1574 lines
37 KiB
C
1574 lines
37 KiB
C
#ifndef GIM_LINEAR_H_INCLUDED
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#define GIM_LINEAR_H_INCLUDED
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/*! \file gim_linear_math.h
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*\author Francisco Leon Najera
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Type Independant Vector and matrix operations.
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*/
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/*
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-----------------------------------------------------------------------------
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This source file is part of GIMPACT Library.
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For the latest info, see http://gimpact.sourceforge.net/
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Copyright (c) 2006 Francisco Leon Najera. C.C. 80087371.
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email: projectileman@yahoo.com
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This library is free software; you can redistribute it and/or
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modify it under the terms of EITHER:
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(1) The GNU Lesser General Public License as published by the Free
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Software Foundation; either version 2.1 of the License, or (at
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your option) any later version. The text of the GNU Lesser
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General Public License is included with this library in the
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file GIMPACT-LICENSE-LGPL.TXT.
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(2) The BSD-style license that is included with this library in
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the file GIMPACT-LICENSE-BSD.TXT.
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(3) The zlib/libpng license that is included with this library in
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the file GIMPACT-LICENSE-ZLIB.TXT.
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This library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the files
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GIMPACT-LICENSE-LGPL.TXT, GIMPACT-LICENSE-ZLIB.TXT and GIMPACT-LICENSE-BSD.TXT for more details.
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-----------------------------------------------------------------------------
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*/
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#include "gim_math.h"
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#include "gim_geom_types.h"
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//! Zero out a 2D vector
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#define VEC_ZERO_2(a) \
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{ \
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(a)[0] = (a)[1] = 0.0f; \
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}\
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//! Zero out a 3D vector
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#define VEC_ZERO(a) \
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{ \
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(a)[0] = (a)[1] = (a)[2] = 0.0f; \
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}\
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/// Zero out a 4D vector
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#define VEC_ZERO_4(a) \
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{ \
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(a)[0] = (a)[1] = (a)[2] = (a)[3] = 0.0f; \
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}\
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/// Vector copy
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#define VEC_COPY_2(b,a) \
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{ \
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(b)[0] = (a)[0]; \
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(b)[1] = (a)[1]; \
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}\
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/// Copy 3D vector
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#define VEC_COPY(b,a) \
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{ \
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(b)[0] = (a)[0]; \
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(b)[1] = (a)[1]; \
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(b)[2] = (a)[2]; \
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}\
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/// Copy 4D vector
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#define VEC_COPY_4(b,a) \
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{ \
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(b)[0] = (a)[0]; \
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(b)[1] = (a)[1]; \
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(b)[2] = (a)[2]; \
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(b)[3] = (a)[3]; \
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}\
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/// VECTOR SWAP
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#define VEC_SWAP(b,a) \
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{ \
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GIM_SWAP_NUMBERS((b)[0],(a)[0]);\
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GIM_SWAP_NUMBERS((b)[1],(a)[1]);\
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GIM_SWAP_NUMBERS((b)[2],(a)[2]);\
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}\
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/// Vector difference
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#define VEC_DIFF_2(v21,v2,v1) \
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{ \
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(v21)[0] = (v2)[0] - (v1)[0]; \
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(v21)[1] = (v2)[1] - (v1)[1]; \
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}\
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/// Vector difference
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#define VEC_DIFF(v21,v2,v1) \
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{ \
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(v21)[0] = (v2)[0] - (v1)[0]; \
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(v21)[1] = (v2)[1] - (v1)[1]; \
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(v21)[2] = (v2)[2] - (v1)[2]; \
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}\
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/// Vector difference
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#define VEC_DIFF_4(v21,v2,v1) \
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{ \
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(v21)[0] = (v2)[0] - (v1)[0]; \
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(v21)[1] = (v2)[1] - (v1)[1]; \
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(v21)[2] = (v2)[2] - (v1)[2]; \
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(v21)[3] = (v2)[3] - (v1)[3]; \
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}\
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/// Vector sum
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#define VEC_SUM_2(v21,v2,v1) \
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{ \
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(v21)[0] = (v2)[0] + (v1)[0]; \
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(v21)[1] = (v2)[1] + (v1)[1]; \
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}\
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/// Vector sum
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#define VEC_SUM(v21,v2,v1) \
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{ \
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(v21)[0] = (v2)[0] + (v1)[0]; \
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(v21)[1] = (v2)[1] + (v1)[1]; \
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(v21)[2] = (v2)[2] + (v1)[2]; \
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}\
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/// Vector sum
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#define VEC_SUM_4(v21,v2,v1) \
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{ \
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(v21)[0] = (v2)[0] + (v1)[0]; \
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(v21)[1] = (v2)[1] + (v1)[1]; \
