY] = v.mV[VY] * s;
- mQ[VZ] = v.mV[VZ] * s;
- mQ[VW] = c;
- normalize();
-}
-
-LLQuaternion::LLQuaternion(const LLVector3 &x_axis,
- const LLVector3 &y_axis,
- const LLVector3 &z_axis)
-{
- LLMatrix3 mat;
- mat.setRows(x_axis, y_axis, z_axis);
- *this = mat.quaternion();
- normalize();
-}
-
-// Quatizations
-void LLQuaternion::quantize16(F32 lower, F32 upper)
-{
- F32 x = mQ[VX];
- F32 y = mQ[VY];
- F32 z = mQ[VZ];
- F32 s = mQ[VS];
-
- x = U16_to_F32(F32_to_U16_ROUND(x, lower, upper), lower, upper);
- y = U16_to_F32(F32_to_U16_ROUND(y, lower, upper), lower, upper);
- z = U16_to_F32(F32_to_U16_ROUND(z, lower, upper), lower, upper);
- s = U16_to_F32(F32_to_U16_ROUND(s, lower, upper), lower, upper);
-
- mQ[VX] = x;
- mQ[VY] = y;
- mQ[VZ] = z;
- mQ[VS] = s;
-
- normalize();
-}
-
-void LLQuaternion::quantize8(F32 lower, F32 upper)
-{
- mQ[VX] = U8_to_F32(F32_to_U8_ROUND(mQ[VX], lower, upper), lower, upper);
- mQ[VY] = U8_to_F32(F32_to_U8_ROUND(mQ[VY], lower, upper), lower, upper);
- mQ[VZ] = U8_to_F32(F32_to_U8_ROUND(mQ[VZ], lower, upper), lower, upper);
- mQ[VS] = U8_to_F32(F32_to_U8_ROUND(mQ[VS], lower, upper), lower, upper);
-
- normalize();
-}
-
-// LLVector3 Magnitude and Normalization Functions
-
-
-// Set LLQuaternion routines
-
-const LLQuaternion& LLQuaternion::setAngleAxis(F32 angle, F32 x, F32 y, F32 z)
-{
- LLVector3 vec(x, y, z);
- vec.normalize();
-
- angle *= 0.5f;
- F32 c, s;
- c = cosf(angle);
- s = sinf(angle);
-
- mQ[VX] = vec.mV[VX]*s;
- mQ[VY] = vec.mV[VY]*s;
- mQ[VZ] = vec.mV[VZ]*s;
- mQ[VW] = c;
-
- normalize();
- return (*this);
-}
-
-const LLQuaternion& LLQuaternion::setAngleAxis(F32 angle, const LLVector3 &vec)
-{
- LLVector3 v(vec);
- v.normalize();
-
- angle *= 0.5f;
- F32 c, s;
- c = cosf(angle);
- s = sinf(angle);
-
- mQ[VX] = v.mV[VX]*s;
- mQ[VY] = v.mV[VY]*s;
- mQ[VZ] = v.mV[VZ]*s;
- mQ[VW] = c;
-
- normalize();
- return (*this);
-}
-
-const LLQuaternion& LLQuaternion::setAngleAxis(F32 angle, const LLVector4 &vec)
-{
- LLVector3 v(vec.mV[VX], vec.mV[VY], vec.mV[VZ]);
- v.normalize();
-
- F32 c, s;
- c = cosf(angle*0.5f);
- s = sinf(angle*0.5f);
-
- mQ[VX] = v.mV[VX]*s;
- mQ[VY] = v.mV[VY]*s;
- mQ[VZ] = v.mV[VZ]*s;
- mQ[VW] = c;
-
- normalize();
- return (*this);
-}
-
-const LLQuaternion& LLQuaternion::setEulerAngles(F32 roll, F32 pitch, F32 yaw)
-{
- LLMatrix3 rot_mat(roll, pitch, yaw);
- rot_mat.orthogonalize();
- *this = rot_mat.quaternion();
-
- normalize();
- return (*this);
-}
-
-// deprecated
-const LLQuaternion& LLQuaternion::set(const LLMatrix3 &mat)
-{
- *this = mat.quaternion();
- normalize();
- return (*this);
-}
-
-// deprecated
-const LLQuaternion& LLQuaternion::set(const LLMatrix4 &mat)
-{
- *this = mat.quaternion();
- normalize();
- return (*this);
-}
-
-// deprecated
-const LLQuaternion& LLQuaternion::setQuat(F32 angle, F32 x, F32 y, F32 z)
-{
- LLVector3 vec(x, y, z);
- vec.normalize();
-
- angle *= 0.5f;
- F32 c, s;
- c = cosf(angle);
- s = sinf(angle);
-
- mQ[VX] = vec.mV[VX]*s;
- mQ[VY] = vec.mV[VY]*s;
- mQ[VZ] = vec.mV[VZ]*s;
- mQ[VW] = c;
-
- normalize();
- return (*this);
-}
-
-// deprecated
-const LLQuaternion& LLQuaternion::setQuat(F32 angle, const LLVector3 &vec)
-{
- LLVector3 v(vec);
- v.normalize();
-
- angle *= 0.5f;
- F32 c, s;
- c = cosf(angle);
- s = sinf(angle);
-
- mQ[VX] = v.mV[VX]*s;
- mQ[VY] = v.mV[VY]*s;
- mQ[VZ] = v.mV[VZ]*s;
- mQ[VW] = c;
-
- normalize();
- return (*this);
-}
-
-const LLQuaternion& LLQuaternion::setQuat(F32 angle, const LLVector4 &vec)
-{
- LLVector3 v(vec.mV[VX], vec.mV[VY], vec.mV[VZ]);
- v.normalize();
-
- F32 c, s;
- c = cosf(angle*0.5f);
- s = sinf(angle*0.5f);
-
- mQ[VX] = v.mV[VX]*s;
- mQ[VY] = v.mV[VY]*s;
- mQ[VZ] = v.mV[VZ]*s;
- mQ[VW] = c;
-
- normalize();
- return (*this);
-}
-
-const LLQuaternion& LLQuaternion::setQuat(F32 roll, F32 pitch, F32 yaw)
-{
- LLMatrix3 rot_mat(roll, pitch, yaw);
- rot_mat.orthogonalize();
- *this = rot_mat.quaternion();
-
- normalize();
- return (*this);
-}
-
-const LLQuaternion& LLQuaternion::setQuat(const LLMatrix3 &mat)
-{
- *this = mat.quaternion();
- normalize();
- return (*this);
-}
-
-const LLQuaternion& LLQuaternion::setQuat(const LLMatrix4 &mat)
-{
- *this = mat.quaternion();
- normalize();
- return (*this);
-//#if 1
-// // NOTE: LLQuaternion's are actually inverted with respect to
-// // the matrices, so this code also assumes inverted quaternions
-// // (-x, -y, -z, w). The result is that roll,pitch,yaw are applied
-// // in reverse order (yaw,pitch,roll).
-// F64 cosX = cos(roll);
-// F64 cosY = cos(pitch);
-// F64 cosZ = cos(yaw);
-//
-// F64 sinX = sin(roll);
-// F64 sinY = sin(pitch);
-// F64 sinZ = sin(yaw);
-//
-// mQ[VW] = (F32)sqrt(cosY*cosZ - sinX*sinY*sinZ + cosX*cosZ + cosX*cosY + 1.0)*.5;
-// if (fabs(mQ[VW]) < F_APPROXIMATELY_ZERO)
-// {
-// // null rotation, any axis will do
-// mQ[VX] = 0.0f;
-// mQ[VY] = 1.0f;
-// mQ[VZ] = 0.0f;
-// }
-// else
-// {
-// F32 inv_s = 1.0f / (4.0f * mQ[VW]);
-// mQ[VX] = (F32)-(-sinX*cosY - cosX*sinY*sinZ - sinX*cosZ) * inv_s;
-// mQ[VY] = (F32)-(-cosX*sinY*cosZ + sinX*sinZ - sinY) * inv_s;
-// mQ[VZ] = (F32)-(-cosY*sinZ - sinX*sinY*cosZ - cosX*sinZ) * inv_s;
-// }
-//
-//#else // This only works on a certain subset of roll/pitch/yaw
-//
-// F64 cosX = cosf(roll/2.0);
-// F64 cosY = cosf(pitch/2.0);
-// F64 cosZ = cosf(yaw/2.0);
-//
-// F64 sinX = sinf(roll/2.0);
-// F64 sinY = sinf(pitch/2.0);
-// F64 sinZ = sinf(yaw/2.0);
-//
-// mQ[VW] = (F32)(cosX*cosY*cosZ + sinX*sinY*sinZ);
-// mQ[VX] = (F32)(sinX*cosY*cosZ - cosX*sinY*sinZ);
-// mQ[VY] = (F32)(cosX*sinY*cosZ + sinX*cosY*sinZ);
-// mQ[VZ] = (F32)(cosX*cosY*sinZ - sinX*sinY*cosZ);
-//#endif
-//
-// normalize();
-// 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 matrix, or the CORRECT matrix form an INVERSE quaternion.
