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647 lines
32 KiB
C
647 lines
32 KiB
C
/*
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* Data structures for Quaternions
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* See http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Hamilton.html
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*
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* Copyright (c) Criterion Software Limited
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*/
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#ifndef RTQUAT_H
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#define RTQUAT_H
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/**
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* \defgroup rtquat RtQuat
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* \ingroup rttool
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*
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* Quaternion Toolkit for RenderWare.
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*
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* See also http://www.gamasutra.com/features/19980703/quaternions_01.htm
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*/
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/*
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* See http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Hamilton.html
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* On 16 October 1843 (a Monday) Hamilton was walking in along the Royal
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* Canal with his wife to preside at a Council meeting of the Royal Irish
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* Academy.
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*
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* Although his wife talked to him now and again Hamilton hardly
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* heard, for the discovery of the quaternions, the first noncommutative
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* algebra to be studied, was taking shape in his mind:-
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*
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* "And here there dawned on me the notion that we must admit, in
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* some sense, a fourth dimension of space for the purpose of calculating
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* with triples ... An electric circuit seemed to close, and a spark
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* flashed forth."
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*/
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/****************************************************************************
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Includes
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*/
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#include <math.h>
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/* renderware */
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#include "rwcore.h"
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#include "rtquat.rpe" /* automatically generated header file */
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#define RW_TOL_ORTHONORMAL ((RwReal)0.01)
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/****************************************************************************
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Global Types
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*/
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typedef struct RtQuat RtQuat;
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/**
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* \ingroup rtquat
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* \struct RtQuat
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* A structure describing a Quaternion
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*
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*/
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struct RtQuat
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{
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RwV3d imag; /**< The imaginary part(s) */
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RwReal real; /**< The real part */
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};
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/****************************************************************************
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Defines
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*/
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#define RtQuatInitMacro( result, _x, _y, _z, _w) \
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MACRO_START \
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{ \
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(result)->real = (_w); \
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(result)->imag.x = (_x); \
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(result)->imag.y = (_y); \
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(result)->imag.z = (_z); \
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} \
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MACRO_STOP
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#if (!defined(RtQuatAssignMacro))
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#define RtQuatAssignMacro(_target, _source) \
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( *(_target) = *(_source) )
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#endif /* (!defined(RtQuatAssignMacro)) */
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#define RtQuatAddMacro( result, q1, q2 ) \
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MACRO_START \
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{ \
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(result)->real = (q1)->real + (q2)->real; \
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RwV3dAddMacro(&(result)->imag, &(q1)->imag, &(q2)->imag); \
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} \
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MACRO_STOP
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#define RtQuatIncrementRealPartMacro(result, s, q) \
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MACRO_START \
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{ \
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(result)->real = (q)->real + s; \
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(result)->imag.x = (q)->imag.x; \