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(v21)[2] = (v2)[2] + (v1)[2]; \
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(v21)[3] = (v2)[3] + (v1)[3]; \
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}\
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/// scalar times vector
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#define VEC_SCALE_2(c,a,b) \
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{ \
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(c)[0] = (a)*(b)[0]; \
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(c)[1] = (a)*(b)[1]; \
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}\
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/// scalar times vector
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#define VEC_SCALE(c,a,b) \
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{ \
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(c)[0] = (a)*(b)[0]; \
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(c)[1] = (a)*(b)[1]; \
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(c)[2] = (a)*(b)[2]; \
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}\
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/// scalar times vector
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#define VEC_SCALE_4(c,a,b) \
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{ \
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(c)[0] = (a)*(b)[0]; \
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(c)[1] = (a)*(b)[1]; \
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(c)[2] = (a)*(b)[2]; \
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(c)[3] = (a)*(b)[3]; \
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}\
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/// accumulate scaled vector
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#define VEC_ACCUM_2(c,a,b) \
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{ \
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(c)[0] += (a)*(b)[0]; \
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(c)[1] += (a)*(b)[1]; \
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}\
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/// accumulate scaled vector
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#define VEC_ACCUM(c,a,b) \
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{ \
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(c)[0] += (a)*(b)[0]; \
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(c)[1] += (a)*(b)[1]; \
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(c)[2] += (a)*(b)[2]; \
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}\
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/// accumulate scaled vector
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#define VEC_ACCUM_4(c,a,b) \
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{ \
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(c)[0] += (a)*(b)[0]; \
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(c)[1] += (a)*(b)[1]; \
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(c)[2] += (a)*(b)[2]; \
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(c)[3] += (a)*(b)[3]; \
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}\
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/// Vector dot product
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#define VEC_DOT_2(a,b) ((a)[0]*(b)[0] + (a)[1]*(b)[1])
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/// Vector dot product
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#define VEC_DOT(a,b) ((a)[0]*(b)[0] + (a)[1]*(b)[1] + (a)[2]*(b)[2])
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/// Vector dot product
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#define VEC_DOT_4(a,b) ((a)[0]*(b)[0] + (a)[1]*(b)[1] + (a)[2]*(b)[2] + (a)[3]*(b)[3])
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/// vector impact parameter (squared)
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#define VEC_IMPACT_SQ(bsq,direction,position) {\
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GREAL _llel_ = VEC_DOT(direction, position);\
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bsq = VEC_DOT(position, position) - _llel_*_llel_;\
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}\
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/// vector impact parameter
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#define VEC_IMPACT(bsq,direction,position) {\
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VEC_IMPACT_SQ(bsq,direction,position); \
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GIM_SQRT(bsq,bsq); \
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}\
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/// Vector length
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#define VEC_LENGTH_2(a,l)\
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{\
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GREAL _pp = VEC_DOT_2(a,a);\
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GIM_SQRT(_pp,l);\
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}\
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/// Vector length
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#define VEC_LENGTH(a,l)\
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{\
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GREAL _pp = VEC_DOT(a,a);\
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GIM_SQRT(_pp,l);\
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}\
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/// Vector length
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#define VEC_LENGTH_4(a,l)\
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{\
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GREAL _pp = VEC_DOT_4(a,a);\
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GIM_SQRT(_pp,l);\
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}\
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/// Vector inv length
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#define VEC_INV_LENGTH_2(a,l)\
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{\
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GREAL _pp = VEC_DOT_2(a,a);\
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GIM_INV_SQRT(_pp,l);\
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}\
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/// Vector inv length
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#define VEC_INV_LENGTH(a,l)\
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{\
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GREAL _pp = VEC_DOT(a,a);\
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GIM_INV_SQRT(_pp,l);\
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}\
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/// Vector inv length
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#define VEC_INV_LENGTH_4(a,l)\
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{\
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GREAL _pp = VEC_DOT_4(a,a);\
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GIM_INV_SQRT(_pp,l);\
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}\
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/// distance between two points
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#define VEC_DISTANCE(_len,_va,_vb) {\
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vec3f _tmp_; \
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VEC_DIFF(_tmp_, _vb, _va); \
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VEC_LENGTH(_tmp_,_len); \
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}\
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/// Vector length
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#define VEC_CONJUGATE_LENGTH(a,l)\
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{\
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GREAL _pp = 1.0 - a[0]*a[0] - a[1]*a[1] - a[2]*a[2];\
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GIM_SQRT(_pp,l);\
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}\
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/// Vector length
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#define VEC_NORMALIZE(a) { \
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GREAL len;\
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VEC_INV_LENGTH(a,len); \
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if(len<G_REAL_INFINITY)\
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{\
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a[0] *= len; \
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a[1] *= len; \
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a[2] *= len; \
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} \