-// Because we use similar logic in LLMatrix3::quaternion(),
-// we are internally consistant so everything works OK :)
-LLMatrix3 LLQuaternion::getMatrix3(void) const
-{
- LLMatrix3 mat;
- F32 xx, xy, xz, xw, yy, yz, yw, zz, zw;
-
- xx = mQ[VX] * mQ[VX];
- xy = mQ[VX] * mQ[VY];
- xz = mQ[VX] * mQ[VZ];
- xw = mQ[VX] * mQ[VW];
-
- yy = mQ[VY] * mQ[VY];
- yz = mQ[VY] * mQ[VZ];
- yw = mQ[VY] * mQ[VW];
-
- zz = mQ[VZ] * mQ[VZ];
- zw = mQ[VZ] * mQ[VW];
-
- mat.mMatrix[0][0] = 1.f - 2.f * ( yy + zz );
- mat.mMatrix[0][1] = 2.f * ( xy + zw );
- mat.mMatrix[0][2] = 2.f * ( xz - yw );
-
- mat.mMatrix[1][0] = 2.f * ( xy - zw );
- mat.mMatrix[1][1] = 1.f - 2.f * ( xx + zz );
- mat.mMatrix[1][2] = 2.f * ( yz + xw );
-
- mat.mMatrix[2][0] = 2.f * ( xz + yw );
- mat.mMatrix[2][1] = 2.f * ( yz - xw );
- mat.mMatrix[2][2] = 1.f - 2.f * ( xx + yy );
-
- return mat;
-}
-
-LLMatrix4 LLQuaternion::getMatrix4(void) const
-{
- LLMatrix4 mat;
- F32 xx, xy, xz, xw, yy, yz, yw, zz, zw;
-
- xx = mQ[VX] * mQ[VX];
- xy = mQ[VX] * mQ[VY];
- xz = mQ[VX] * mQ[VZ];
- xw = mQ[VX] * mQ[VW];
-
- yy = mQ[VY] * mQ[VY];
- yz = mQ[VY] * mQ[VZ];
- yw = mQ[VY] * mQ[VW];
-
- zz = mQ[VZ] * mQ[VZ];
- zw = mQ[VZ] * mQ[VW];
-
- mat.mMatrix[0][0] = 1.f - 2.f * ( yy + zz );
- mat.mMatrix[0][1] = 2.f * ( xy + zw );
- mat.mMatrix[0][2] = 2.f * ( xz - yw );
-
- mat.mMatrix[1][0] = 2.f * ( xy - zw );
- mat.mMatrix[1][1] = 1.f - 2.f * ( xx + zz );
- mat.mMatrix[1][2] = 2.f * ( yz + xw );
-
- mat.mMatrix[2][0] = 2.f * ( xz + yw );
- mat.mMatrix[2][1] = 2.f * ( yz - xw );
- mat.mMatrix[2][2] = 1.f - 2.f * ( xx + yy );
-
- // TODO -- should we set the translation portion to zero?
-
- return mat;
-}
-
-
-
-
-// Other useful methods
-
-
-// calculate the shortest rotation from a to b
-void LLQuaternion::shortestArc(const LLVector3 &a, const LLVector3 &b)
-{
- // Make a local copy of both vectors.
- LLVector3 vec_a = a;
- LLVector3 vec_b = b;
-
- // Make sure neither vector is zero length. Also normalize
- // the vectors while we are at it.
- F32 vec_a_mag = vec_a.normalize();
- F32 vec_b_mag = vec_b.normalize();
- if (vec_a_mag < F_APPROXIMATELY_ZERO ||
- vec_b_mag < F_APPROXIMATELY_ZERO)
- {
- // Can't calculate a rotation from this.
- // Just return ZERO_ROTATION instead.
- loadIdentity();
- return;
- }
-
- // Create an axis to rotate around, and the cos of the angle to rotate.
- LLVector3 axis = vec_a % vec_b;
- F32 cos_theta = vec_a * vec_b;
-
- // Check the angle between the vectors to see if they are parallel or anti-parallel.
- if (cos_theta > 1.0 - F_APPROXIMATELY_ZERO)
- {
- // a and b are parallel. No rotation is necessary.
- loadIdentity();
- }
- else if (cos_theta < -1.0 + F_APPROXIMATELY_ZERO)
- {
- // a and b are anti-parallel.
- // Rotate 180 degrees around some orthogonal axis.
- // Find the projection of the x-axis onto a, and try
- // using the vector between the projection and the x-axis
- // as the orthogonal axis.
- LLVector3 proj = vec_a.mV[VX] / (vec_a * vec_a) * vec_a;
- LLVector3 ortho_axis(1.f, 0.f, 0.f);
- ortho_axis -= proj;
-
- // Turn this into an orthonormal axis.
- F32 ortho_length = ortho_axis.normalize();
- // If the axis' length is 0, then our guess at an orthogonal axis
- // was wrong (a is parallel to the x-axis).
- if (ortho_length < F_APPROXIMATELY_ZERO)
- {
- // Use the z-axis instead.
- ortho_axis.setVec(0.f, 0.f, 1.f);
- }
-
- // Construct a quaternion from this orthonormal axis.
- mQ[VX] = ortho_axis.mV[VX];
- mQ[VY] = ortho_axis.mV[VY];
- mQ[VZ] = ortho_axis.mV[VZ];
- mQ[VW] = 0.f;
- }
- else
- {
- // a and b are NOT parallel or anti-parallel.
- // Return the rotation between these vectors.
- F32 theta = (F32)acos(cos_theta);
-
- setAngleAxis(theta, axis);
- }
-}
-
-// constrains rotation to a cone angle specified in radians
-const LLQuaternion &LLQuaternion::constrain(F32 radians)
-{
- const F32 cos_angle_lim = cosf( radians/2 ); // mQ[VW] limit
- const F32 sin_angle_lim = sinf( radians/2 ); // rotation axis length limit
-
- if (mQ[VW] < 0.f)
- {
- mQ[VX] *= -1.f;
- mQ[VY] *= -1.f;
- mQ[VZ] *= -1.f;
- mQ[VW] *= -1.f;
- }
-
- // if rotation angle is greater than limit (cos is less than limit)
- if( mQ[VW] < cos_angle_lim )
- {
- mQ[VW] = cos_angle_lim;
- F32 axis_len = sqrtf( mQ[VX]*mQ[VX] + mQ[VY]*mQ[VY] + mQ[VZ]*mQ[VZ] ); // sin(theta/2)
- F32 axis_mult_fact = sin_angle_lim / axis_len;
- mQ[VX] *= axis_mult_fact;
- mQ[VY] *= axis_mult_fact;
- mQ[VZ] *= axis_mult_fact;
- }
-
- return *this;
-}
-
-// Operators
-
-std::ostream& operator<<(std::ostream &s, const LLQuaternion &a)
-{
- s << "{ "
- << a.mQ[VX] << ", " << a.mQ[VY] << ", " << a.mQ[VZ] << ", " << a.mQ[VW]
- << " }";
- return s;
-}
-
-
-// Does NOT renormalize the result
-LLQuaternion operator*(const LLQuaternion &a, const LLQuaternion &b)
-{
-// LLQuaternion::mMultCount++;
-
- LLQuaternion q(
- b.mQ[3] * a.mQ[0] + b.mQ[0] * a.mQ[3] + b.mQ[1] * a.mQ[2] - b.mQ[2] * a.mQ[1],
- b.mQ[3] * a.mQ[1] + b.mQ[1] * a.mQ[3] + b.mQ[2] * a.mQ[0] - b.mQ[0] * a.mQ[2],
- b.mQ[3] * a.mQ[2] + b.mQ[2] * a.mQ[3] + b.mQ[0] * a.mQ[1] - b.mQ[1] * a.mQ[0],
- b.mQ[3] * a.mQ[3] - b.mQ[0] * a.mQ[0] - b.mQ[1] * a.mQ[1] - b.mQ[2] * a.mQ[2]
- );
- return q;
-}
-
-/*
-LLMatrix4 operator*(const LLMatrix4 &m, const LLQuaternion &q)
-{
- LLMatrix4 qmat(q);
- return (m*qmat);
-}
-*/
-
-
-
-LLVector4 operator*(const LLVector4 &a, const LLQuaternion &rot)
-{
- F32 rw = - rot.mQ[VX] * a.mV[VX] - rot.mQ[VY] * a.mV[VY] - rot.mQ[VZ] * a.mV[VZ];
