962 lines
23 KiB
C++
962 lines
23 KiB
C++
/**
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* @file llquaternion.cpp
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* @brief LLQuaternion class implementation.
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*
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* $LicenseInfo:firstyear=2000&license=viewergpl$
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*
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* Copyright (c) 2000-2009, Linden Research, Inc.
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*
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* Second Life Viewer Source Code
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* The source code in this file ("Source Code") is provided by Linden Lab
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* to you under the terms of the GNU General Public License, version 2.0
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* ("GPL"), unless you have obtained a separate licensing agreement
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* ("Other License"), formally executed by you and Linden Lab. Terms of
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* the GPL can be found in doc/GPL-license.txt in this distribution, or
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* online at http://secondlifegrid.net/programs/open_source/licensing/gplv2
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*
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* There are special exceptions to the terms and conditions of the GPL as
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* it is applied to this Source Code. View the full text of the exception
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* in the file doc/FLOSS-exception.txt in this software distribution, or
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* online at
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* http://secondlifegrid.net/programs/open_source/licensing/flossexception
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*
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* By copying, modifying or distributing this software, you acknowledge
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* that you have read and understood your obligations described above,
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* and agree to abide by those obligations.
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*
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* ALL LINDEN LAB SOURCE CODE IS PROVIDED "AS IS." LINDEN LAB MAKES NO
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* WARRANTIES, EXPRESS, IMPLIED OR OTHERWISE, REGARDING ITS ACCURACY,
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* COMPLETENESS OR PERFORMANCE.
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* $/LicenseInfo$
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*/
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#include "linden_common.h"
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#include "llmath.h" // for F_PI
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#include "llquaternion.h"
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//#include "vmath.h"
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#include "v3math.h"
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#include "v3dmath.h"
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#include "v4math.h"
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#include "m4math.h"
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#include "m3math.h"
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#include "llquantize.h"
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// WARNING: Don't use this for global const definitions! using this
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// at the top of a *.cpp file might not give you what you think.
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const LLQuaternion LLQuaternion::DEFAULT;
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// Constructors
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LLQuaternion::LLQuaternion(const LLMatrix4 &mat)
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{
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*this = mat.quaternion();
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normalize();
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}
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LLQuaternion::LLQuaternion(const LLMatrix3 &mat)
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{
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*this = mat.quaternion();
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normalize();
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}
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LLQuaternion::LLQuaternion(F32 angle, const LLVector4 &vec)
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{
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LLVector3 v(vec.mV[VX], vec.mV[VY], vec.mV[VZ]);
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v.normalize();
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F32 c, s;
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c = cosf(angle*0.5f);
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s = sinf(angle*0.5f);
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mQ[VX] = v.mV[VX] * s;
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mQ[VY] = v.mV[VY] * s;
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mQ[VZ] = v.mV[VZ] * s;
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mQ[VW] = c;
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normalize();
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}
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LLQuaternion::LLQuaternion(F32 angle, const LLVector3 &vec)
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{
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LLVector3 v(vec);
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v.normalize();
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F32 c, s;
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c = cosf(angle*0.5f);
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s = sinf(angle*0.5f);
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mQ[VX] = v.mV[VX] * s;
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mQ[VY] = v.mV[VY] * s;
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mQ[VZ] = v.mV[VZ] * s;
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mQ[VW] = c;
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normalize();
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}
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LLQuaternion::LLQuaternion(const LLVector3 &x_axis,
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const LLVector3 &y_axis,
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const LLVector3 &z_axis)
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{
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LLMatrix3 mat;
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mat.setRows(x_axis, y_axis, z_axis);
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*this = mat.quaternion();
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normalize();
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}
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// Quatizations
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void LLQuaternion::quantize16(F32 lower, F32 upper)
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{
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F32 x = mQ[VX];
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F32 y = mQ[VY];
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F32 z = mQ[VZ];
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F32 s = mQ[VS];