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}\
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/// Set Vector size
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#define VEC_RENORMALIZE(a,newlen) { \
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GREAL len;\
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VEC_INV_LENGTH(a,len); \
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if(len<G_REAL_INFINITY)\
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{\
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len *= newlen;\
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a[0] *= len; \
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a[1] *= len; \
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a[2] *= len; \
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} \
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}\
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/// Vector cross
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#define VEC_CROSS(c,a,b) \
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{ \
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c[0] = (a)[1] * (b)[2] - (a)[2] * (b)[1]; \
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c[1] = (a)[2] * (b)[0] - (a)[0] * (b)[2]; \
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c[2] = (a)[0] * (b)[1] - (a)[1] * (b)[0]; \
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}\
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/*! Vector perp -- assumes that n is of unit length
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* accepts vector v, subtracts out any component parallel to n */
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#define VEC_PERPENDICULAR(vp,v,n) \
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{ \
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GREAL dot = VEC_DOT(v, n); \
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vp[0] = (v)[0] - dot*(n)[0]; \
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vp[1] = (v)[1] - dot*(n)[1]; \
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vp[2] = (v)[2] - dot*(n)[2]; \
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}\
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/*! Vector parallel -- assumes that n is of unit length */
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#define VEC_PARALLEL(vp,v,n) \
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{ \
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GREAL dot = VEC_DOT(v, n); \
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vp[0] = (dot) * (n)[0]; \
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vp[1] = (dot) * (n)[1]; \
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vp[2] = (dot) * (n)[2]; \
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}\
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/*! Same as Vector parallel -- n can have any length
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* accepts vector v, subtracts out any component perpendicular to n */
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#define VEC_PROJECT(vp,v,n) \
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{ \
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GREAL scalar = VEC_DOT(v, n); \
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scalar/= VEC_DOT(n, n); \
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vp[0] = (scalar) * (n)[0]; \
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vp[1] = (scalar) * (n)[1]; \
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vp[2] = (scalar) * (n)[2]; \
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}\
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/*! accepts vector v*/
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#define VEC_UNPROJECT(vp,v,n) \
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{ \
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GREAL scalar = VEC_DOT(v, n); \
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scalar = VEC_DOT(n, n)/scalar; \
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vp[0] = (scalar) * (n)[0]; \
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vp[1] = (scalar) * (n)[1]; \
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vp[2] = (scalar) * (n)[2]; \
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}\
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/*! Vector reflection -- assumes n is of unit length
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Takes vector v, reflects it against reflector n, and returns vr */
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#define VEC_REFLECT(vr,v,n) \
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{ \
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GREAL dot = VEC_DOT(v, n); \
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vr[0] = (v)[0] - 2.0 * (dot) * (n)[0]; \
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vr[1] = (v)[1] - 2.0 * (dot) * (n)[1]; \
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vr[2] = (v)[2] - 2.0 * (dot) * (n)[2]; \
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}\
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/*! Vector blending
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Takes two vectors a, b, blends them together with two scalars */
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#define VEC_BLEND_AB(vr,sa,a,sb,b) \
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{ \
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vr[0] = (sa) * (a)[0] + (sb) * (b)[0]; \
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vr[1] = (sa) * (a)[1] + (sb) * (b)[1]; \
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vr[2] = (sa) * (a)[2] + (sb) * (b)[2]; \
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}\
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/*! Vector blending
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Takes two vectors a, b, blends them together with s <=1 */
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#define VEC_BLEND(vr,a,b,s) VEC_BLEND_AB(vr,(1-s),a,s,b)
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#define VEC_SET3(a,b,op,c) a[0]=b[0] op c[0]; a[1]=b[1] op c[1]; a[2]=b[2] op c[2];
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//! Finds the bigger cartesian coordinate from a vector
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#define VEC_MAYOR_COORD(vec, maxc)\
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{\
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GREAL A[] = {fabs(vec[0]),fabs(vec[1]),fabs(vec[2])};\
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maxc = A[0]>A[1]?(A[0]>A[2]?0:2):(A[1]>A[2]?1:2);\
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}\
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//! Finds the 2 smallest cartesian coordinates from a vector
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#define VEC_MINOR_AXES(vec, i0, i1)\
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{\
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VEC_MAYOR_COORD(vec,i0);\
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i0 = (i0+1)%3;\
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i1 = (i0+1)%3;\
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}\
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#define VEC_EQUAL(v1,v2) (v1[0]==v2[0]&&v1[1]==v2[1]&&v1[2]==v2[2])
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#define VEC_NEAR_EQUAL(v1,v2) (GIM_NEAR_EQUAL(v1[0],v2[0])&&GIM_NEAR_EQUAL(v1[1],v2[1])&&GIM_NEAR_EQUAL(v1[2],v2[2]))
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/// Vector cross
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#define X_AXIS_CROSS_VEC(dst,src)\
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{ \
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dst[0] = 0.0f; \
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dst[1] = -src[2]; \
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dst[2] = src[1]; \
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}\
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#define Y_AXIS_CROSS_VEC(dst,src)\
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{ \
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dst[0] = src[2]; \
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dst[1] = 0.0f; \
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dst[2] = -src[0]; \
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}\
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#define Z_AXIS_CROSS_VEC(dst,src)\
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{ \
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dst[0] = -src[1]; \
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dst[1] = src[0]; \