- F32 rx = rot.mQ[VW] * a.mV[VX] + rot.mQ[VY] * a.mV[VZ] - rot.mQ[VZ] * a.mV[VY];
- F32 ry = rot.mQ[VW] * a.mV[VY] + rot.mQ[VZ] * a.mV[VX] - rot.mQ[VX] * a.mV[VZ];
- F32 rz = rot.mQ[VW] * a.mV[VZ] + rot.mQ[VX] * a.mV[VY] - rot.mQ[VY] * a.mV[VX];
-
- F32 nx = - rw * rot.mQ[VX] + rx * rot.mQ[VW] - ry * rot.mQ[VZ] + rz * rot.mQ[VY];
- F32 ny = - rw * rot.mQ[VY] + ry * rot.mQ[VW] - rz * rot.mQ[VX] + rx * rot.mQ[VZ];
- F32 nz = - rw * rot.mQ[VZ] + rz * rot.mQ[VW] - rx * rot.mQ[VY] + ry * rot.mQ[VX];
-
- return LLVector4(nx, ny, nz, a.mV[VW]);
-}
-
-LLVector3 operator*(const LLVector3 &a, const LLQuaternion &rot)
-{
- F32 rw = - rot.mQ[VX] * a.mV[VX] - rot.mQ[VY] * a.mV[VY] - rot.mQ[VZ] * a.mV[VZ];
- F32 rx = rot.mQ[VW] * a.mV[VX] + rot.mQ[VY] * a.mV[VZ] - rot.mQ[VZ] * a.mV[VY];
- F32 ry = rot.mQ[VW] * a.mV[VY] + rot.mQ[VZ] * a.mV[VX] - rot.mQ[VX] * a.mV[VZ];
- F32 rz = rot.mQ[VW] * a.mV[VZ] + rot.mQ[VX] * a.mV[VY] - rot.mQ[VY] * a.mV[VX];
-
- F32 nx = - rw * rot.mQ[VX] + rx * rot.mQ[VW] - ry * rot.mQ[VZ] + rz * rot.mQ[VY];
- F32 ny = - rw * rot.mQ[VY] + ry * rot.mQ[VW] - rz * rot.mQ[VX] + rx * rot.mQ[VZ];
- F32 nz = - rw * rot.mQ[VZ] + rz * rot.mQ[VW] - rx * rot.mQ[VY] + ry * rot.mQ[VX];
-
- return LLVector3(nx, ny, nz);
-}
-
-LLVector3d operator*(const LLVector3d &a, const LLQuaternion &rot)
-{
- F64 rw = - rot.mQ[VX] * a.mdV[VX] - rot.mQ[VY] * a.mdV[VY] - rot.mQ[VZ] * a.mdV[VZ];
- F64 rx = rot.mQ[VW] * a.mdV[VX] + rot.mQ[VY] * a.mdV[VZ] - rot.mQ[VZ] * a.mdV[VY];
- F64 ry = rot.mQ[VW] * a.mdV[VY] + rot.mQ[VZ] * a.mdV[VX] - rot.mQ[VX] * a.mdV[VZ];
- F64 rz = rot.mQ[VW] * a.mdV[VZ] + rot.mQ[VX] * a.mdV[VY] - rot.mQ[VY] * a.mdV[VX];
-
- F64 nx = - rw * rot.mQ[VX] + rx * rot.mQ[VW] - ry * rot.mQ[VZ] + rz * rot.mQ[VY];
- F64 ny = - rw * rot.mQ[VY] + ry * rot.mQ[VW] - rz * rot.mQ[VX] + rx * rot.mQ[VZ];
- F64 nz = - rw * rot.mQ[VZ] + rz * rot.mQ[VW] - rx * rot.mQ[VY] + ry * rot.mQ[VX];
-
- return LLVector3d(nx, ny, nz);
-}
-
-F32 dot(const LLQuaternion &a, const LLQuaternion &b)
-{
- return a.mQ[VX] * b.mQ[VX] +
- a.mQ[VY] * b.mQ[VY] +
- a.mQ[VZ] * b.mQ[VZ] +
- a.mQ[VW] * b.mQ[VW];
-}
-
-// DEMO HACK: This lerp is probably inocrrect now due intermediate normalization
-// it should look more like the lerp below
-#if 0
-// linear interpolation
-LLQuaternion lerp(F32 t, const LLQuaternion &p, const LLQuaternion &q)
-{
- LLQuaternion r;
- r = t * (q - p) + p;
- r.normalize();
- return r;
-}
-#endif
-
-// lerp from identity to q
-LLQuaternion lerp(F32 t, const LLQuaternion &q)
-{
- LLQuaternion r;
- r.mQ[VX] = t * q.mQ[VX];
- r.mQ[VY] = t * q.mQ[VY];
- r.mQ[VZ] = t * q.mQ[VZ];
- r.mQ[VW] = t * (q.mQ[VZ] - 1.f) + 1.f;
- r.normalize();
- return r;
-}
-
-LLQuaternion lerp(F32 t, const LLQuaternion &p, const LLQuaternion &q)
-{
- LLQuaternion r;
- F32 inv_t;
-
- inv_t = 1.f - t;
-
- r.mQ[VX] = t * q.mQ[VX] + (inv_t * p.mQ[VX]);
- r.mQ[VY] = t * q.mQ[VY] + (inv_t * p.mQ[VY]);
- r.mQ[VZ] = t * q.mQ[VZ] + (inv_t * p.mQ[VZ]);
- r.mQ[VW] = t * q.mQ[VW] + (inv_t * p.mQ[VW]);
- r.normalize();
- return r;
-}
-
-
-// spherical linear interpolation
-LLQuaternion slerp( F32 u, const LLQuaternion &a, const LLQuaternion &b )
-{
- // cosine theta = dot product of a and b
- F32 cos_t = a.mQ[0]*b.mQ[0] + a.mQ[1]*b.mQ[1] + a.mQ[2]*b.mQ[2] + a.mQ[3]*b.mQ[3];
-
- // if b is on opposite hemisphere from a, use -a instead
- int bflip;
- if (cos_t < 0.0f)
- {
- cos_t = -cos_t;
- bflip = TRUE;
- }
- else
- bflip = FALSE;
-
- // if B is (within precision limits) the same as A,
- // just linear interpolate between A and B.
- F32 alpha; // interpolant
- F32 beta; // 1 - interpolant
- if (1.0f - cos_t < 0.00001f)
- {
- beta = 1.0f - u;
- alpha = u;
- }
- else
- {
- F32 theta = acosf(cos_t);
- F32 sin_t = sinf(theta);
- beta = sinf(theta - u*theta) / sin_t;
- alpha = sinf(u*theta) / sin_t;
- }
-
- if (bflip)
- beta = -beta;
-
- // interpolate
- LLQuaternion ret;
- ret.mQ[0] = beta*a.mQ[0] + alpha*b.mQ[0];
- ret.mQ[1] = beta*a.mQ[1] + alpha*b.mQ[1];
- ret.mQ[2] = beta*a.mQ[2] + alpha*b.mQ[2];
- ret.mQ[3] = beta*a.mQ[3] + alpha*b.mQ[3];
-
- return ret;
-}
-
-// lerp whenever possible
-LLQuaternion nlerp(F32 t, const LLQuaternion &a, const LLQuaternion &b)
-{
- if (dot(a, b) < 0.f)
- {
- return slerp(t, a, b);
- }
- else
- {
- return lerp(t, a, b);
- }
-}
-
-LLQuaternion nlerp(F32 t, const LLQuaternion &q)
-{
- if (q.mQ[VW] < 0.f)
- {
- return slerp(t, q);
- }
- else
- {
- return lerp(t, q);
- }
-}
-
-// slerp from identity quaternion to another quaternion
-LLQuaternion slerp(F32 t, const LLQuaternion &q)
-{
- F32 c = q.mQ[VW];
- if (1.0f == t || 1.0f == c)
- {
- // the trivial cases
- return q;
- }
-
- LLQuaternion r;
- F32 s, angle, stq, stp;
-
- s = (F32) sqrt(1.f - c*c);
-
- if (c < 0.0f)
- {
- // when c < 0.0 then theta > PI/2
- // since quat and -quat are the same rotation we invert one of
- // p or q to reduce unecessary spins
- // A equivalent way to do it is to convert acos(c) as if it had
- // been negative, and to negate stp
- angle = (F32) acos(-c);
- stp = -(F32) sin(angle * (1.f - t));
- stq = (F32) sin(angle * t);
- }
- else
- {
- angle = (F32) acos(c);
- stp = (F32) sin(angle * (1.f - t));
- stq = (F32) sin(angle * t);
- }
-
- r.mQ[VX] = (q.mQ[VX] * stq) / s;
- r.mQ[VY] = (q.mQ[VY] * stq) / s;
- r.mQ[VZ] = (q.mQ[VZ] * stq) / s;
- r.mQ[VW] = (stp + q.mQ[VW] * stq) / s;
-
- return r;
-}
-
-LLQuaternion mayaQ(F32 xRot, F32 yRot, F32 zRot, LLQuaternion::Order order)