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(result)->imag.y = (q)->imag.y; \
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(result)->imag.z = (q)->imag.z; \
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} \
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MACRO_STOP
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#define RtQuatDecrementRealPartMacro(result, s, q) \
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MACRO_START \
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{ \
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(result)->real = (q)->real - s; \
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(result)->imag.x = (q)->imag.x; \
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(result)->imag.y = (q)->imag.y; \
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(result)->imag.z = (q)->imag.z; \
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} \
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MACRO_STOP
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#define RtQuatIncrementMacro( result, dq ) \
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MACRO_START \
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{ \
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(result)->real = (result)->real + (dq)->real; \
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RwV3dAddMacro(&(result)->imag, &(result)->imag, &(dq)->imag); \
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} \
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MACRO_STOP
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#define RtQuatSubMacro( result, q1, q2 ) \
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MACRO_START \
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{ \
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(result)->real = (q1)->real - (q2)->real; \
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RwV3dSubMacro(&(result)->imag, &(q1)->imag, &(q2)->imag); \
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} \
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MACRO_STOP
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#define RtQuatNegateMacro( result, q ) \
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MACRO_START \
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{ \
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(result)->real = -(q)->real; \
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(result)->imag.x = -(q)->imag.x; \
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(result)->imag.y = -(q)->imag.y; \
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(result)->imag.z = -(q)->imag.z; \
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} \
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MACRO_STOP
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#define RtQuatConjugateMacro( result, q) \
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MACRO_START \
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{ \
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(result)->real = (q)->real; \
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(result)->imag.x = -(q)->imag.x; \
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(result)->imag.y = -(q)->imag.y; \
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(result)->imag.z = -(q)->imag.z; \
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} \
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MACRO_STOP
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#define RtQuatScaleMacro(result, q, scale ) \
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MACRO_START \
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{ \
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(result)->real = (q)->real * scale; \
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RwV3dScaleMacro(&(result)->imag, &(q)->imag, scale); \
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} \
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MACRO_STOP
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#define RtQuatModulusSquaredMacro( q ) \
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((q)->real * (q)->real + \
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RwV3dDotProductMacro(&(q)->imag, &(q)->imag))
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#define RtQuatModulusMacro( result, q ) \
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MACRO_START \
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{ \
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(result) = RtQuatModulusSquaredMacro(q); \
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rwSqrtMacro(&result, result); \
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} \
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MACRO_STOP
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#define RtQuatMultiplyMacro( result, q1, q2) \
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MACRO_START \
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{ \
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/* \
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* Assumes q1 != result != q2 \
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*/ \
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(result)->real = \
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(q1)->real * (q2)->real - \
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RwV3dDotProductMacro(&(q1)->imag,&(q2)->imag); \
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RwV3dCrossProductMacro(&(result)->imag, &(q1)->imag, &(q2)->imag); \
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RwV3dIncrementScaledMacro(&(result)->imag, &(q2)->imag, (q1)->real); \
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RwV3dIncrementScaledMacro(&(result)->imag, &(q1)->imag, (q2)->real); \
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} \
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MACRO_STOP
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#define RtQuatReciprocalMacro( result, q) \
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MACRO_START \
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{ \
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/* \
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* Assumes result != q \
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*/ \
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RwReal val = RtQuatModulusSquaredMacro(q); \
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\
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if (val > (RwReal) 0) \
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{ \