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dst[2] = 0.0f; \
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}\
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/// initialize matrix
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#define IDENTIFY_MATRIX_3X3(m) \
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{ \
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m[0][0] = 1.0; \
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m[0][1] = 0.0; \
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m[0][2] = 0.0; \
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\
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m[1][0] = 0.0; \
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m[1][1] = 1.0; \
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m[1][2] = 0.0; \
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\
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m[2][0] = 0.0; \
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m[2][1] = 0.0; \
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m[2][2] = 1.0; \
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}\
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/*! initialize matrix */
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#define IDENTIFY_MATRIX_4X4(m) \
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{ \
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m[0][0] = 1.0; \
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m[0][1] = 0.0; \
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m[0][2] = 0.0; \
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m[0][3] = 0.0; \
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\
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m[1][0] = 0.0; \
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m[1][1] = 1.0; \
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m[1][2] = 0.0; \
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m[1][3] = 0.0; \
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\
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m[2][0] = 0.0; \
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m[2][1] = 0.0; \
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m[2][2] = 1.0; \
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m[2][3] = 0.0; \
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\
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m[3][0] = 0.0; \
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m[3][1] = 0.0; \
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m[3][2] = 0.0; \
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m[3][3] = 1.0; \
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}\
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/*! initialize matrix */
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#define ZERO_MATRIX_4X4(m) \
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{ \
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m[0][0] = 0.0; \
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m[0][1] = 0.0; \
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m[0][2] = 0.0; \
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m[0][3] = 0.0; \
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\
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m[1][0] = 0.0; \
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m[1][1] = 0.0; \
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m[1][2] = 0.0; \
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m[1][3] = 0.0; \
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\
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m[2][0] = 0.0; \
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m[2][1] = 0.0; \
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|
m[2][2] = 0.0; \
|
|
m[2][3] = 0.0; \
|
|
\
|
|
m[3][0] = 0.0; \
|
|
m[3][1] = 0.0; \
|
|
m[3][2] = 0.0; \
|
|
m[3][3] = 0.0; \
|
|
}\
|
|
|
|
/*! matrix rotation X */
|
|
#define ROTX_CS(m,cosine,sine) \
|
|
{ \
|
|
/* rotation about the x-axis */ \
|
|
\
|
|
m[0][0] = 1.0; \
|
|
m[0][1] = 0.0; \
|
|
m[0][2] = 0.0; \
|
|
m[0][3] = 0.0; \
|
|
\
|
|
m[1][0] = 0.0; \
|
|
m[1][1] = (cosine); \
|
|
m[1][2] = (sine); \
|
|
m[1][3] = 0.0; \
|
|
\
|
|
m[2][0] = 0.0; \
|
|
m[2][1] = -(sine); \
|
|
m[2][2] = (cosine); \
|
|
m[2][3] = 0.0; \
|
|
\
|
|
m[3][0] = 0.0; \
|
|
m[3][1] = 0.0; \
|
|
m[3][2] = 0.0; \
|
|
m[3][3] = 1.0; \
|
|
}\
|
|
|
|
/*! matrix rotation Y */
|
|
#define ROTY_CS(m,cosine,sine) \
|
|
{ \
|
|
/* rotation about the y-axis */ \
|
|
\
|
|
m[0][0] = (cosine); \
|
|
m[0][1] = 0.0; \
|
|
m[0][2] = -(sine); \
|
|
m[0][3] = 0.0; \
|
|
\
|
|
m[1][0] = 0.0; \
|
|
m[1][1] = 1.0; \
|
|
m[1][2] = 0.0; \
|
|
m[1][3] = 0.0; \
|
|
\
|
|
m[2][0] = (sine); \
|
|
m[2][1] = 0.0; \
|
|
m[2][2] = (cosine); \
|
|
m[2][3] = 0.0; \
|
|
\
|
|
m[3][0] = 0.0; \
|
|
m[3][1] = 0.0; \
|
|
m[3][2] = 0.0; \
|
|
m[3][3] = 1.0; \
|
|
}\
|
|
|
|
/*! matrix rotation Z */
|
|
#define ROTZ_CS(m,cosine,sine) \
|
|
{ \
|
|
/* rotation about the z-axis */ \
|
|
\
|
|
m[0][0] = (cosine); \
|
|
m[0][1] = (sine); \
|
|
m[0][2] = 0.0; \
|
|
m[0][3] = 0.0; \
|
|
\
|
|
m[1][0] = -(sine); \
|
|
m[1][1] = (cosine); \
|
|
m[1][2] = 0.0; \
|
|
m[1][3] = 0.0; \
|
|
\
|
|
m[2][0] = 0.0; \
|
|
m[2][1] = 0.0; \
|
|
m[2][2] = 1.0; \
|
|
m[2][3] = 0.0; \
|
|
\
|
|
m[3][0] = 0.0; \
|
|
m[3][1] = 0.0; \
|
|
m[3][2] = 0.0; \
|
|
m[3][3] = 1.0; \
|
|
}\
|
|
|
|
/*! matrix copy */
|
|
#define COPY_MATRIX_2X2(b,a) \
|
|
{ \
|
|
b[0][0] = a[0][0]; \
|
|
b[0][1] = a[0][1]; \
|
|
\
|
|
b[1][0] = a[1][0]; \
|
|
b[1][1] = a[1][1]; \
|
|
\
|
|
}\
|
|
|
|
|
|
/*! matrix copy */
|
|
#define COPY_MATRIX_2X3(b,a) \
|
|
{ \
|
|
b[0][0] = a[0][0]; \
|
|
b[0][1] = a[0][1]; \
|
|
b[0][2] = a[0][2]; \
|
|
\
|
|
b[1][0] = a[1][0]; \
|
|
b[1][1] = a[1][1]; \
|
|
b[1][2] = a[1][2]; \
|
|
}\
|
|
|
|
|
|
/*! matrix copy */
|
|
#define COPY_MATRIX_3X3(b,a) \
|
|
{ \
|
|
b[0][0] = a[0][0]; \
|
|
b[0][1] = a[0][1]; \
|
|
b[0][2] = a[0][2]; \
|
|
\
|
|
b[1][0] = a[1][0]; \
|
|
b[1][1] = a[1][1]; \
|
|
b[1][2] = a[1][2]; \
|
|
\
|
|
b[2][0] = a[2][0]; \
|
|
b[2][1] = a[2][1]; \
|
|
b[2][2] = a[2][2]; \
|
|
}\
|
|
|
|
|
|
/*! matrix copy */
|
|
#define COPY_MATRIX_4X4(b,a) \
|
|
{ \
|
|
b[0][0] = a[0][0]; \
|
|
b[0][1] = a[0][1]; \
|
|
b[0][2] = a[0][2]; \
|
|
b[0][3] = a[0][3]; \
|
|
\
|
|
b[1][0] = a[1][0]; \
|
|
b[1][1] = a[1][1]; \
|
|
b[1][2] = a[1][2]; \
|
|
b[1][3] = a[1][3]; \
|
|
\
|
|
b[2][0] = a[2][0]; \
|
|
b[2][1] = a[2][1]; \
|
|
b[2][2] = a[2][2]; \
|
|
b[2][3] = a[2][3]; \
|
|
\
|
|
b[3][0] = a[3][0]; \
|
|
b[3][1] = a[3][1]; \
|
|
b[3][2] = a[3][2]; \
|
|
b[3][3] = a[3][3]; \
|
|
}\
|
|
|
|
|
|
/*! matrix transpose */
|
|
#define TRANSPOSE_MATRIX_2X2(b,a) \
|
|
{ \
|
|
b[0][0] = a[0][0]; \
|
|
b[0][1] = a[1][0]; \
|
|
\
|
|
b[1][0] = a[0][1]; \
|
|
b[1][1] = a[1][1]; \
|
|
}\
|
|
|
|
|
|
/*! matrix transpose */
|
|
#define TRANSPOSE_MATRIX_3X3(b,a) \
|
|
{ \
|
|
b[0][0] = a[0][0]; \
|
|
b[0][1] = a[1][0]; \
|
|
b[0][2] = a[2][0]; \
|
|
\
|
|
b[1][0] = a[0][1]; \
|
|
b[1][1] = a[1][1]; \
|
|
b[1][2] = a[2][1]; \
|
|
\
|
|
b[2][0] = a[0][2]; \
|
|
b[2][1] = a[1][2]; \
|
|
b[2][2] = a[2][2]; \
|
|
}\
|
|
|
|
|
|
/*! matrix transpose */
|
|
#define TRANSPOSE_MATRIX_4X4(b,a) \
|
|
{ \
|
|
b[0][0] = a[0][0]; \
|
|
b[0][1] = a[1][0]; \
|
|
b[0][2] = a[2][0]; \
|
|
b[0][3] = a[3][0]; \
|
|
\
|
|
b[1][0] = a[0][1]; \
|
|
b[1][1] = a[1][1]; \
|
|
b[1][2] = a[2][1]; \
|
|
b[1][3] = a[3][1]; \
|
|
\
|
|
b[2][0] = a[0][2]; \
|
|
b[2][1] = a[1][2]; \
|
|
b[2][2] = a[2][2]; \
|
|
b[2][3] = a[3][2]; \
|
|
\
|
|
b[3][0] = a[0][3]; \
|
|
b[3][1] = a[1][3]; \
|
|
b[3][2] = a[2][3]; \
|
|
b[3][3] = a[3][3]; \
|
|
}\
|
|
|
|
|
|
/*! multiply matrix by scalar */
|
|
#define SCALE_MATRIX_2X2(b,s,a) \
|
|
{ \
|
|
b[0][0] = (s) * a[0][0]; \
|
|
b[0][1] = (s) * a[0][1]; \
|
|
\
|
|
b[1][0] = (s) * a[1][0]; \
|
|
b[1][1] = (s) * a[1][1]; \
|
|
}\
|
|
|
|
|
|
/*! multiply matrix by scalar */
|
|
#define SCALE_MATRIX_3X3(b,s,a) \
|
|
{ \
|
|
b[0][0] = (s) * a[0][0]; \
|
|
b[0][1] = (s) * a[0][1]; \
|
|
b[0][2] = (s) * a[0][2]; \
|
|
\
|
|
b[1][0] = (s) * a[1][0]; \
|
|
b[1][1] = (s) * a[1][1]; \
|
|
b[1][2] = (s) * a[1][2]; \
|
|
\
|
|
b[2][0] = (s) * a[2][0]; \
|
|
b[2][1] = (s) * a[2][1]; \
|
|
b[2][2] = (s) * a[2][2]; \
|
|
}\
|
|
|
|
|
|
/*! multiply matrix by scalar */
|
|
#define SCALE_MATRIX_4X4(b,s,a) \
|
|
{ \
|
|
b[0][0] = (s) * a[0][0]; \
|
|
b[0][1] = (s) * a[0][1]; \
|
|
b[0][2] = (s) * a[0][2]; \
|
|
b[0][3] = (s) * a[0][3]; \
|
|
\
|
|
b[1][0] = (s) * a[1][0]; \
|
|
b[1][1] = (s) * a[1][1]; \
|
|
b[1][2] = (s) * a[1][2]; \
|
|
b[1][3] = (s) * a[1][3]; \
|
|
\
|
|
b[2][0] = (s) * a[2][0]; \
|
|
b[2][1] = (s) * a[2][1]; \
|
|
b[2][2] = (s) * a[2][2]; \
|
|
b[2][3] = (s) * a[2][3]; \
|
|
\
|
|
b[3][0] = s * a[3][0]; \