-{
- LLQuaternion xQ( xRot*DEG_TO_RAD, LLVector3(1.0f, 0.0f, 0.0f) );
- LLQuaternion yQ( yRot*DEG_TO_RAD, LLVector3(0.0f, 1.0f, 0.0f) );
- LLQuaternion zQ( zRot*DEG_TO_RAD, LLVector3(0.0f, 0.0f, 1.0f) );
- LLQuaternion ret;
- switch( order )
- {
- case LLQuaternion::XYZ:
- ret = xQ * yQ * zQ;
- break;
- case LLQuaternion::YZX:
- ret = yQ * zQ * xQ;
- break;
- case LLQuaternion::ZXY:
- ret = zQ * xQ * yQ;
- break;
- case LLQuaternion::XZY:
- ret = xQ * zQ * yQ;
- break;
- case LLQuaternion::YXZ:
- ret = yQ * xQ * zQ;
- break;
- case LLQuaternion::ZYX:
- ret = zQ * yQ * xQ;
- break;
- }
- return ret;
-}
-
-const char *OrderToString( const LLQuaternion::Order order )
-{
- const char *p = NULL;
- switch( order )
- {
- default:
- case LLQuaternion::XYZ:
- p = "XYZ";
- break;
- case LLQuaternion::YZX:
- p = "YZX";
- break;
- case LLQuaternion::ZXY:
- p = "ZXY";
- break;
- case LLQuaternion::XZY:
- p = "XZY";
- break;
- case LLQuaternion::YXZ:
- p = "YXZ";
- break;
- case LLQuaternion::ZYX:
- p = "ZYX";
- break;
- }
- return p;
-}
-
-LLQuaternion::Order StringToOrder( const char *str )
-{
- if (strncmp(str, "XYZ", 3)==0 || strncmp(str, "xyz", 3)==0)
- return LLQuaternion::XYZ;
-
- if (strncmp(str, "YZX", 3)==0 || strncmp(str, "yzx", 3)==0)
- return LLQuaternion::YZX;
-
- if (strncmp(str, "ZXY", 3)==0 || strncmp(str, "zxy", 3)==0)
- return LLQuaternion::ZXY;
-
- if (strncmp(str, "XZY", 3)==0 || strncmp(str, "xzy", 3)==0)
- return LLQuaternion::XZY;
-
- if (strncmp(str, "YXZ", 3)==0 || strncmp(str, "yxz", 3)==0)
- return LLQuaternion::YXZ;
-
- if (strncmp(str, "ZYX", 3)==0 || strncmp(str, "zyx", 3)==0)
- return LLQuaternion::ZYX;
-
- return LLQuaternion::XYZ;
-}
-
-void LLQuaternion::getAngleAxis(F32* angle, LLVector3 &vec) const
-{
- F32 cos_a = mQ[VW];
- if (cos_a > 1.0f) cos_a = 1.0f;
- if (cos_a < -1.0f) cos_a = -1.0f;
-
- F32 sin_a = (F32) sqrt( 1.0f - cos_a * cos_a );
-
- if ( fabs( sin_a ) < 0.0005f )
- sin_a = 1.0f;
- else
- sin_a = 1.f/sin_a;
-
- F32 temp_angle = 2.0f * (F32) acos( cos_a );
- if (temp_angle > F_PI)
- {
- // The (angle,axis) pair should never have angles outside [PI, -PI]
- // since we want the _shortest_ (angle,axis) solution.
- // Since acos is defined for [0, PI], and we multiply by 2.0, we
- // can push the angle outside the acceptible range.
- // When this happens we set the angle to the other portion of a
- // full 2PI rotation, and negate the axis, which reverses the
- // direction of the rotation (by the right-hand rule).
- *angle = 2.f * F_PI - temp_angle;
- vec.mV[VX] = - mQ[VX] * sin_a;
- vec.mV[VY] = - mQ[VY] * sin_a;
- vec.mV[VZ] = - mQ[VZ] * sin_a;
- }
- else
- {
- *angle = temp_angle;
- vec.mV[VX] = mQ[VX] * sin_a;
- vec.mV[VY] = mQ[VY] * sin_a;
- vec.mV[VZ] = mQ[VZ] * sin_a;
- }
-}
-
-
-// quaternion does not need to be normalized
-void LLQuaternion::getEulerAngles(F32 *roll, F32 *pitch, F32 *yaw) const
-{
- LLMatrix3 rot_mat(*this);
- rot_mat.orthogonalize();
- rot_mat.getEulerAngles(roll, pitch, yaw);
-
-// // NOTE: LLQuaternion's are actually inverted with respect to
-// // the matrices, so this code also assumes inverted quaternions
-// // (-x, -y, -z, w). The result is that roll,pitch,yaw are applied
-// // in reverse order (yaw,pitch,roll).
-// F32 x = -mQ[VX], y = -mQ[VY], z = -mQ[VZ], w = mQ[VW];
-// F64 m20 = 2.0*(x*z-y*w);
-// if (1.0f - fabsf(m20) < F_APPROXIMATELY_ZERO)
-// {
-// *roll = 0.0f;
-// *pitch = (F32)asin(m20);
-// *yaw = (F32)atan2(2.0*(x*y-z*w), 1.0 - 2.0*(x*x+z*z));
-// }
-// else
-// {
-// *roll = (F32)atan2(-2.0*(y*z+x*w), 1.0-2.0*(x*x+y*y));
-// *pitch = (F32)asin(m20);
-// *yaw = (F32)atan2(-2.0*(x*y+z*w), 1.0-2.0*(y*y+z*z));
-// }
-}
-
-// Saves space by using the fact that our quaternions are normalized
-LLVector3 LLQuaternion::packToVector3() const
-{
- if( mQ[VW] >= 0 )
- {
- return LLVector3( mQ[VX], mQ[VY], mQ[VZ] );
- }
- else
- {
- return LLVector3( -mQ[VX], -mQ[VY], -mQ[VZ] );
- }
-}
-
-// Saves space by using the fact that our quaternions are normalized
-void LLQuaternion::unpackFromVector3( const LLVector3& vec )
-{
- mQ[VX] = vec.mV[VX];
- mQ[VY] = vec.mV[VY];
- mQ[VZ] = vec.mV[VZ];
- F32 t = 1.f - vec.magVecSquared();
- if( t > 0 )
- {
- mQ[VW] = sqrt( t );
- }
- else
- {
- // Need this to avoid trying to find the square root of a negative number due
- // to floating point error.
- mQ[VW] = 0;
- }
-}
-
-BOOL LLQuaternion::parseQuat(const std::string& buf, LLQuaternion* value)
-{
- if( buf.empty() || value == NULL)
- {
- return FALSE;
- }
-
- LLQuaternion quat;
- S32 count = sscanf( buf.c_str(), "%f %f %f %f", quat.mQ + 0, quat.mQ + 1, quat.mQ + 2, quat.mQ + 3 );
- if( 4 == count )
- {
- value->set( quat );
- return TRUE;
- }
-
- return FALSE;
-}
-
-
-// End
+/**
+ * @file llquaternion.cpp
+ * @brief LLQuaternion class implementation.
+ *
+ * $LicenseInfo:firstyear=2000&license=viewergpl$
+ *
+ * Copyright (c) 2000-2009, 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
+ * 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.
+ * $/LicenseInfo$
+ */
+
+#include "linden_common.h"
+
+#include "llmath.h" // for F_PI
+
+#include "llquaternion.h"
+
+//#include "vmath.h"
+#include "v3math.h"
+#include "v3dmath.h"
+#include "v4math.h"
+#include "m4math.h"
+#include "m3math.h"
+#include "llquantize.h"
+
+// WARNING: Don't use this for global const definitions! using this
+// at the top of a *.cpp file might not give you what you think.