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x = U16_to_F32(F32_to_U16_ROUND(x, lower, upper), lower, upper);
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y = U16_to_F32(F32_to_U16_ROUND(y, lower, upper), lower, upper);
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z = U16_to_F32(F32_to_U16_ROUND(z, lower, upper), lower, upper);
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s = U16_to_F32(F32_to_U16_ROUND(s, lower, upper), lower, upper);
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mQ[VX] = x;
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mQ[VY] = y;
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mQ[VZ] = z;
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mQ[VS] = s;
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normalize();
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}
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void LLQuaternion::quantize8(F32 lower, F32 upper)
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{
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mQ[VX] = U8_to_F32(F32_to_U8_ROUND(mQ[VX], lower, upper), lower, upper);
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mQ[VY] = U8_to_F32(F32_to_U8_ROUND(mQ[VY], lower, upper), lower, upper);
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mQ[VZ] = U8_to_F32(F32_to_U8_ROUND(mQ[VZ], lower, upper), lower, upper);
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mQ[VS] = U8_to_F32(F32_to_U8_ROUND(mQ[VS], lower, upper), lower, upper);
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normalize();
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}
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// LLVector3 Magnitude and Normalization Functions
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// Set LLQuaternion routines
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const LLQuaternion& LLQuaternion::setAngleAxis(F32 angle, F32 x, F32 y, F32 z)
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{
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LLVector3 vec(x, y, z);
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vec.normalize();
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angle *= 0.5f;
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F32 c, s;
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c = cosf(angle);
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s = sinf(angle);
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mQ[VX] = vec.mV[VX]*s;
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mQ[VY] = vec.mV[VY]*s;
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mQ[VZ] = vec.mV[VZ]*s;
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mQ[VW] = c;
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normalize();
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return (*this);
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}
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const LLQuaternion& LLQuaternion::setAngleAxis(F32 angle, const LLVector3 &vec)
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{
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LLVector3 v(vec);
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v.normalize();
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angle *= 0.5f;
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F32 c, s;
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c = cosf(angle);
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s = sinf(angle);
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mQ[VX] = v.mV[VX]*s;
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mQ[VY] = v.mV[VY]*s;
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mQ[VZ] = v.mV[VZ]*s;
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mQ[VW] = c;
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normalize();
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return (*this);
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}
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const LLQuaternion& LLQuaternion::setAngleAxis(F32 angle, const LLVector4 &vec)
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{
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LLVector3 v(vec.mV[VX], vec.mV[VY], vec.mV[VZ]);
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v.normalize();
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F32 c, s;
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c = cosf(angle*0.5f);
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s = sinf(angle*0.5f);
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mQ[VX] = v.mV[VX]*s;
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mQ[VY] = v.mV[VY]*s;
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mQ[VZ] = v.mV[VZ]*s;
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mQ[VW] = c;
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normalize();
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return (*this);
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}
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const LLQuaternion& LLQuaternion::setEulerAngles(F32 roll, F32 pitch, F32 yaw)
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{
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LLMatrix3 rot_mat(roll, pitch, yaw);
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rot_mat.orthogonalize();
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*this = rot_mat.quaternion();
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normalize();
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return (*this);
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}
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// deprecated
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const LLQuaternion& LLQuaternion::set(const LLMatrix3 &mat)
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{
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*this = mat.quaternion();
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normalize();
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return (*this);
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}
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// deprecated
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const LLQuaternion& LLQuaternion::set(const LLMatrix4 &mat)
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{
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*this = mat.quaternion();
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normalize();
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return (*this);
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}
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// deprecated
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const LLQuaternion& LLQuaternion::setQuat(F32 angle, F32 x, F32 y, F32 z)
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{
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LLVector3 vec(x, y, z);
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vec.normalize();
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angle *= 0.5f;
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F32 c, s;
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c = cosf(angle);
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s = sinf(angle);
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mQ[VX] = vec.mV[VX]*s;
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mQ[VY] = vec.mV[VY]*s;
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mQ[VZ] = vec.mV[VZ]*s;
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mQ[VW] = c;
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normalize();
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return (*this);
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}
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// deprecated