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val = ((RwReal)1) / val; \
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(result)->real = (q)->real * val; \
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val = -val; \
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RwV3dScaleMacro(&(result)->imag, &(q)->imag, val); \
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} \
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} \
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MACRO_STOP
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#define RtQuatSquareMacro( result, q ) \
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MACRO_START \
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{ \
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/* \
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* Assumes result != q \
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*/ \
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RwReal val = ((RwReal)2) * (q)->real ; \
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\
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(result)->real = \
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(q)->real * (q)->real - \
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RwV3dDotProductMacro(&(q)->imag, &(q)->imag); \
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RwV3dScaleMacro(&(result)->imag, &(q)->imag, val); \
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} \
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MACRO_STOP
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#define RtQuatSquareRootMacro( result, q ) \
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MACRO_START \
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{ \
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/* \
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* Assumes result != q \
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* other root is of course -result \
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*/ \
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RwReal val; \
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\
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RtQuatModulusMacro(val,q); \
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val = ((q)->real + val) * ((RwReal) 0.5); \
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\
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if (val > ((RwReal)0)) \
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{ \
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rwSqrtMacro(&val, val); \
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(result)->real = val; \
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val = ((RwReal)0.5) / val; \
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RwV3dScale(&(result)->imag, &(q)->imag, val); \
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} \
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else \
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{ \
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result->imag.x = -(q)->real; \
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rwSqrtMacro(&(result->imag.x), result->imag.x); \
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result->imag.y = ((RwReal)0); \
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result->imag.x = ((RwReal)0); \
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result->real = ((RwReal)0); \
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} \
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} \
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MACRO_STOP
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#define RtQuatLogMacro(result, q) \
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MACRO_START \
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{ \
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/* \
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* Assumes result != q \
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*/ \
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const RwReal mod2 = RtQuatModulusSquaredMacro(q); \
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RwReal sin_b; \
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RwReal radians; \
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RwReal factor; \
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\
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sin_b = RwV3dDotProduct(&(q)->imag, &(q)->imag); \
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rwSqrtMacro(&sin_b, sin_b); \
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radians = (RwReal) RwATan2(sin_b, (q)->real); \
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factor = (sin_b > (RwReal) 0) ? (((RwReal)radians) / sin_b) : 0 ; \
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\
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RwV3dScaleMacro(&(result)->imag, &(q)->imag, factor); \
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(result)->real = ((RwReal) RwLog(mod2)) * ((RwReal) 0.5); \
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\
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} \
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MACRO_STOP
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#define RtQuatExpMacro(result, q) \
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MACRO_START \
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{ \
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/* \
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* Assumes result != q \
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*/ \
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const RwReal exp_a = (RwReal)RwExp((q)->real); \
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RwReal mod_b; \
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RwReal factor; \
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\
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mod_b = RwV3dDotProduct(&(q)->imag, &(q)->imag); \
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rwSqrtMacro(&mod_b, mod_b); \
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factor = ( (mod_b > (RwReal) 0) ? \
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(exp_a * ((RwReal)RwSin(mod_b)) / mod_b) : \
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0 ) ; \
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\
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RwV3dScaleMacro(&(result)->imag, &(q)->imag, factor); \
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(result)->real = exp_a * (RwReal)RwCos(mod_b); \