+const LLQuaternion LLQuaternion::DEFAULT;
+
+// Constructors
+
+LLQuaternion::LLQuaternion(const LLMatrix4 &mat)
+{
+ *this = mat.quaternion();
+ normalize();
+}
+
+LLQuaternion::LLQuaternion(const LLMatrix3 &mat)
+{
+ *this = mat.quaternion();
+ normalize();
+}
+
+LLQuaternion::LLQuaternion(F32 angle, const LLVector4 &vec)
+{
+ LLVector3 v(vec.mV[VX], vec.mV[VY], vec.mV[VZ]);
+ v.normalize();
+
+ F32 c, s;
+ c = cosf(angle*0.5f);
+ s = sinf(angle*0.5f);
+
+ mQ[VX] = v.mV[VX] * s;
+ mQ[VY] = v.mV[VY] * s;
+ mQ[VZ] = v.mV[VZ] * s;
+ mQ[VW] = c;
+ normalize();
+}
+
+LLQuaternion::LLQuaternion(F32 angle, const LLVector3 &vec)
+{
+ LLVector3 v(vec);
+ v.normalize();
+
+ F32 c, s;
+ c = cosf(angle*0.5f);
+ s = sinf(angle*0.5f);
+
+ mQ[VX] = v.mV[VX] * s;
+ mQ[VY] = v.mV[VY] * s;
+ mQ[VZ] = v.mV[VZ] * s;
+ mQ[VW] = c;
+ normalize();
+}
+
+LLQuaternion::LLQuaternion(const LLVector3 &x_axis,
+ const LLVector3 &y_axis,
+ const LLVector3 &z_axis)
+{
+ LLMatrix3 mat;
+ mat.setRows(x_axis, y_axis, z_axis);
+ *this = mat.quaternion();
+ normalize();
+}
+
+// Quatizations
+void LLQuaternion::quantize16(F32 lower, F32 upper)
+{
+ F32 x = mQ[VX];
+ F32 y = mQ[VY];
+ F32 z = mQ[VZ];
+ F32 s = mQ[VS];
+
+ x = U16_to_F32(F32_to_U16_ROUND(x, lower, upper), lower, upper);
+ y = U16_to_F32(F32_to_U16_ROUND(y, lower, upper), lower, upper);
+ z = U16_to_F32(F32_to_U16_ROUND(z, lower, upper), lower, upper);
+ s = U16_to_F32(F32_to_U16_ROUND(s, lower, upper), lower, upper);
+
+ mQ[VX] = x;
+ mQ[VY] = y;
+ mQ[VZ] = z;
+ mQ[VS] = s;
+
+ normalize();
+}
+
+void LLQuaternion::quantize8(F32 lower, F32 upper)
+{
+ mQ[VX] = U8_to_F32(F32_to_U8_ROUND(mQ[VX], lower, upper), lower, upper);
+ mQ[VY] = U8_to_F32(F32_to_U8_ROUND(mQ[VY], lower, upper), lower, upper);
+ mQ[VZ] = U8_to_F32(F32_to_U8_ROUND(mQ[VZ], lower, upper), lower, upper);
+ mQ[VS] = U8_to_F32(F32_to_U8_ROUND(mQ[VS], lower, upper), lower, upper);
+
+ normalize();
+}
+
+// LLVector3 Magnitude and Normalization Functions
+
+
+// Set LLQuaternion routines
+
+const LLQuaternion& LLQuaternion::setAngleAxis(F32 angle, F32 x, F32 y, F32 z)
+{
+ LLVector3 vec(x, y, z);
+ vec.normalize();
+
+ angle *= 0.5f;
+ F32 c, s;
+ c = cosf(angle);
+ s = sinf(angle);
+
+ mQ[VX] = vec.mV[VX]*s;
+ mQ[VY] = vec.mV[VY]*s;
+ mQ[VZ] = vec.mV[VZ]*s;
+ mQ[VW] = c;
+
+ normalize();
+ return (*this);
+}
+
+const LLQuaternion& LLQuaternion::setAngleAxis(F32 angle, const LLVector3 &vec)
+{
+ LLVector3 v(vec);
+ v.normalize();
+
+ angle *= 0.5f;
+ F32 c, s;
+ c = cosf(angle);
+ s = sinf(angle);
+
+ mQ[VX] = v.mV[VX]*s;
+ mQ[VY] = v.mV[VY]*s;
+ mQ[VZ] = v.mV[VZ]*s;
+ mQ[VW] = c;
+
+ normalize();
+ return (*this);
+}
+
+const LLQuaternion& LLQuaternion::setAngleAxis(F32 angle, const LLVector4 &vec)
+{
+ LLVector3 v(vec.mV[VX], vec.mV[VY], vec.mV[VZ]);
+ v.normalize();
+
+ F32 c, s;
+ c = cosf(angle*0.5f);
+ s = sinf(angle*0.5f);
+
+ mQ[VX] = v.mV[VX]*s;
+ mQ[VY] = v.mV[VY]*s;
+ mQ[VZ] = v.mV[VZ]*s;
+ mQ[VW] = c;
+
+ normalize();
+ return (*this);
+}
+
+const LLQuaternion& LLQuaternion::setEulerAngles(F32 roll, F32 pitch, F32 yaw)
+{
+ LLMatrix3 rot_mat(roll, pitch, yaw);
+ rot_mat.orthogonalize();
+ *this = rot_mat.quaternion();
+
+ normalize();
+ return (*this);
+}
+
+// deprecated
+const LLQuaternion& LLQuaternion::set(const LLMatrix3 &mat)
+{
+ *this = mat.quaternion();
+ normalize();
+ return (*this);
+}
+
+// deprecated
+const LLQuaternion& LLQuaternion::set(const LLMatrix4 &mat)
+{
+ *this = mat.quaternion();
+ normalize();
+ return (*this);
+}
+
+// deprecated
+const LLQuaternion& LLQuaternion::setQuat(F32 angle, F32 x, F32 y, F32 z)
+{
+ LLVector3 vec(x, y, z);
+ vec.normalize();
+
+ angle *= 0.5f;
+ F32 c, s;
+ c = cosf(angle);
+ s = sinf(angle);
+
+ mQ[VX] = vec.mV[VX]*s;
+ mQ[VY] = vec.mV[VY]*s;
+ mQ[VZ] = vec.mV[VZ]*s;
+ mQ[VW] = c;
+
+ normalize();
+ return (*this);
+}
+
+// deprecated
+const LLQuaternion& LLQuaternion::setQuat(F32 angle, const LLVector3 &vec)
+{
+ LLVector3 v(vec);
+ v.normalize();
+
+ angle *= 0.5f;
+ F32 c, s;
+ c = cosf(angle);
+ s = sinf(angle);
+
+ mQ[VX] = v.mV[VX]*s;
+ mQ[VY] = v.mV[VY]*s;
+ mQ[VZ] = v.mV[VZ]*s;
+ mQ[VW] = c;
+
+ normalize();
+ return (*this);
+}
+
+const LLQuaternion& LLQuaternion::setQuat(F32 angle, const LLVector4 &vec)
+{
+ LLVector3 v(vec.mV[VX], vec.mV[VY], vec.mV[VZ]);
+ v.normalize();
+
+ F32 c, s;
+ c = cosf(angle*0.5f);
+ s = sinf(angle*0.5f);
+
+ mQ[VX] = v.mV[VX]*s;
+ mQ[VY] = v.mV[VY]*s;
+ mQ[VZ] = v.mV[VZ]*s;
+ mQ[VW] = c;
+
+ normalize();
+ return (*this);
+}
+
+const LLQuaternion& LLQuaternion::setQuat(F32 roll, F32 pitch, F32 yaw)
+{
+ LLMatrix3 rot_mat(roll, pitch, yaw);
+ rot_mat.orthogonalize();
+ *this = rot_mat.quaternion();
+
+ normalize();
+ return (*this);
+}
+
+const LLQuaternion& LLQuaternion::setQuat(const LLMatrix3 &mat)
+{
+ *this = mat.quaternion();
+ normalize();
+ return (*this);
+}
+
+const LLQuaternion& LLQuaternion::setQuat(const LLMatrix4 &mat)
+{
+ *this = mat.quaternion();
+ normalize();
+ return (*this);
+//#if 1
+// // NOTE: LLQuaternion's are actually inverted with respect to
+// // the matrices, so this code also assumes inverted quaternions
+// // (-x, -y, -z, w). The result is that roll,pitch,yaw are applied
+// // in reverse order (yaw,pitch,roll).
+// F64 cosX = cos(roll);
+// F64 cosY = cos(pitch);
+// F64 cosZ = cos(yaw);
+//
+// F64 sinX = sin(roll);
+// F64 sinY = sin(pitch);
+// F64 sinZ = sin(yaw);
+//
+// mQ[VW] = (F32)sqrt(cosY*cosZ - sinX*sinY*sinZ + cosX*cosZ + cosX*cosY + 1.0)*.5;
+// if (fabs(mQ[VW]) < F_APPROXIMATELY_ZERO)
+// {
+// // null rotation, any axis will do
+// mQ[VX] = 0.0f;
+// mQ[VY] = 1.0f;
+// mQ[VZ] = 0.0f;
+// }
+// else
+// {
+// F32 inv_s = 1.0f / (4.0f * mQ[VW]);
+// mQ[VX] = (F32)-(-sinX*cosY - cosX*sinY*sinZ - sinX*cosZ) * inv_s;
+// mQ[VY] = (F32)-(-cosX*sinY*cosZ + sinX*sinZ - sinY) * inv_s;
+// mQ[VZ] = (F32)-(-cosY*sinZ - sinX*sinY*cosZ - cosX*sinZ) * inv_s;
+// }
+//
+//#else // This only works on a certain subset of roll/pitch/yaw
+//
+// F64 cosX = cosf(roll/2.0);
+// F64 cosY = cosf(pitch/2.0);
+// F64 cosZ = cosf(yaw/2.0);
+//
+// F64 sinX = sinf(roll/2.0);
+// F64 sinY = sinf(pitch/2.0);
+// F64 sinZ = sinf(yaw/2.0);
+//
+// mQ[VW] = (F32)(cosX*cosY*cosZ + sinX*sinY*sinZ);
+// mQ[VX] = (F32)(sinX*cosY*cosZ - cosX*sinY*sinZ);
+// mQ[VY] = (F32)(cosX*sinY*cosZ + sinX*cosY*sinZ);
+// mQ[VZ] = (F32)(cosX*cosY*sinZ - sinX*sinY*cosZ);
+//#endif
+//
+// normalize();
+// 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 matrix, or the CORRECT matrix form an INVERSE quaternion.