|
|
b[3][1] = s * a[3][1]; \
|
|
b[3][2] = s * a[3][2]; \
|
|
b[3][3] = s * a[3][3]; \
|
|
}\
|
|
|
|
|
|
/*! multiply matrix by scalar */
|
|
#define SCALE_VEC_MATRIX_2X2(b,svec,a) \
|
|
{ \
|
|
b[0][0] = svec[0] * a[0][0]; \
|
|
b[1][0] = svec[0] * a[1][0]; \
|
|
\
|
|
b[0][1] = svec[1] * a[0][1]; \
|
|
b[1][1] = svec[1] * a[1][1]; \
|
|
}\
|
|
|
|
|
|
/*! multiply matrix by scalar. Each columns is scaled by each scalar vector component */
|
|
#define SCALE_VEC_MATRIX_3X3(b,svec,a) \
|
|
{ \
|
|
b[0][0] = svec[0] * a[0][0]; \
|
|
b[1][0] = svec[0] * a[1][0]; \
|
|
b[2][0] = svec[0] * a[2][0]; \
|
|
\
|
|
b[0][1] = svec[1] * a[0][1]; \
|
|
b[1][1] = svec[1] * a[1][1]; \
|
|
b[2][1] = svec[1] * a[2][1]; \
|
|
\
|
|
b[0][2] = svec[2] * a[0][2]; \
|
|
b[1][2] = svec[2] * a[1][2]; \
|
|
b[2][2] = svec[2] * a[2][2]; \
|
|
}\
|
|
|
|
|
|
/*! multiply matrix by scalar */
|
|
#define SCALE_VEC_MATRIX_4X4(b,svec,a) \
|
|
{ \
|
|
b[0][0] = svec[0] * a[0][0]; \
|
|
b[1][0] = svec[0] * a[1][0]; \
|
|
b[2][0] = svec[0] * a[2][0]; \
|
|
b[3][0] = svec[0] * a[3][0]; \
|
|
\
|
|
b[0][1] = svec[1] * a[0][1]; \
|
|
b[1][1] = svec[1] * a[1][1]; \
|
|
b[2][1] = svec[1] * a[2][1]; \
|
|
b[3][1] = svec[1] * a[3][1]; \
|
|
\
|
|
b[0][2] = svec[2] * a[0][2]; \
|
|
b[1][2] = svec[2] * a[1][2]; \
|
|
b[2][2] = svec[2] * a[2][2]; \
|
|
b[3][2] = svec[2] * a[3][2]; \
|
|
\
|
|
b[0][3] = svec[3] * a[0][3]; \
|
|
b[1][3] = svec[3] * a[1][3]; \
|
|
b[2][3] = svec[3] * a[2][3]; \
|
|
b[3][3] = svec[3] * a[3][3]; \
|
|
}\
|
|
|
|
|
|
/*! multiply matrix by scalar */
|
|
#define ACCUM_SCALE_MATRIX_2X2(b,s,a) \
|
|
{ \
|
|
b[0][0] += (s) * a[0][0]; \
|
|
b[0][1] += (s) * a[0][1]; \
|
|
\
|
|
b[1][0] += (s) * a[1][0]; \
|
|
b[1][1] += (s) * a[1][1]; \
|
|
}\
|
|
|
|
|
|
/*! multiply matrix by scalar */
|
|
#define ACCUM_SCALE_MATRIX_3X3(b,s,a) \
|
|
{ \
|
|
b[0][0] += (s) * a[0][0]; \
|
|
b[0][1] += (s) * a[0][1]; \
|
|
b[0][2] += (s) * a[0][2]; \
|
|
\
|
|
b[1][0] += (s) * a[1][0]; \
|
|
b[1][1] += (s) * a[1][1]; \
|
|
b[1][2] += (s) * a[1][2]; \
|
|
\
|
|
b[2][0] += (s) * a[2][0]; \
|
|
b[2][1] += (s) * a[2][1]; \
|
|
b[2][2] += (s) * a[2][2]; \
|
|
}\
|
|
|
|
|
|
/*! multiply matrix by scalar */
|
|
#define ACCUM_SCALE_MATRIX_4X4(b,s,a) \
|
|
{ \
|
|
b[0][0] += (s) * a[0][0]; \
|
|
b[0][1] += (s) * a[0][1]; \
|
|
b[0][2] += (s) * a[0][2]; \
|
|
b[0][3] += (s) * a[0][3]; \
|
|
\
|
|
b[1][0] += (s) * a[1][0]; \
|
|
b[1][1] += (s) * a[1][1]; \
|
|
b[1][2] += (s) * a[1][2]; \
|
|
b[1][3] += (s) * a[1][3]; \
|
|
\
|
|
b[2][0] += (s) * a[2][0]; \
|
|
b[2][1] += (s) * a[2][1]; \
|
|
b[2][2] += (s) * a[2][2]; \
|
|
b[2][3] += (s) * a[2][3]; \
|
|
\
|
|
b[3][0] += (s) * a[3][0]; \
|
|
b[3][1] += (s) * a[3][1]; \
|
|
b[3][2] += (s) * a[3][2]; \
|
|
b[3][3] += (s) * a[3][3]; \
|
|
}\
|
|
|
|
/*! matrix product */
|
|
/*! c[x][y] = a[x][0]*b[0][y]+a[x][1]*b[1][y]+a[x][2]*b[2][y]+a[x][3]*b[3][y];*/
|
|
#define MATRIX_PRODUCT_2X2(c,a,b) \
|
|
{ \
|
|
c[0][0] = a[0][0]*b[0][0]+a[0][1]*b[1][0]; \
|
|
c[0][1] = a[0][0]*b[0][1]+a[0][1]*b[1][1]; \
|
|
\
|
|
c[1][0] = a[1][0]*b[0][0]+a[1][1]*b[1][0]; \
|
|
c[1][1] = a[1][0]*b[0][1]+a[1][1]*b[1][1]; \
|
|
\
|
|
}\
|
|
|
|
/*! matrix product */
|
|
/*! c[x][y] = a[x][0]*b[0][y]+a[x][1]*b[1][y]+a[x][2]*b[2][y]+a[x][3]*b[3][y];*/
|
|
#define MATRIX_PRODUCT_3X3(c,a,b) \
|
|
{ \
|
|
c[0][0] = a[0][0]*b[0][0]+a[0][1]*b[1][0]+a[0][2]*b[2][0]; \
|
|
c[0][1] = a[0][0]*b[0][1]+a[0][1]*b[1][1]+a[0][2]*b[2][1]; \
|
|
c[0][2] = a[0][0]*b[0][2]+a[0][1]*b[1][2]+a[0][2]*b[2][2]; \
|
|
\
|
|
c[1][0] = a[1][0]*b[0][0]+a[1][1]*b[1][0]+a[1][2]*b[2][0]; \
|
|
c[1][1] = a[1][0]*b[0][1]+a[1][1]*b[1][1]+a[1][2]*b[2][1]; \
|
|
c[1][2] = a[1][0]*b[0][2]+a[1][1]*b[1][2]+a[1][2]*b[2][2]; \
|
|
\
|
|
c[2][0] = a[2][0]*b[0][0]+a[2][1]*b[1][0]+a[2][2]*b[2][0]; \
|
|
c[2][1] = a[2][0]*b[0][1]+a[2][1]*b[1][1]+a[2][2]*b[2][1]; \
|
|
c[2][2] = a[2][0]*b[0][2]+a[2][1]*b[1][2]+a[2][2]*b[2][2]; \
|
|
}\
|
|
|
|
|
|
/*! matrix product */
|
|
/*! c[x][y] = a[x][0]*b[0][y]+a[x][1]*b[1][y]+a[x][2]*b[2][y]+a[x][3]*b[3][y];*/
|
|
#define MATRIX_PRODUCT_4X4(c,a,b) \
|
|
{ \
|
|
c[0][0] = a[0][0]*b[0][0]+a[0][1]*b[1][0]+a[0][2]*b[2][0]+a[0][3]*b[3][0];\
|
|
c[0][1] = a[0][0]*b[0][1]+a[0][1]*b[1][1]+a[0][2]*b[2][1]+a[0][3]*b[3][1];\
|
|
c[0][2] = a[0][0]*b[0][2]+a[0][1]*b[1][2]+a[0][2]*b[2][2]+a[0][3]*b[3][2];\
|
|
c[0][3] = a[0][0]*b[0][3]+a[0][1]*b[1][3]+a[0][2]*b[2][3]+a[0][3]*b[3][3];\
|
|
\
|
|
c[1][0] = a[1][0]*b[0][0]+a[1][1]*b[1][0]+a[1][2]*b[2][0]+a[1][3]*b[3][0];\
|
|
c[1][1] = a[1][0]*b[0][1]+a[1][1]*b[1][1]+a[1][2]*b[2][1]+a[1][3]*b[3][1];\
|
|
c[1][2] = a[1][0]*b[0][2]+a[1][1]*b[1][2]+a[1][2]*b[2][2]+a[1][3]*b[3][2];\
|
|
c[1][3] = a[1][0]*b[0][3]+a[1][1]*b[1][3]+a[1][2]*b[2][3]+a[1][3]*b[3][3];\
|
|
\
|
|
c[2][0] = a[2][0]*b[0][0]+a[2][1]*b[1][0]+a[2][2]*b[2][0]+a[2][3]*b[3][0];\
|
|
c[2][1] = a[2][0]*b[0][1]+a[2][1]*b[1][1]+a[2][2]*b[2][1]+a[2][3]*b[3][1];\
|
|
c[2][2] = a[2][0]*b[0][2]+a[2][1]*b[1][2]+a[2][2]*b[2][2]+a[2][3]*b[3][2];\
|
|
c[2][3] = a[2][0]*b[0][3]+a[2][1]*b[1][3]+a[2][2]*b[2][3]+a[2][3]*b[3][3];\
|
|
\
|
|
c[3][0] = a[3][0]*b[0][0]+a[3][1]*b[1][0]+a[3][2]*b[2][0]+a[3][3]*b[3][0];\
|
|
c[3][1] = a[3][0]*b[0][1]+a[3][1]*b[1][1]+a[3][2]*b[2][1]+a[3][3]*b[3][1];\
|
|
c[3][2] = a[3][0]*b[0][2]+a[3][1]*b[1][2]+a[3][2]*b[2][2]+a[3][3]*b[3][2];\
|
|
c[3][3] = a[3][0]*b[0][3]+a[3][1]*b[1][3]+a[3][2]*b[2][3]+a[3][3]*b[3][3];\
|
|
}\
|
|
|
|
|
|
/*! matrix times vector */
|
|
#define MAT_DOT_VEC_2X2(p,m,v) \
|
|
{ \
|
|
p[0] = m[0][0]*v[0] + m[0][1]*v[1]; \
|
|
p[1] = m[1][0]*v[0] + m[1][1]*v[1]; \
|
|
}\
|
|
|
|
|
|
/*! matrix times vector */
|
|
#define MAT_DOT_VEC_3X3(p,m,v) \
|
|
{ \
|
|
p[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]*v[2]; \
|
|
p[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2]; \
|
|
p[2] = m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2]; \
|
|
}\
|
|
|
|
|
|
/*! matrix times vector
|
|
v is a vec4f
|
|
*/
|
|
#define MAT_DOT_VEC_4X4(p,m,v) \
|
|
{ \
|
|
p[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]*v[2] + m[0][3]*v[3]; \
|
|
p[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2] + m[1][3]*v[3]; \
|
|
p[2] = m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2] + m[2][3]*v[3]; \
|
|
p[3] = m[3][0]*v[0] + m[3][1]*v[1] + m[3][2]*v[2] + m[3][3]*v[3]; \
|
|
}\
|
|
|
|
/*! matrix times vector
|
|
v is a vec3f
|
|
and m is a mat4f<br>
|
|
Last column is added as the position
|
|
*/
|
|
#define MAT_DOT_VEC_3X4(p,m,v) \
|
|
{ \
|
|
p[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]*v[2] + m[0][3]; \
|
|
p[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2] + m[1][3]; \
|
|
p[2] = m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2] + m[2][3]; \
|
|
}\
|
|
|
|
|
|
/*! vector transpose times matrix */
|
|
/*! p[j] = v[0]*m[0][j] + v[1]*m[1][j] + v[2]*m[2][j]; */
|
|
#define VEC_DOT_MAT_3X3(p,v,m) \
|
|
{ \
|
|
p[0] = v[0]*m[0][0] + v[1]*m[1][0] + v[2]*m[2][0]; \
|
|
p[1] = v[0]*m[0][1] + v[1]*m[1][1] + v[2]*m[2][1]; \
|
|
p[2] = v[0]*m[0][2] + v[1]*m[1][2] + v[2]*m[2][2]; \
|
|
}\
|
|
|
|
|
|
/*! affine matrix times vector */
|
|
/** The matrix is assumed to be an affine matrix, with last two
|
|
* entries representing a translation */
|
|
#define MAT_DOT_VEC_2X3(p,m,v) \
|
|
{ \
|
|
p[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]; \
|
|
p[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]; \
|
|
}\
|
|
|
|
//! Transform a plane
|
|
#define MAT_TRANSFORM_PLANE_4X4(pout,m,plane)\
|
|
{ \
|
|
pout[0] = m[0][0]*plane[0] + m[0][1]*plane[1] + m[0][2]*plane[2];\
|
|
pout[1] = m[1][0]*plane[0] + m[1][1]*plane[1] + m[1][2]*plane[2];\
|
|
pout[2] = m[2][0]*plane[0] + m[2][1]*plane[1] + m[2][2]*plane[2];\
|
|
pout[3] = m[0][3]*pout[0] + m[1][3]*pout[1] + m[2][3]*pout[2] + plane[3];\
|
|
}\
|
|
|
|
|
|
|
|
/** inverse transpose of matrix times vector
|
|
*
|
|
* This macro computes inverse transpose of matrix m,
|
|
* and multiplies vector v into it, to yeild vector p
|
|
*
|
|
* DANGER !!! Do Not use this on normal vectors!!!
|
|
* It will leave normals the wrong length !!!
|
|
* See macro below for use on normals.
|
|
*/
|
|
#define INV_TRANSP_MAT_DOT_VEC_2X2(p,m,v) \
|
|
{ \
|
|
GREAL det; \
|
|
\
|
|
det = m[0][0]*m[1][1] - m[0][1]*m[1][0]; \
|
|
p[0] = m[1][1]*v[0] - m[1][0]*v[1]; \
|
|
p[1] = - m[0][1]*v[0] + m[0][0]*v[1]; \
|
|
\
|
|
/* if matrix not singular, and not orthonormal, then renormalize */ \
|
|
if ((det!=1.0f) && (det != 0.0f)) { \
|
|
det = 1.0f / det; \
|
|
p[0] *= det; \
|
|
p[1] *= det; \
|
|
} \
|
|
}\
|
|
|
|
|
|
/** transform normal vector by inverse transpose of matrix
|
|
* and then renormalize the vector
|
|
*
|
|
* This macro computes inverse transpose of matrix m,
|
|
* and multiplies vector v into it, to yeild vector p
|
|
* Vector p is then normalized.