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} \
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MACRO_STOP
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#define RtQuatPowMacro( result, q, e) \
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MACRO_START \
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{ \
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RtQuat qLog; \
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\
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RtQuatLogMacro(&qLog, q); \
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RtQuatScaleMacro(&qLog, &qLog, e); \
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RtQuatExpMacro(result, &qLog); \
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} \
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MACRO_STOP
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#define RtQuatUnitLogMacro(result, q) \
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MACRO_START \
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{ \
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/* \
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* Assumes result != q \
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*/ \
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RwReal sin_b ; \
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RwReal radians ; \
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RwReal factor ; \
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\
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sin_b = RwV3dDotProduct(&(q)->imag, &(q)->imag); \
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rwSqrtMacro(&sin_b, sin_b); \
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radians = (RwReal)RwATan2(sin_b, (q)->real); \
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factor = (sin_b > (RwReal) 0) ? (((RwReal)radians) / sin_b) : 0 ; \
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\
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RwV3dScaleMacro(&(result)->imag, &(q)->imag, factor); \
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(result)->real = (RwReal)0; \
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\
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} \
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MACRO_STOP
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#define RtQuatUnitExpMacro(result, q) \
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MACRO_START \
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{ \
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/* \
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* Assumes result != q \
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*/ \
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RwReal mod_b; \
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RwReal factor; \
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\
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mod_b = RwV3dDotProduct(&(q)->imag, &(q)->imag); \
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rwSqrtMacro(&mod_b, mod_b); \
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factor = (mod_b > (RwReal) 0) ? (((RwReal)RwSin(mod_b)) / mod_b) : 0 ; \
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\
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RwV3dScaleMacro(&(result)->imag, &(q)->imag, factor); \
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(result)->real = (RwReal)RwCos(mod_b); \
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\
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} \
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MACRO_STOP
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#define RtQuatUnitPowMacro( result, q, e) \
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MACRO_START \
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{ \
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RtQuat qLog; \
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\
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RtQuatUnitLogMacro(&qLog, q); \
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RwV3dScaleMacro(&qLog.imag, &qLog.imag, e); \
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RtQuatUnitExpMacro(result, &qLog); \
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} \
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MACRO_STOP
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#define RtQuatConvertToMatrixMacro(qpQuat, mpMatrix) \
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MACRO_START \
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{ \
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RwReal rS; \
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RwV3d rV; \
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RwV3d rW; \
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RwV3d square; \
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RwV3d cross; \
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\
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rS = ((RwReal) 2) / RtQuatModulusSquaredMacro((qpQuat)); \
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\
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RwV3dScale(&rV, &(qpQuat)->imag, rS); \
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RwV3dScale(&rW, &rV, (qpQuat)->real); \
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\
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square.x = (qpQuat)->imag.x * rV.x; \
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square.y = (qpQuat)->imag.y * rV.y; \
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square.z = (qpQuat)->imag.z * rV.z; \
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\
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cross.x = (qpQuat)->imag.y * rV.z; \
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cross.y = (qpQuat)->imag.z * rV.x; \
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cross.z = (qpQuat)->imag.x * rV.y; \
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\
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(mpMatrix)->right.x = ((RwReal) 1) - (square.y + square.z); \
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(mpMatrix)->right.y = cross.z + rW.z; \
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(mpMatrix)->right.z = cross.y - rW.y; \
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\
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(mpMatrix)->up.x = cross.z - rW.z; \
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(mpMatrix)->up.y = ((RwReal) 1) - (square.z + square.x); \