+// Because we use similar logic in LLMatrix3::quaternion(),
+// we are internally consistant so everything works OK :)
+LLMatrix3 LLQuaternion::getMatrix3(void) const
+{
+ LLMatrix3 mat;
+ F32 xx, xy, xz, xw, yy, yz, yw, zz, zw;
+
+ xx = mQ[VX] * mQ[VX];
+ xy = mQ[VX] * mQ[VY];
+ xz = mQ[VX] * mQ[VZ];
+ xw = mQ[VX] * mQ[VW];
+
+ yy = mQ[VY] * mQ[VY];
+ yz = mQ[VY] * mQ[VZ];
+ yw = mQ[VY] * mQ[VW];
+
+ zz = mQ[VZ] * mQ[VZ];
+ zw = mQ[VZ] * mQ[VW];
+
+ mat.mMatrix[0][0] = 1.f - 2.f * ( yy + zz );
+ mat.mMatrix[0][1] = 2.f * ( xy + zw );
+ mat.mMatrix[0][2] = 2.f * ( xz - yw );
+
+ mat.mMatrix[1][0] = 2.f * ( xy - zw );
+ mat.mMatrix[1][1] = 1.f - 2.f * ( xx + zz );
+ mat.mMatrix[1][2] = 2.f * ( yz + xw );
+
+ mat.mMatrix[2][0] = 2.f * ( xz + yw );
+ mat.mMatrix[2][1] = 2.f * ( yz - xw );
+ mat.mMatrix[2][2] = 1.f - 2.f * ( xx + yy );
+
+ return mat;
+}
+
+LLMatrix4 LLQuaternion::getMatrix4(void) const
+{
+ LLMatrix4 mat;
+ F32 xx, xy, xz, xw, yy, yz, yw, zz, zw;
+
+ xx = mQ[VX] * mQ[VX];
+ xy = mQ[VX] * mQ[VY];
+ xz = mQ[VX] * mQ[VZ];
+ xw = mQ[VX] * mQ[VW];
+
+ yy = mQ[VY] * mQ[VY];
+ yz = mQ[VY] * mQ[VZ];
+ yw = mQ[VY] * mQ[VW];
+
+ zz = mQ[VZ] * mQ[VZ];
+ zw = mQ[VZ] * mQ[VW];
+
+ mat.mMatrix[0][0] = 1.f - 2.f * ( yy + zz );
+ mat.mMatrix[0][1] = 2.f * ( xy + zw );
+ mat.mMatrix[0][2] = 2.f * ( xz - yw );
+
+ mat.mMatrix[1][0] = 2.f * ( xy - zw );
+ mat.mMatrix[1][1] = 1.f - 2.f * ( xx + zz );
+ mat.mMatrix[1][2] = 2.f * ( yz + xw );
+
+ mat.mMatrix[2][0] = 2.f * ( xz + yw );
+ mat.mMatrix[2][1] = 2.f * ( yz - xw );
+ mat.mMatrix[2][2] = 1.f - 2.f * ( xx + yy );
+
+ // TODO -- should we set the translation portion to zero?
+
+ return mat;
+}
+
+
+
+
+// Other useful methods
+
+
+// calculate the shortest rotation from a to b
+void LLQuaternion::shortestArc(const LLVector3 &a, const LLVector3 &b)
+{
+ // Make a local copy of both vectors.
+ LLVector3 vec_a = a;
+ LLVector3 vec_b = b;
+
+ // Make sure neither vector is zero length. Also normalize
+ // the vectors while we are at it.
+ F32 vec_a_mag = vec_a.normalize();
+ F32 vec_b_mag = vec_b.normalize();
+ if (vec_a_mag < F_APPROXIMATELY_ZERO ||
+ vec_b_mag < F_APPROXIMATELY_ZERO)
+ {
+ // Can't calculate a rotation from this.
+ // Just return ZERO_ROTATION instead.
+ loadIdentity();
+ return;
+ }
+
+ // Create an axis to rotate around, and the cos of the angle to rotate.
+ LLVector3 axis = vec_a % vec_b;
+ F32 cos_theta = vec_a * vec_b;
+
+ // Check the angle between the vectors to see if they are parallel or anti-parallel.
+ if (cos_theta > 1.0 - F_APPROXIMATELY_ZERO)
+ {
+ // a and b are parallel. No rotation is necessary.
+ loadIdentity();
+ }
+ else if (cos_theta < -1.0 + F_APPROXIMATELY_ZERO)
+ {
+ // a and b are anti-parallel.
+ // Rotate 180 degrees around some orthogonal axis.
+ // Find the projection of the x-axis onto a, and try
+ // using the vector between the projection and the x-axis
+ // as the orthogonal axis.
+ LLVector3 proj = vec_a.mV[VX] / (vec_a * vec_a) * vec_a;
+ LLVector3 ortho_axis(1.f, 0.f, 0.f);
+ ortho_axis -= proj;
+
+ // Turn this into an orthonormal axis.
+ F32 ortho_length = ortho_axis.normalize();
+ // If the axis' length is 0, then our guess at an orthogonal axis
+ // was wrong (a is parallel to the x-axis).
+ if (ortho_length < F_APPROXIMATELY_ZERO)
+ {
+ // Use the z-axis instead.
+ ortho_axis.setVec(0.f, 0.f, 1.f);
+ }
+
+ // Construct a quaternion from this orthonormal axis.
+ mQ[VX] = ortho_axis.mV[VX];
+ mQ[VY] = ortho_axis.mV[VY];
+ mQ[VZ] = ortho_axis.mV[VZ];
+ mQ[VW] = 0.f;
+ }
+ else
+ {
+ // a and b are NOT parallel or anti-parallel.
+ // Return the rotation between these vectors.