|
|
*/
|
|
#define NORM_XFORM_2X2(p,m,v) \
|
|
{ \
|
|
GREAL len; \
|
|
\
|
|
/* do nothing if off-diagonals are zero and diagonals are \
|
|
* equal */ \
|
|
if ((m[0][1] != 0.0) || (m[1][0] != 0.0) || (m[0][0] != m[1][1])) { \
|
|
p[0] = m[1][1]*v[0] - m[1][0]*v[1]; \
|
|
p[1] = - m[0][1]*v[0] + m[0][0]*v[1]; \
|
|
\
|
|
len = p[0]*p[0] + p[1]*p[1]; \
|
|
GIM_INV_SQRT(len,len); \
|
|
p[0] *= len; \
|
|
p[1] *= len; \
|
|
} else { \
|
|
VEC_COPY_2 (p, v); \
|
|
} \
|
|
}\
|
|
|
|
|
|
/** outer product of vector times vector transpose
|
|
*
|
|
* The outer product of vector v and vector transpose t yeilds
|
|
* dyadic matrix m.
|
|
*/
|
|
#define OUTER_PRODUCT_2X2(m,v,t) \
|
|
{ \
|
|
m[0][0] = v[0] * t[0]; \
|
|
m[0][1] = v[0] * t[1]; \
|
|
\
|
|
m[1][0] = v[1] * t[0]; \
|
|
m[1][1] = v[1] * t[1]; \
|
|
}\
|
|
|
|
|
|
/** outer product of vector times vector transpose
|
|
*
|
|
* The outer product of vector v and vector transpose t yeilds
|
|
* dyadic matrix m.
|
|
*/
|
|
#define OUTER_PRODUCT_3X3(m,v,t) \
|
|
{ \
|
|
m[0][0] = v[0] * t[0]; \
|
|
m[0][1] = v[0] * t[1]; \
|
|
m[0][2] = v[0] * t[2]; \
|
|
\
|
|
m[1][0] = v[1] * t[0]; \
|
|
m[1][1] = v[1] * t[1]; \
|
|
m[1][2] = v[1] * t[2]; \
|
|
\
|
|
m[2][0] = v[2] * t[0]; \
|
|
m[2][1] = v[2] * t[1]; \
|
|
m[2][2] = v[2] * t[2]; \
|
|
}\
|
|
|
|
|
|
/** outer product of vector times vector transpose
|
|
*
|
|
* The outer product of vector v and vector transpose t yeilds
|
|
* dyadic matrix m.
|
|
*/
|
|
#define OUTER_PRODUCT_4X4(m,v,t) \
|
|
{ \
|
|
m[0][0] = v[0] * t[0]; \
|
|
m[0][1] = v[0] * t[1]; \
|
|
m[0][2] = v[0] * t[2]; \
|
|
m[0][3] = v[0] * t[3]; \
|
|
\
|
|
m[1][0] = v[1] * t[0]; \
|
|
m[1][1] = v[1] * t[1]; \
|
|
m[1][2] = v[1] * t[2]; \
|
|
m[1][3] = v[1] * t[3]; \
|
|
\
|
|
m[2][0] = v[2] * t[0]; \
|
|
m[2][1] = v[2] * t[1]; \
|
|
m[2][2] = v[2] * t[2]; \
|
|
m[2][3] = v[2] * t[3]; \
|
|
\
|
|
m[3][0] = v[3] * t[0]; \
|
|
m[3][1] = v[3] * t[1]; \
|
|
m[3][2] = v[3] * t[2]; \
|
|
m[3][3] = v[3] * t[3]; \
|
|
}\
|
|
|
|
|
|
/** outer product of vector times vector transpose
|
|
*
|
|
* The outer product of vector v and vector transpose t yeilds
|
|
* dyadic matrix m.
|
|
*/
|
|
#define ACCUM_OUTER_PRODUCT_2X2(m,v,t) \
|
|
{ \
|
|
m[0][0] += v[0] * t[0]; \
|
|
m[0][1] += v[0] * t[1]; \
|
|
\
|
|
m[1][0] += v[1] * t[0]; \
|
|
m[1][1] += v[1] * t[1]; \
|
|
}\
|
|
|
|
|
|
/** outer product of vector times vector transpose
|
|
*
|
|
* The outer product of vector v and vector transpose t yeilds
|
|
* dyadic matrix m.
|
|
*/
|
|
#define ACCUM_OUTER_PRODUCT_3X3(m,v,t) \
|
|
{ \
|
|
m[0][0] += v[0] * t[0]; \
|
|
m[0][1] += v[0] * t[1]; \
|
|
m[0][2] += v[0] * t[2]; \
|
|
\
|
|
m[1][0] += v[1] * t[0]; \
|
|
m[1][1] += v[1] * t[1]; \
|
|
m[1][2] += v[1] * t[2]; \
|
|
\
|
|
m[2][0] += v[2] * t[0]; \
|
|
m[2][1] += v[2] * t[1]; \
|
|
m[2][2] += v[2] * t[2]; \
|
|
}\
|
|
|
|
|
|
/** outer product of vector times vector transpose
|
|
*
|
|
* The outer product of vector v and vector transpose t yeilds
|
|
* dyadic matrix m.
|
|
*/
|
|
#define ACCUM_OUTER_PRODUCT_4X4(m,v,t) \
|
|
{ \
|
|
m[0][0] += v[0] * t[0]; \
|
|
m[0][1] += v[0] * t[1]; \
|
|
m[0][2] += v[0] * t[2]; \
|
|
m[0][3] += v[0] * t[3]; \
|
|
\
|
|
m[1][0] += v[1] * t[0]; \
|
|
m[1][1] += v[1] * t[1]; \
|
|
m[1][2] += v[1] * t[2]; \
|
|
m[1][3] += v[1] * t[3]; \
|
|
\
|
|
m[2][0] += v[2] * t[0]; \
|
|
m[2][1] += v[2] * t[1]; \
|
|
m[2][2] += v[2] * t[2]; \
|
|
m[2][3] += v[2] * t[3]; \
|
|
\
|
|
m[3][0] += v[3] * t[0]; \
|
|
m[3][1] += v[3] * t[1]; \
|
|
m[3][2] += v[3] * t[2]; \
|
|
m[3][3] += v[3] * t[3]; \
|
|
}\
|
|
|
|
|
|
/** determinant of matrix
|
|
*
|
|
* Computes determinant of matrix m, returning d
|
|
*/
|
|
#define DETERMINANT_2X2(d,m) \
|
|
{ \
|
|
d = m[0][0] * m[1][1] - m[0][1] * m[1][0]; \
|
|
}\
|
|
|
|
|
|
/** determinant of matrix
|
|
*
|
|
* Computes determinant of matrix m, returning d
|
|
*/
|
|
#define DETERMINANT_3X3(d,m) \
|
|
{ \
|
|
d = m[0][0] * (m[1][1]*m[2][2] - m[1][2] * m[2][1]); \
|
|
d -= m[0][1] * (m[1][0]*m[2][2] - m[1][2] * m[2][0]); \
|
|
d += m[0][2] * (m[1][0]*m[2][1] - m[1][1] * m[2][0]); \
|
|
}\
|
|
|
|
|
|
/** i,j,th cofactor of a 4x4 matrix
|
|
*
|
|
*/
|
|
#define COFACTOR_4X4_IJ(fac,m,i,j) \
|
|
{ \
|
|
GUINT __ii[4], __jj[4], __k; \
|
|
\
|
|
for (__k=0; __k<i; __k++) __ii[__k] = __k; \
|
|
for (__k=i; __k<3; __k++) __ii[__k] = __k+1; \
|
|
for (__k=0; __k<j; __k++) __jj[__k] = __k; \
|
|
for (__k=j; __k<3; __k++) __jj[__k] = __k+1; \
|
|
\
|
|
(fac) = m[__ii[0]][__jj[0]] * (m[__ii[1]][__jj[1]]*m[__ii[2]][__jj[2]] \
|
|
- m[__ii[1]][__jj[2]]*m[__ii[2]][__jj[1]]); \
|
|
(fac) -= m[__ii[0]][__jj[1]] * (m[__ii[1]][__jj[0]]*m[__ii[2]][__jj[2]] \
|
|
- m[__ii[1]][__jj[2]]*m[__ii[2]][__jj[0]]);\
|
|
(fac) += m[__ii[0]][__jj[2]] * (m[__ii[1]][__jj[0]]*m[__ii[2]][__jj[1]] \