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const LLQuaternion& LLQuaternion::setQuat(F32 angle, const LLVector3 &vec)
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{
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LLVector3 v(vec);
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v.normalize();
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angle *= 0.5f;
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F32 c, s;
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c = cosf(angle);
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s = sinf(angle);
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mQ[VX] = v.mV[VX]*s;
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mQ[VY] = v.mV[VY]*s;
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mQ[VZ] = v.mV[VZ]*s;
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mQ[VW] = c;
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normalize();
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return (*this);
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}
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const LLQuaternion& LLQuaternion::setQuat(F32 angle, const LLVector4 &vec)
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{
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LLVector3 v(vec.mV[VX], vec.mV[VY], vec.mV[VZ]);
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v.normalize();
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F32 c, s;
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c = cosf(angle*0.5f);
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s = sinf(angle*0.5f);
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mQ[VX] = v.mV[VX]*s;
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mQ[VY] = v.mV[VY]*s;
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mQ[VZ] = v.mV[VZ]*s;
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mQ[VW] = c;
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normalize();
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return (*this);
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}
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const LLQuaternion& LLQuaternion::setQuat(F32 roll, F32 pitch, F32 yaw)
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{
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LLMatrix3 rot_mat(roll, pitch, yaw);
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rot_mat.orthogonalize();
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*this = rot_mat.quaternion();
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normalize();
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return (*this);
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}
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const LLQuaternion& LLQuaternion::setQuat(const LLMatrix3 &mat)
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{
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*this = mat.quaternion();
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normalize();
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return (*this);
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}
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const LLQuaternion& LLQuaternion::setQuat(const LLMatrix4 &mat)
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{
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*this = mat.quaternion();
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normalize();
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return (*this);
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//#if 1
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// // NOTE: LLQuaternion's are actually inverted with respect to
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// // the matrices, so this code also assumes inverted quaternions
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// // (-x, -y, -z, w). The result is that roll,pitch,yaw are applied
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// // in reverse order (yaw,pitch,roll).
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// F64 cosX = cos(roll);
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// F64 cosY = cos(pitch);
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// F64 cosZ = cos(yaw);
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//
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// F64 sinX = sin(roll);
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// F64 sinY = sin(pitch);
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// F64 sinZ = sin(yaw);
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//
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// mQ[VW] = (F32)sqrt(cosY*cosZ - sinX*sinY*sinZ + cosX*cosZ + cosX*cosY + 1.0)*.5;
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// if (fabs(mQ[VW]) < F_APPROXIMATELY_ZERO)
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// {
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// // null rotation, any axis will do
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// mQ[VX] = 0.0f;
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// mQ[VY] = 1.0f;
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// mQ[VZ] = 0.0f;
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// }
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// else
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// {
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// F32 inv_s = 1.0f / (4.0f * mQ[VW]);
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// mQ[VX] = (F32)-(-sinX*cosY - cosX*sinY*sinZ - sinX*cosZ) * inv_s;
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// mQ[VY] = (F32)-(-cosX*sinY*cosZ + sinX*sinZ - sinY) * inv_s;
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// mQ[VZ] = (F32)-(-cosY*sinZ - sinX*sinY*cosZ - cosX*sinZ) * inv_s;
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// }
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//
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//#else // This only works on a certain subset of roll/pitch/yaw
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//
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// F64 cosX = cosf(roll/2.0);
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// F64 cosY = cosf(pitch/2.0);
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// F64 cosZ = cosf(yaw/2.0);
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//
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// F64 sinX = sinf(roll/2.0);
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// F64 sinY = sinf(pitch/2.0);
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// F64 sinZ = sinf(yaw/2.0);
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//
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// mQ[VW] = (F32)(cosX*cosY*cosZ + sinX*sinY*sinZ);
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// mQ[VX] = (F32)(sinX*cosY*cosZ - cosX*sinY*sinZ);
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// mQ[VY] = (F32)(cosX*sinY*cosZ + sinX*cosY*sinZ);
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// mQ[VZ] = (F32)(cosX*cosY*sinZ - sinX*sinY*cosZ);
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//#endif
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//
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// normalize();
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// return (*this);
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}
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// SJB: This code is correct for a logicly stored (non-transposed) matrix;
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// Our matrices are stored transposed, OpenGL style, so this generates the
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// INVERSE matrix, or the CORRECT matrix form an INVERSE quaternion.