+ F32 theta = (F32)acos(cos_theta);
+
+ setAngleAxis(theta, axis);
+ }
+}
+
+// constrains rotation to a cone angle specified in radians
+const LLQuaternion &LLQuaternion::constrain(F32 radians)
+{
+ const F32 cos_angle_lim = cosf( radians/2 ); // mQ[VW] limit
+ const F32 sin_angle_lim = sinf( radians/2 ); // rotation axis length limit
+
+ if (mQ[VW] < 0.f)
+ {
+ mQ[VX] *= -1.f;
+ mQ[VY] *= -1.f;
+ mQ[VZ] *= -1.f;
+ mQ[VW] *= -1.f;
+ }
+
+ // if rotation angle is greater than limit (cos is less than limit)
+ if( mQ[VW] < cos_angle_lim )
+ {
+ mQ[VW] = cos_angle_lim;
+ F32 axis_len = sqrtf( mQ[VX]*mQ[VX] + mQ[VY]*mQ[VY] + mQ[VZ]*mQ[VZ] ); // sin(theta/2)
+ F32 axis_mult_fact = sin_angle_lim / axis_len;
+ mQ[VX] *= axis_mult_fact;
+ mQ[VY] *= axis_mult_fact;
+ mQ[VZ] *= axis_mult_fact;
+ }
+
+ return *this;
+}
+
+// Operators
+
+std::ostream& operator<<(std::ostream &s, const LLQuaternion &a)
+{
+ s << "{ "
+ << a.mQ[VX] << ", " << a.mQ[VY] << ", " << a.mQ[VZ] << ", " << a.mQ[VW]
+ << " }";
+ return s;
+}
+
+
+// Does NOT renormalize the result
+LLQuaternion operator*(const LLQuaternion &a, const LLQuaternion &b)
+{
+// LLQuaternion::mMultCount++;
+
+ LLQuaternion q(
+ b.mQ[3] * a.mQ[0] + b.mQ[0] * a.mQ[3] + b.mQ[1] * a.mQ[2] - b.mQ[2] * a.mQ[1],
+ b.mQ[3] * a.mQ[1] + b.mQ[1] * a.mQ[3] + b.mQ[2] * a.mQ[0] - b.mQ[0] * a.mQ[2],
+ b.mQ[3] * a.mQ[2] + b.mQ[2] * a.mQ[3] + b.mQ[0] * a.mQ[1] - b.mQ[1] * a.mQ[0],
+ b.mQ[3] * a.mQ[3] - b.mQ[0] * a.mQ[0] - b.mQ[1] * a.mQ[1] - b.mQ[2] * a.mQ[2]
+ );
+ return q;
+}
+
+/*
+LLMatrix4 operator*(const LLMatrix4 &m, const LLQuaternion &q)
+{
+ LLMatrix4 qmat(q);
+ return (m*qmat);
+}
+*/
+
+
+
+LLVector4 operator*(const LLVector4 &a, const LLQuaternion &rot)
+{
+ F32 rw = - rot.mQ[VX] * a.mV[VX] - rot.mQ[VY] * a.mV[VY] - rot.mQ[VZ] * a.mV[VZ];
+ F32 rx = rot.mQ[VW] * a.mV[VX] + rot.mQ[VY] * a.mV[VZ] - rot.mQ[VZ] * a.mV[VY];
+ F32 ry = rot.mQ[VW] * a.mV[VY] + rot.mQ[VZ] * a.mV[VX] - rot.mQ[VX] * a.mV[VZ];
+ F32 rz = rot.mQ[VW] * a.mV[VZ] + rot.mQ[VX] * a.mV[VY] - rot.mQ[VY] * a.mV[VX];
+
+ F32 nx = - rw * rot.mQ[VX] + rx * rot.mQ[VW] - ry * rot.mQ[VZ] + rz * rot.mQ[VY];
+ F32 ny = - rw * rot.mQ[VY] + ry * rot.mQ[VW] - rz * rot.mQ[VX] + rx * rot.mQ[VZ];
+ F32 nz = - rw * rot.mQ[VZ] + rz * rot.mQ[VW] - rx * rot.mQ[VY] + ry * rot.mQ[VX];
+
+ return LLVector4(nx, ny, nz, a.mV[VW]);
+}
+
+LLVector3 operator*(const LLVector3 &a, const LLQuaternion &rot)
+{
+ F32 rw = - rot.mQ[VX] * a.mV[VX] - rot.mQ[VY] * a.mV[VY] - rot.mQ[VZ] * a.mV[VZ];
+ F32 rx = rot.mQ[VW] * a.mV[VX] + rot.mQ[VY] * a.mV[VZ] - rot.mQ[VZ] * a.mV[VY];
+ F32 ry = rot.mQ[VW] * a.mV[VY] + rot.mQ[VZ] * a.mV[VX] - rot.mQ[VX] * a.mV[VZ];
+ F32 rz = rot.mQ[VW] * a.mV[VZ] + rot.mQ[VX] * a.mV[VY] - rot.mQ[VY] * a.mV[VX];
+
+ F32 nx = - rw * rot.mQ[VX] + rx * rot.mQ[VW] - ry * rot.mQ[VZ] + rz * rot.mQ[VY];
+ F32 ny = - rw * rot.mQ[VY] + ry * rot.mQ[VW] - rz * rot.mQ[VX] + rx * rot.mQ[VZ];
+ F32 nz = - rw * rot.mQ[VZ] + rz * rot.mQ[VW] - rx * rot.mQ[VY] + ry * rot.mQ[VX];
+
+ return LLVector3(nx, ny, nz);
+}
+
+LLVector3d operator*(const LLVector3d &a, const LLQuaternion &rot)
+{
+ F64 rw = - rot.mQ[VX] * a.mdV[VX] - rot.mQ[VY] * a.mdV[VY] - rot.mQ[VZ] * a.mdV[VZ];
+ F64 rx = rot.mQ[VW] * a.mdV[VX] + rot.mQ[VY] * a.mdV[VZ] - rot.mQ[VZ] * a.mdV[VY];
+ F64 ry = rot.mQ[VW] * a.mdV[VY] + rot.mQ[VZ] * a.mdV[VX] - rot.mQ[VX] * a.mdV[VZ];
+ F64 rz = rot.mQ[VW] * a.mdV[VZ] + rot.mQ[VX] * a.mdV[VY] - rot.mQ[VY] * a.mdV[VX];
+
+ F64 nx = - rw * rot.mQ[VX] + rx * rot.mQ[VW] - ry * rot.mQ[VZ] + rz * rot.mQ[VY];
+ F64 ny = - rw * rot.mQ[VY] + ry * rot.mQ[VW] - rz * rot.mQ[VX] + rx * rot.mQ[VZ];
+ F64 nz = - rw * rot.mQ[VZ] + rz * rot.mQ[VW] - rx * rot.mQ[VY] + ry * rot.mQ[VX];
+
+ return LLVector3d(nx, ny, nz);
+}
+
+F32 dot(const LLQuaternion &a, const LLQuaternion &b)
+{
+ return a.mQ[VX] * b.mQ[VX] +
+ a.mQ[VY] * b.mQ[VY] +
+ a.mQ[VZ] * b.mQ[VZ] +
+ a.mQ[VW] * b.mQ[VW];
+}
+
+// DEMO HACK: This lerp is probably inocrrect now due intermediate normalization
+// it should look more like the lerp below
+#if 0
+// linear interpolation
+LLQuaternion lerp(F32 t, const LLQuaternion &p, const LLQuaternion &q)
+{
+ LLQuaternion r;
+ r = t * (q - p) + p;
+ r.normalize();
+ return r;
+}
+#endif
+
+// lerp from identity to q
+LLQuaternion lerp(F32 t, const LLQuaternion &q)
+{
+ LLQuaternion r;
+ r.mQ[VX] = t * q.mQ[VX];
+ r.mQ[VY] = t * q.mQ[VY];
+ r.mQ[VZ] = t * q.mQ[VZ];
+ r.mQ[VW] = t * (q.mQ[VZ] - 1.f) + 1.f;
+ r.normalize();
+ return r;
+}
+
+LLQuaternion lerp(F32 t, const LLQuaternion &p, const LLQuaternion &q)
+{
+ LLQuaternion r;
+ F32 inv_t;
+
+ inv_t = 1.f - t;
+
+ r.mQ[VX] = t * q.mQ[VX] + (inv_t * p.mQ[VX]);
+ r.mQ[VY] = t * q.mQ[VY] + (inv_t * p.mQ[VY]);
+ r.mQ[VZ] = t * q.mQ[VZ] + (inv_t * p.mQ[VZ]);
+ r.mQ[VW] = t * q.mQ[VW] + (inv_t * p.mQ[VW]);
+ r.normalize();
+ return r;
+}
+
+
+// spherical linear interpolation
+LLQuaternion slerp( F32 u, const LLQuaternion &a, const LLQuaternion &b )
+{
+ // cosine theta = dot product of a and b
+ F32 cos_t = a.mQ[0]*b.mQ[0] + a.mQ[1]*b.mQ[1] + a.mQ[2]*b.mQ[2] + a.mQ[3]*b.mQ[3];
+
+ // if b is on opposite hemisphere from a, use -a instead
+ int bflip;
+ if (cos_t < 0.0f)
+ {
+ cos_t = -cos_t;
+ bflip = TRUE;
+ }
+ else
+ bflip = FALSE;
+
+ // if B is (within precision limits) the same as A,
+ // just linear interpolate between A and B.