|
|
- m[__ii[1]][__jj[1]]*m[__ii[2]][__jj[0]]);\
|
|
\
|
|
__k = i+j; \
|
|
if ( __k != (__k/2)*2) { \
|
|
(fac) = -(fac); \
|
|
} \
|
|
}\
|
|
|
|
|
|
/** determinant of matrix
|
|
*
|
|
* Computes determinant of matrix m, returning d
|
|
*/
|
|
#define DETERMINANT_4X4(d,m) \
|
|
{ \
|
|
GREAL cofac; \
|
|
COFACTOR_4X4_IJ (cofac, m, 0, 0); \
|
|
d = m[0][0] * cofac; \
|
|
COFACTOR_4X4_IJ (cofac, m, 0, 1); \
|
|
d += m[0][1] * cofac; \
|
|
COFACTOR_4X4_IJ (cofac, m, 0, 2); \
|
|
d += m[0][2] * cofac; \
|
|
COFACTOR_4X4_IJ (cofac, m, 0, 3); \
|
|
d += m[0][3] * cofac; \
|
|
}\
|
|
|
|
|
|
/** cofactor of matrix
|
|
*
|
|
* Computes cofactor of matrix m, returning a
|
|
*/
|
|
#define COFACTOR_2X2(a,m) \
|
|
{ \
|
|
a[0][0] = (m)[1][1]; \
|
|
a[0][1] = - (m)[1][0]; \
|
|
a[1][0] = - (m)[0][1]; \
|
|
a[1][1] = (m)[0][0]; \
|
|
}\
|
|
|
|
|
|
/** cofactor of matrix
|
|
*
|
|
* Computes cofactor of matrix m, returning a
|
|
*/
|
|
#define COFACTOR_3X3(a,m) \
|
|
{ \
|
|
a[0][0] = m[1][1]*m[2][2] - m[1][2]*m[2][1]; \
|
|
a[0][1] = - (m[1][0]*m[2][2] - m[2][0]*m[1][2]); \
|
|
a[0][2] = m[1][0]*m[2][1] - m[1][1]*m[2][0]; \
|
|
a[1][0] = - (m[0][1]*m[2][2] - m[0][2]*m[2][1]); \
|
|
a[1][1] = m[0][0]*m[2][2] - m[0][2]*m[2][0]; \
|
|
a[1][2] = - (m[0][0]*m[2][1] - m[0][1]*m[2][0]); \
|
|
a[2][0] = m[0][1]*m[1][2] - m[0][2]*m[1][1]; \
|
|
a[2][1] = - (m[0][0]*m[1][2] - m[0][2]*m[1][0]); \
|
|
a[2][2] = m[0][0]*m[1][1] - m[0][1]*m[1][0]); \
|
|
}\
|
|
|
|
|
|
/** cofactor of matrix
|
|
*
|
|
* Computes cofactor of matrix m, returning a
|
|
*/
|
|
#define COFACTOR_4X4(a,m) \
|
|
{ \
|
|
int i,j; \
|
|
\
|
|
for (i=0; i<4; i++) { \
|
|
for (j=0; j<4; j++) { \
|
|
COFACTOR_4X4_IJ (a[i][j], m, i, j); \
|
|
} \
|
|
} \
|
|
}\
|
|
|
|
|
|
/** adjoint of matrix
|
|
*
|
|
* Computes adjoint of matrix m, returning a
|
|
* (Note that adjoint is just the transpose of the cofactor matrix)
|
|
*/
|
|
#define ADJOINT_2X2(a,m) \
|
|
{ \
|
|
a[0][0] = (m)[1][1]; \
|
|
a[1][0] = - (m)[1][0]; \
|
|
a[0][1] = - (m)[0][1]; \
|
|
a[1][1] = (m)[0][0]; \
|
|
}\
|
|
|
|
|
|
/** adjoint of matrix
|
|
*
|
|
* Computes adjoint of matrix m, returning a
|
|
* (Note that adjoint is just the transpose of the cofactor matrix)
|
|
*/
|
|
#define ADJOINT_3X3(a,m) \
|
|
{ \
|
|
a[0][0] = m[1][1]*m[2][2] - m[1][2]*m[2][1]; \
|
|
a[1][0] = - (m[1][0]*m[2][2] - m[2][0]*m[1][2]); \
|
|
a[2][0] = m[1][0]*m[2][1] - m[1][1]*m[2][0]; \
|
|
a[0][1] = - (m[0][1]*m[2][2] - m[0][2]*m[2][1]); \
|
|
a[1][1] = m[0][0]*m[2][2] - m[0][2]*m[2][0]; \
|
|
a[2][1] = - (m[0][0]*m[2][1] - m[0][1]*m[2][0]); \
|
|
a[0][2] = m[0][1]*m[1][2] - m[0][2]*m[1][1]; \
|
|
a[1][2] = - (m[0][0]*m[1][2] - m[0][2]*m[1][0]); \
|
|
a[2][2] = m[0][0]*m[1][1] - m[0][1]*m[1][0]); \
|
|
}\
|
|
|
|
|
|
/** adjoint of matrix
|
|
*
|
|
* Computes adjoint of matrix m, returning a
|
|
* (Note that adjoint is just the transpose of the cofactor matrix)
|
|
*/
|
|
#define ADJOINT_4X4(a,m) \
|
|
{ \
|
|
char _i_,_j_; \
|
|
\
|
|
for (_i_=0; _i_<4; _i_++) { \
|
|
for (_j_=0; _j_<4; _j_++) { \
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|
COFACTOR_4X4_IJ (a[_j_][_i_], m, _i_, _j_); \
|
|
} \
|
|
} \
|
|
}\
|
|
|
|
|
|
/** compute adjoint of matrix and scale
|
|
*
|
|
* Computes adjoint of matrix m, scales it by s, returning a
|
|
*/
|
|
#define SCALE_ADJOINT_2X2(a,s,m) \
|
|
{ \
|
|
a[0][0] = (s) * m[1][1]; \
|
|
a[1][0] = - (s) * m[1][0]; \
|
|
a[0][1] = - (s) * m[0][1]; \
|
|
a[1][1] = (s) * m[0][0]; \
|
|
}\
|
|
|
|
|
|
/** compute adjoint of matrix and scale
|
|
*
|
|
* Computes adjoint of matrix m, scales it by s, returning a
|
|
*/
|
|
#define SCALE_ADJOINT_3X3(a,s,m) \
|
|
{ \
|
|
a[0][0] = (s) * (m[1][1] * m[2][2] - m[1][2] * m[2][1]); \
|
|
a[1][0] = (s) * (m[1][2] * m[2][0] - m[1][0] * m[2][2]); \
|
|
a[2][0] = (s) * (m[1][0] * m[2][1] - m[1][1] * m[2][0]); \
|
|
\
|
|
a[0][1] = (s) * (m[0][2] * m[2][1] - m[0][1] * m[2][2]); \
|
|
a[1][1] = (s) * (m[0][0] * m[2][2] - m[0][2] * m[2][0]); \
|
|
a[2][1] = (s) * (m[0][1] * m[2][0] - m[0][0] * m[2][1]); \
|
|
\
|
|
a[0][2] = (s) * (m[0][1] * m[1][2] - m[0][2] * m[1][1]); \
|
|
a[1][2] = (s) * (m[0][2] * m[1][0] - m[0][0] * m[1][2]); \
|
|
a[2][2] = (s) * (m[0][0] * m[1][1] - m[0][1] * m[1][0]); \
|
|
}\
|
|
|
|
|
|
/** compute adjoint of matrix and scale
|
|
*
|
|
* Computes adjoint of matrix m, scales it by s, returning a
|
|
*/
|
|
#define SCALE_ADJOINT_4X4(a,s,m) \
|
|
{ \
|
|
char _i_,_j_; \
|
|
for (_i_=0; _i_<4; _i_++) { \
|
|
for (_j_=0; _j_<4; _j_++) { \
|
|
COFACTOR_4X4_IJ (a[_j_][_i_], m, _i_, _j_); \
|
|
a[_j_][_i_] *= s; \
|
|
} \
|
|
} \
|
|
}\
|
|
|
|
/** inverse of matrix
|
|
*
|
|
* Compute inverse of matrix a, returning determinant m and
|
|
* inverse b
|
|
*/
|
|
#define INVERT_2X2(b,det,a) \
|
|
{ \
|
|
GREAL _tmp_; \
|
|