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// Because we use similar logic in LLMatrix3::quaternion(),
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// we are internally consistant so everything works OK :)
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LLMatrix3 LLQuaternion::getMatrix3(void) const
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{
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LLMatrix3 mat;
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F32 xx, xy, xz, xw, yy, yz, yw, zz, zw;
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xx = mQ[VX] * mQ[VX];
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xy = mQ[VX] * mQ[VY];
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xz = mQ[VX] * mQ[VZ];
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xw = mQ[VX] * mQ[VW];
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yy = mQ[VY] * mQ[VY];
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yz = mQ[VY] * mQ[VZ];
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yw = mQ[VY] * mQ[VW];
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zz = mQ[VZ] * mQ[VZ];
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zw = mQ[VZ] * mQ[VW];
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mat.mMatrix[0][0] = 1.f - 2.f * ( yy + zz );
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mat.mMatrix[0][1] = 2.f * ( xy + zw );
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mat.mMatrix[0][2] = 2.f * ( xz - yw );
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mat.mMatrix[1][0] = 2.f * ( xy - zw );
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mat.mMatrix[1][1] = 1.f - 2.f * ( xx + zz );
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mat.mMatrix[1][2] = 2.f * ( yz + xw );
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mat.mMatrix[2][0] = 2.f * ( xz + yw );
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mat.mMatrix[2][1] = 2.f * ( yz - xw );
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mat.mMatrix[2][2] = 1.f - 2.f * ( xx + yy );
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return mat;
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}
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LLMatrix4 LLQuaternion::getMatrix4(void) const
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{
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LLMatrix4 mat;
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F32 xx, xy, xz, xw, yy, yz, yw, zz, zw;
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xx = mQ[VX] * mQ[VX];
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xy = mQ[VX] * mQ[VY];
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xz = mQ[VX] * mQ[VZ];
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xw = mQ[VX] * mQ[VW];
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yy = mQ[VY] * mQ[VY];
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yz = mQ[VY] * mQ[VZ];
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yw = mQ[VY] * mQ[VW];
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zz = mQ[VZ] * mQ[VZ];
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zw = mQ[VZ] * mQ[VW];
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mat.mMatrix[0][0] = 1.f - 2.f * ( yy + zz );
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mat.mMatrix[0][1] = 2.f * ( xy + zw );
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mat.mMatrix[0][2] = 2.f * ( xz - yw );
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mat.mMatrix[1][0] = 2.f * ( xy - zw );
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mat.mMatrix[1][1] = 1.f - 2.f * ( xx + zz );
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mat.mMatrix[1][2] = 2.f * ( yz + xw );
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mat.mMatrix[2][0] = 2.f * ( xz + yw );
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mat.mMatrix[2][1] = 2.f * ( yz - xw );
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mat.mMatrix[2][2] = 1.f - 2.f * ( xx + yy );
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// TODO -- should we set the translation portion to zero?
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return mat;
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}
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// Other useful methods
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// calculate the shortest rotation from a to b
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void LLQuaternion::shortestArc(const LLVector3 &a, const LLVector3 &b)
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{
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// Make a local copy of both vectors.
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LLVector3 vec_a = a;
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LLVector3 vec_b = b;
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// Make sure neither vector is zero length. Also normalize
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// the vectors while we are at it.
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F32 vec_a_mag = vec_a.normalize();
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F32 vec_b_mag = vec_b.normalize();
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if (vec_a_mag < F_APPROXIMATELY_ZERO ||
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vec_b_mag < F_APPROXIMATELY_ZERO)
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{
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// Can't calculate a rotation from this.
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// Just return ZERO_ROTATION instead.
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loadIdentity();
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return;
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}
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// Create an axis to rotate around, and the cos of the angle to rotate.
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LLVector3 axis = vec_a % vec_b;
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F32 cos_theta = vec_a * vec_b;
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// Check the angle between the vectors to see if they are parallel or anti-parallel.
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if (cos_theta > 1.0 - F_APPROXIMATELY_ZERO)
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{
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// a and b are parallel. No rotation is necessary.
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loadIdentity();
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}
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else if (cos_theta < -1.0 + F_APPROXIMATELY_ZERO)
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{
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// a and b are anti-parallel.
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// Rotate 180 degrees around some orthogonal axis.
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// Find the projection of the x-axis onto a, and try
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// using the vector between the projection and the x-axis
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// as the orthogonal axis.
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LLVector3 proj = vec_a.mV[VX] / (vec_a * vec_a) * vec_a;
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LLVector3 ortho_axis(1.f, 0.f, 0.f);
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ortho_axis -= proj;
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// Turn this into an orthonormal axis.
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F32 ortho_length = ortho_axis.normalize();
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// If the axis' length is 0, then our guess at an orthogonal axis
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// was wrong (a is parallel to the x-axis).
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if (ortho_length < F_APPROXIMATELY_ZERO)
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{
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// Use the z-axis instead.
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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
|