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(mpMatrix)->up.z = cross.x + rW.x; \
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\
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(mpMatrix)->at.x = cross.y + rW.y; \
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(mpMatrix)->at.y = cross.x - rW.x; \
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(mpMatrix)->at.z = ((RwReal) 1) - (square.x + square.y); \
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\
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/* Set position */ \
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(mpMatrix)->pos.x = ((RwReal) 0); \
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(mpMatrix)->pos.y = ((RwReal) 0); \
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(mpMatrix)->pos.z = ((RwReal) 0); \
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\
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/* Matrix is orthogonal */ \
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rwMatrixSetFlags((mpMatrix), \
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(rwMATRIXTYPEORTHOGANAL & \
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~rwMATRIXINTERNALIDENTITY) ); \
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\
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} \
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MACRO_STOP
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#define RtQuatUnitConvertToMatrixMacro(qpQuat, mpMatrix) \
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MACRO_START \
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{ \
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const RwReal x = (qpQuat)->imag.x; \
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const RwReal y = (qpQuat)->imag.y; \
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const RwReal z = (qpQuat)->imag.z; \
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const RwReal w = (qpQuat)->real; \
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RwV3d square; \
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RwV3d cross; \
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RwV3d wimag; \
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\
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square.x = x * x; \
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square.y = y * y; \
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square.z = z * z; \
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\
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cross.x = y * z; \
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cross.y = z * x; \
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cross.z = x * y; \
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\
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wimag.x = w * x; \
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wimag.y = w * y; \
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wimag.z = w * z; \
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\
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(mpMatrix)->right.x = 1 - 2 * (square.y + square.z); \
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(mpMatrix)->right.y = 2 * (cross.z + wimag.z); \
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(mpMatrix)->right.z = 2 * (cross.y - wimag.y); \
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\
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(mpMatrix)->up.x = 2 * (cross.z - wimag.z); \
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(mpMatrix)->up.y = 1 - 2 * (square.x + square.z); \
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(mpMatrix)->up.z = 2 * (cross.x + wimag.x); \
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\
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(mpMatrix)->at.x = 2 * (cross.y + wimag.y); \
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(mpMatrix)->at.y = 2 * (cross.x - wimag.x); \
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(mpMatrix)->at.z = (1 - 2 * (square.x + square.y)); \
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\
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/* Set position */ \
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(mpMatrix)->pos.x = ((RwReal) 0); \
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(mpMatrix)->pos.y = ((RwReal) 0); \
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(mpMatrix)->pos.z = ((RwReal) 0); \
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\
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/* Matrix is orthonormal */ \
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rwMatrixSetFlags((mpMatrix), \
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(rwMATRIXTYPEORTHONORMAL & \
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~rwMATRIXINTERNALIDENTITY) ); \
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} \
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MACRO_STOP
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#if (! ( defined(RWDEBUG) || defined(RWSUPPRESSINLINE) ))
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#define RtQuatInit( result, _x, _y, _z, _w) \
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RtQuatInitMacro( result, _x, _y, _z, _w)
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#define RtQuatAssign( to, from ) \
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RtQuatAssignMacro( to, from )
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#define RtQuatAdd( result, q1, q2 ) \
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RtQuatAddMacro( result, q1, q2 )
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#define RtQuatIncrementRealPart(result, s, q) \
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RtQuatIncrementRealPartMacro(result, s, q)
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#define RtQuatDecrementRealPart(result, s, q) \
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RtQuatDecrementRealPartMacro(result, s, q)
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#define RtQuatIncrement( result, dq ) \
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RtQuatIncrementMacro( result, dq )
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#define RtQuatSub( result, q1, q2 ) \
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RtQuatSubMacro( result, q1, q2 )
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#define RtQuatNegate( result, q ) \
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RtQuatNegateMacro( result, q )
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#define RtQuatConjugate( result, q) \
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RtQuatConjugateMacro( result, q)