DETERMINANT_2X2 (det, a); \
|
|
_tmp_ = 1.0 / (det); \
|
|
SCALE_ADJOINT_2X2 (b, _tmp_, a); \
|
|
}\
|
|
|
|
|
|
/** inverse of matrix
|
|
*
|
|
* Compute inverse of matrix a, returning determinant m and
|
|
* inverse b
|
|
*/
|
|
#define INVERT_3X3(b,det,a) \
|
|
{ \
|
|
GREAL _tmp_; \
|
|
DETERMINANT_3X3 (det, a); \
|
|
_tmp_ = 1.0 / (det); \
|
|
SCALE_ADJOINT_3X3 (b, _tmp_, a); \
|
|
}\
|
|
|
|
|
|
/** inverse of matrix
|
|
*
|
|
* Compute inverse of matrix a, returning determinant m and
|
|
* inverse b
|
|
*/
|
|
#define INVERT_4X4(b,det,a) \
|
|
{ \
|
|
GREAL _tmp_; \
|
|
DETERMINANT_4X4 (det, a); \
|
|
_tmp_ = 1.0 / (det); \
|
|
SCALE_ADJOINT_4X4 (b, _tmp_, a); \
|
|
}\
|
|
|
|
//! Get the triple(3) row of a transform matrix
|
|
#define MAT_GET_ROW(mat,vec3,rowindex)\
|
|
{\
|
|
vec3[0] = mat[rowindex][0];\
|
|
vec3[1] = mat[rowindex][1];\
|
|
vec3[2] = mat[rowindex][2]; \
|
|
}\
|
|
|
|
//! Get the tuple(2) row of a transform matrix
|
|
#define MAT_GET_ROW2(mat,vec2,rowindex)\
|
|
{\
|
|
vec2[0] = mat[rowindex][0];\
|
|
vec2[1] = mat[rowindex][1];\
|
|
}\
|
|
|
|
|
|
//! Get the quad (4) row of a transform matrix
|
|
#define MAT_GET_ROW4(mat,vec4,rowindex)\
|
|
{\
|
|
vec4[0] = mat[rowindex][0];\
|
|
vec4[1] = mat[rowindex][1];\
|
|
vec4[2] = mat[rowindex][2];\
|
|
vec4[3] = mat[rowindex][3];\
|
|
}\
|
|
|
|
//! Get the triple(3) col of a transform matrix
|
|
#define MAT_GET_COL(mat,vec3,colindex)\
|
|
{\
|
|
vec3[0] = mat[0][colindex];\
|
|
vec3[1] = mat[1][colindex];\
|
|
vec3[2] = mat[2][colindex]; \
|
|
}\
|
|
|
|
//! Get the tuple(2) col of a transform matrix
|
|
#define MAT_GET_COL2(mat,vec2,colindex)\
|
|
{\
|
|
vec2[0] = mat[0][colindex];\
|
|
vec2[1] = mat[1][colindex];\
|
|
}\
|
|
|
|
|
|
//! Get the quad (4) col of a transform matrix
|
|
#define MAT_GET_COL4(mat,vec4,colindex)\
|
|
{\
|
|
vec4[0] = mat[0][colindex];\
|
|
vec4[1] = mat[1][colindex];\
|
|
vec4[2] = mat[2][colindex];\
|
|
vec4[3] = mat[3][colindex];\
|
|
}\
|
|
|
|
//! Get the triple(3) col of a transform matrix
|
|
#define MAT_GET_X(mat,vec3)\
|
|
{\
|
|
MAT_GET_COL(mat,vec3,0);\
|
|
}\
|
|
|
|
//! Get the triple(3) col of a transform matrix
|
|
#define MAT_GET_Y(mat,vec3)\
|
|
{\
|
|
MAT_GET_COL(mat,vec3,1);\
|
|
}\
|
|
|
|
//! Get the triple(3) col of a transform matrix
|
|
#define MAT_GET_Z(mat,vec3)\
|
|
{\
|
|
MAT_GET_COL(mat,vec3,2);\
|
|
}\
|
|
|
|
|
|
//! Get the triple(3) col of a transform matrix
|
|
#define MAT_SET_X(mat,vec3)\
|
|
{\
|
|
mat[0][0] = vec3[0];\
|
|
mat[1][0] = vec3[1];\
|
|
mat[2][0] = vec3[2];\
|
|
}\
|
|
|
|
//! Get the triple(3) col of a transform matrix
|
|
#define MAT_SET_Y(mat,vec3)\
|
|
{\
|
|
mat[0][1] = vec3[0];\
|
|
mat[1][1] = vec3[1];\
|
|
mat[2][1] = vec3[2];\
|
|
}\
|
|
|
|
//! Get the triple(3) col of a transform matrix
|
|
#define MAT_SET_Z(mat,vec3)\
|
|
{\
|
|
mat[0][2] = vec3[0];\
|
|
mat[1][2] = vec3[1];\
|
|
mat[2][2] = vec3[2];\
|
|
}\
|
|
|
|
|
|
//! Get the triple(3) col of a transform matrix
|
|
#define MAT_GET_TRANSLATION(mat,vec3)\
|
|
{\
|
|
vec3[0] = mat[0][3];\
|
|
vec3[1] = mat[1][3];\
|
|
vec3[2] = mat[2][3]; \
|
|
}\
|
|
|
|
//! Set the triple(3) col of a transform matrix
|
|
#define MAT_SET_TRANSLATION(mat,vec3)\
|
|
{\
|
|
mat[0][3] = vec3[0];\
|
|
mat[1][3] = vec3[1];\
|
|
mat[2][3] = vec3[2]; \
|
|
}\
|
|
|
|
|
|
|
|
//! Returns the dot product between a vec3f and the row of a matrix
|
|
#define MAT_DOT_ROW(mat,vec3,rowindex) (vec3[0]*mat[rowindex][0] + vec3[1]*mat[rowindex][1] + vec3[2]*mat[rowindex][2])
|
|
|
|
//! Returns the dot product between a vec2f and the row of a matrix
|
|
#define MAT_DOT_ROW2(mat,vec2,rowindex) (vec2[0]*mat[rowindex][0] + vec2[1]*mat[rowindex][1])
|
|
|
|
//! Returns the dot product between a vec4f and the row of a matrix
|
|
#define MAT_DOT_ROW4(mat,vec4,rowindex) (vec4[0]*mat[rowindex][0] + vec4[1]*mat[rowindex][1] + vec4[2]*mat[rowindex][2] + vec4[3]*mat[rowindex][3])
|
|
|
|
|
|
//! Returns the dot product between a vec3f and the col of a matrix
|
|
#define MAT_DOT_COL(mat,vec3,colindex) (vec3[0]*mat[0][colindex] + vec3[1]*mat[1][colindex] + vec3[2]*mat[2][colindex])
|
|
|
|
//! Returns the dot product between a vec2f and the col of a matrix
|
|
#define MAT_DOT_COL2(mat,vec2,colindex) (vec2[0]*mat[0][colindex] + vec2[1]*mat[1][colindex])
|
|
|
|
//! Returns the dot product between a vec4f and the col of a matrix
|
|
#define MAT_DOT_COL4(mat,vec4,colindex) (vec4[0]*mat[0][colindex] + vec4[1]*mat[1][colindex] + vec4[2]*mat[2][colindex] + vec4[3]*mat[3][colindex])
|
|
|
|
/*!Transpose matrix times vector
|
|
v is a vec3f
|
|
and m is a mat4f<br>
|
|
*/
|
|
#define INV_MAT_DOT_VEC_3X3(p,m,v) \
|
|
{ \
|
|
p[0] = MAT_DOT_COL(m,v,0); \
|
|
p[1] = MAT_DOT_COL(m,v,1); \
|
|
p[2] = MAT_DOT_COL(m,v,2); \
|
|
}\
|
|
|
|
|
|
|
|
#endif // GIM_VECTOR_H_INCLUDED
|