+ F32 alpha; // interpolant
+ F32 beta; // 1 - interpolant
+ if (1.0f - cos_t < 0.00001f)
+ {
+ beta = 1.0f - u;
+ alpha = u;
+ }
+ else
+ {
+ F32 theta = acosf(cos_t);
+ F32 sin_t = sinf(theta);
+ beta = sinf(theta - u*theta) / sin_t;
+ alpha = sinf(u*theta) / sin_t;
+ }
+
+ if (bflip)
+ beta = -beta;
+
+ // interpolate
+ LLQuaternion ret;
+ ret.mQ[0] = beta*a.mQ[0] + alpha*b.mQ[0];
+ ret.mQ[1] = beta*a.mQ[1] + alpha*b.mQ[1];
+ ret.mQ[2] = beta*a.mQ[2] + alpha*b.mQ[2];
+ ret.mQ[3] = beta*a.mQ[3] + alpha*b.mQ[3];
+
+ return ret;
+}
+
+// lerp whenever possible
+LLQuaternion nlerp(F32 t, const LLQuaternion &a, const LLQuaternion &b)
+{
+ if (dot(a, b) < 0.f)
+ {
+ return slerp(t, a, b);
+ }
+ else
+ {
+ return lerp(t, a, b);
+ }
+}
+
+LLQuaternion nlerp(F32 t, const LLQuaternion &q)
+{
+ if (q.mQ[VW] < 0.f)
+ {
+ return slerp(t, q);
+ }
+ else
+ {
+ return lerp(t, q);
+ }
+}
+
+// slerp from identity quaternion to another quaternion
+LLQuaternion slerp(F32 t, const LLQuaternion &q)
+{
+ F32 c = q.mQ[VW];
+ if (1.0f == t || 1.0f == c)
+ {
+ // the trivial cases
+ return q;
+ }
+
+ LLQuaternion r;
+ F32 s, angle, stq, stp;
+
+ s = (F32) sqrt(1.f - c*c);
+
+ if (c < 0.0f)
+ {
+ // when c < 0.0 then theta > PI/2
+ // since quat and -quat are the same rotation we invert one of
+ // p or q to reduce unecessary spins
+ // A equivalent way to do it is to convert acos(c) as if it had
+ // been negative, and to negate stp
+ angle = (F32) acos(-c);
+ stp = -(F32) sin(angle * (1.f - t));
+ stq = (F32) sin(angle * t);
+ }
+ else
+ {
+ angle = (F32) acos(c);
+ stp = (F32) sin(angle * (1.f - t));
+ stq = (F32) sin(angle * t);
+ }
+
+ r.mQ[VX] = (q.mQ[VX] * stq) / s;
+ r.mQ[VY] = (q.mQ[VY] * stq) / s;
+ r.mQ[VZ] = (q.mQ[VZ] * stq) / s;
+ r.mQ[VW] = (stp + q.mQ[VW] * stq) / s;
+
+ return r;
+}
+
+LLQuaternion mayaQ(F32 xRot, F32 yRot, F32 zRot, LLQuaternion::Order order)
+{
+ LLQuaternion xQ( xRot*DEG_TO_RAD, LLVector3(1.0f, 0.0f, 0.0f) );
+ LLQuaternion yQ( yRot*DEG_TO_RAD, LLVector3(0.0f, 1.0f, 0.0f) );
+ LLQuaternion zQ( zRot*DEG_TO_RAD, LLVector3(0.0f, 0.0f, 1.0f) );
+ LLQuaternion ret;
+ switch( order )
+ {
+ case LLQuaternion::XYZ:
+ ret = xQ * yQ * zQ;
+ break;
+ case LLQuaternion::YZX:
+ ret = yQ * zQ * xQ;
+ break;
+ case LLQuaternion::ZXY:
+ ret = zQ * xQ * yQ;
+ break;
+ case LLQuaternion::XZY:
+ ret = xQ * zQ * yQ;
+ break;
+ case LLQuaternion::YXZ:
+ ret = yQ * xQ * zQ;
+ break;
+ case LLQuaternion::ZYX:
+ ret = zQ * yQ * xQ;
+ break;
+ }
+ return ret;
+}
+
+const char *OrderToString( const LLQuaternion::Order order )
+{
+ const char *p = NULL;
+ switch( order )
+ {
+ default:
+ case LLQuaternion::XYZ:
+ p = "XYZ";
+ break;
+ case LLQuaternion::YZX:
+ p = "YZX";
+ break;
+ case LLQuaternion::ZXY:
+ p = "ZXY";
+ break;
+ case LLQuaternion::XZY:
+ p = "XZY";
+ break;
+ case LLQuaternion::YXZ:
+ p = "YXZ";
+ break;
+ case LLQuaternion::ZYX:
+ p = "ZYX";
+ break;
+ }
+ return p;
+}
+
+LLQuaternion::Order StringToOrder( const char *str )
+{
+ if (strncmp(str, "XYZ", 3)==0 || strncmp(str, "xyz", 3)==0)
+ return LLQuaternion::XYZ;
+
+ if (strncmp(str, "YZX", 3)==0 || strncmp(str, "yzx", 3)==0)
+ return LLQuaternion::YZX;
+
+ if (strncmp(str, "ZXY", 3)==0 || strncmp(str, "zxy", 3)==0)
+ return LLQuaternion::ZXY;
+
+ if (strncmp(str, "XZY", 3)==0 || strncmp(str, "xzy", 3)==0)
+ return LLQuaternion::XZY;
+
+ if (strncmp(str, "YXZ", 3)==0 || strncmp(str, "yxz", 3)==0)
+ return LLQuaternion::YXZ;
+
+ if (strncmp(str, "ZYX", 3)==0 || strncmp(str, "zyx", 3)==0)
+ return LLQuaternion::ZYX;
+
+ return LLQuaternion::XYZ;
+}
+
+void LLQuaternion::getAngleAxis(F32* angle, LLVector3 &vec) const
+{
+ F32 cos_a = mQ[VW];
+ if (cos_a > 1.0f) cos_a = 1.0f;
+ if (cos_a < -1.0f) cos_a = -1.0f;
+
+ F32 sin_a = (F32) sqrt( 1.0f - cos_a * cos_a );
+
+ if ( fabs( sin_a ) < 0.0005f )
+ sin_a = 1.0f;
+ else
+ sin_a = 1.f/sin_a;
+
+ F32 temp_angle = 2.0f * (F32) acos( cos_a );
+ if (temp_angle > F_PI)
+ {
+ // The (angle,axis) pair should never have angles outside [PI, -PI]
+ // since we want the _shortest_ (angle,axis) solution.
+ // Since acos is defined for [0, PI], and we multiply by 2.0, we
+ // can push the angle outside the acceptible range.
+ // When this happens we set the angle to the other portion of a
+ // full 2PI rotation, and negate the axis, which reverses the
+ // direction of the rotation (by the right-hand rule).
+ *angle = 2.f * F_PI - temp_angle;
+ vec.mV[VX] = - mQ[VX] * sin_a;
+ vec.mV[VY] = - mQ[VY] * sin_a;
+ vec.mV[VZ] = - mQ[VZ] * sin_a;
+ }
+ else
+ {
+ *angle = temp_angle;
+ vec.mV[VX] = mQ[VX] * sin_a;
+ vec.mV[VY] = mQ[VY] * sin_a;
+ vec.mV[VZ] = mQ[VZ] * sin_a;
+ }
+}
+
+
+// quaternion does not need to be normalized
+void LLQuaternion::getEulerAngles(F32 *roll, F32 *pitch, F32 *yaw) const
+{
+ LLMatrix3 rot_mat(*this);
+ rot_mat.orthogonalize();
+ rot_mat.getEulerAngles(roll, pitch, yaw);
+
+// // NOTE: LLQuaternion's are actually inverted with respect to
+// // the matrices, so this code also assumes inverted quaternions
+// // (-x, -y, -z, w). The result is that roll,pitch,yaw are applied
+// // in reverse order (yaw,pitch,roll).
+// F32 x = -mQ[VX], y = -mQ[VY], z = -mQ[VZ], w = mQ[VW];
+// F64 m20 = 2.0*(x*z-y*w);
+// if (1.0f - fabsf(m20) < F_APPROXIMATELY_ZERO)
+// {
+// *roll = 0.0f;
+// *pitch = (F32)asin(m20);
+// *yaw = (F32)atan2(2.0*(x*y-z*w), 1.0 - 2.0*(x*x+z*z));
+// }
+// else
+// {
+// *roll = (F32)atan2(-2.0*(y*z+x*w), 1.0-2.0*(x*x+y*y));
+// *pitch = (F32)asin(m20);
+// *yaw = (F32)atan2(-2.0*(x*y+z*w), 1.0-2.0*(y*y+z*z));
+// }
+}
+
+// Saves space by using the fact that our quaternions are normalized
+LLVector3 LLQuaternion::packToVector3() const
+{
+ if( mQ[VW] >= 0 )
+ {
+ return LLVector3( mQ[VX], mQ[VY], mQ[VZ] );
+ }
+ else
+ {
+ return LLVector3( -mQ[VX], -mQ[VY], -mQ[VZ] );
+ }
+}
+
+// Saves space by using the fact that our quaternions are normalized
+void LLQuaternion::unpackFromVector3( const LLVector3& vec )
+{
+ mQ[VX] = vec.mV[VX];
+ mQ[VY] = vec.mV[VY];
+ mQ[VZ] = vec.mV[VZ];
+ F32 t = 1.f - vec.magVecSquared();
+ if( t > 0 )
+ {
+ mQ[VW] = sqrt( t );
+ }
+ else
+ {
+ // Need this to avoid trying to find the square root of a negative number due
+ // to floating point error.
+ mQ[VW] = 0;
+ }
+}
+
+BOOL LLQuaternion::parseQuat(const std::string& buf, LLQuaternion* value)
+{
+ if( buf.empty() || value == NULL)
+ {
+ return FALSE;
+ }
+
+ LLQuaternion quat;
+ S32 count = sscanf( buf.c_str(), "%f %f %f %f", quat.mQ + 0, quat.mQ + 1, quat.mQ + 2, quat.mQ + 3 );
+ if( 4 == count )
+ {
+ value->set( quat );
+ return TRUE;
+ }
+
+ return FALSE;
+}
+
+
+// End
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