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#define RtQuatScale(result, q, scale ) \
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RtQuatScaleMacro(result, q, scale )
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#define RtQuatModulusSquared( q ) \
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RtQuatModulusSquaredMacro( q )
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#define RtQuatMultiply( result, q1, q2) \
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RtQuatMultiplyMacro( result, q1, q2)
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#define RtQuatReciprocal( result, q) \
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RtQuatReciprocalMacro( result, q)
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#define RtQuatSquare( result, q ) \
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RtQuatSquareMacro( result, q )
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#define RtQuatSquareRoot( result, q ) \
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RtQuatSquareRootMacro( result, q )
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#define RtQuatLog( result, q ) \
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RtQuatLogMacro( result, q )
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#define RtQuatExp( result, q ) \
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RtQuatExpMacro( result, q )
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#define RtQuatPow( result, q, e ) \
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RtQuatPowMacro( result, q, e )
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#define RtQuatUnitLog( result, q ) \
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RtQuatUnitLogMacro( result, q )
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#define RtQuatUnitExp( result, q ) \
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RtQuatUnitExpMacro( result, q )
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#define RtQuatUnitPow( result, q, e ) \
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RtQuatUnitPowMacro( result, q, e )
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#define RtQuatConvertToMatrix(qpQuat, mpMatrix) \
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RtQuatConvertToMatrixMacro(qpQuat, mpMatrix)
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#define RtQuatUnitConvertToMatrix(qpQuat, mpMatrix) \
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RtQuatUnitConvertToMatrixMacro(qpQuat, mpMatrix)
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#endif /* (! ( defined(RWDEBUG) || defined(RWSUPPRESSINLINE) )) */
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/****************************************************************************
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Function prototypes
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*/
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#ifdef __cplusplus
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extern "C"
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{
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#endif /* __cplusplus */
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extern RwBool
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RtQuatConvertFromMatrix(RtQuat * const qpQuat,
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const RwMatrix * const mpMatrix);
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|
|
extern RtQuat *
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|
RtQuatRotate(RtQuat * quat,
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const RwV3d * axis,
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|
RwReal angle,
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|
RwOpCombineType combineOp);
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|
|
|
extern const RtQuat *
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|
RtQuatQueryRotate(const RtQuat *quat,
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RwV3d * unitAxis,
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|
RwReal * angle);
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|
|
|
extern RwV3d *
|
|
RtQuatTransformVectors(RwV3d * vectorsOut,
|
|
const RwV3d * vectorsIn,
|
|
const RwInt32 numPoints,
|
|
const RtQuat *quat);
|
|
|
|
extern RwReal
|
|
RtQuatModulus(RtQuat * q);
|
|
|
|
#if ( defined(RWDEBUG) || defined(RWSUPPRESSINLINE) )
|
|
|
|
extern void
|
|
RtQuatInit(RtQuat * result, RwReal x, RwReal y, RwReal z, RwReal w);
|
|
|
|
extern void
|
|
RtQuatAssign(RtQuat * to, RtQuat * from);
|
|
|
|
extern void
|
|
RtQuatAdd(RtQuat * result, RtQuat * q1, RtQuat * q2);
|
|
|
|
extern void
|
|
RtQuatIncrementRealPart(RtQuat * result, RwReal s, RtQuat * q);
|
|
|
|
extern void
|
|
RtQuatDecrementRealPart(RtQuat * result, RwReal s, RtQuat * q);
|
|
|
|
extern void
|
|
RtQuatIncrement(RtQuat * result, RtQuat * dq);
|
|
|
|
extern void
|
|
RtQuatSub(RtQuat * result, RtQuat * q1, RtQuat * q2);
|
|
|
|
extern void
|
|
RtQuatNegate(RtQuat * result, RtQuat * q);
|
|
|
|
extern void
|
|
RtQuatConjugate(RtQuat * result, RtQuat * q);
|
|
|
|
extern void
|
|
RtQuatScale(RtQuat * result, RtQuat * q, RwReal scale);
|
|
|
|
extern RwReal
|
|
RtQuatModulusSquared(RtQuat * q);
|
|
|
|
extern void
|
|
RtQuatMultiply(RtQuat * result, RtQuat * q1, RtQuat * q2);
|
|
|
|
extern void
|
|
RtQuatReciprocal(RtQuat * result, RtQuat * q);
|
|
|
|
extern void
|
|
RtQuatSquare(RtQuat * result, RtQuat * q);
|
|
|
|
extern void
|
|
RtQuatSquareRoot(RtQuat * result, RtQuat * q);
|
|
|
|
extern void
|
|
RtQuatLog(RtQuat * result, RtQuat * q);
|
|
|
|
extern void
|
|
RtQuatExp(RtQuat * result, RtQuat * q);
|
|
|
|
extern void
|
|
RtQuatPow(RtQuat * result, RtQuat * q, RwReal e);
|
|
|
|
extern void
|
|
RtQuatUnitLog(RtQuat * result, RtQuat * q);
|
|
|
|
extern void
|
|
RtQuatUnitExp(RtQuat * result, RtQuat * q);
|
|
|
|
extern void
|
|
RtQuatUnitPow(RtQuat * result, RtQuat * q, RwReal e);
|
|
|
|
extern void
|
|
RtQuatConvertToMatrix(const RtQuat * const qpQuat,
|
|
RwMatrix * const mpMatrix);
|
|
|
|
extern void
|
|
RtQuatUnitConvertToMatrix(const RtQuat * const qpQuat,
|
|
RwMatrix * const mpMatrix);
|
|
|
|
#endif /* ( defined(RWDEBUG) || defined(RWSUPPRESSINLINE) ) */
|
|
|
|
#ifdef __cplusplus
|
|
}
|
|
#endif /* __cplusplus */
|
|
|
|
/*
|
|
* Backwards compatibility code
|
|
*/
|
|
|
|
typedef RtQuat RpQuat;
|
|
|
|
#define RpAnimQuatConvertFromMatrix(qpQuat, mpMatrix) \
|
|
RtQuatConvertFromMatrix(qpQuat, mpMatrix)
|
|
|
|
#define RpAnimQuatConvertToMatrix(qpQuat,mpMatrix) \
|
|
RtQuatUnitConvertToMatrix(qpQuat,mpMatrix)
|
|
|
|
|
|
#endif /* RTQUAT_H */
|
|
|