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9a3206795e
VectorUnshear uses the exact same shear vector to remove shear from a sheared vector. ie with: VectorShear (shear, v, w); VectorUnshear (shear, w, x); x == v within fp math limits.
731 lines
19 KiB
C
731 lines
19 KiB
C
/*
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mathlib.h
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Vector math library
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Copyright (C) 1996-1997 Id Software, Inc.
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This program is free software; you can redistribute it and/or
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modify it under the terms of the GNU General Public License
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as published by the Free Software Foundation; either version 2
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of the License, or (at your option) any later version.
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This program 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.
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See the GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program; if not, write to:
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Free Software Foundation, Inc.
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59 Temple Place - Suite 330
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Boston, MA 02111-1307, USA
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*/
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#ifndef __mathlib_h
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#define __mathlib_h
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/** \defgroup mathlib Vector and matrix functions
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\ingroup utils
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*/
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//@{
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#include <math.h>
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#include "QF/qtypes.h"
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#ifndef max
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# define max(a,b) ((a) > (b) ? (a) : (b))
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#endif
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#ifndef min
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# define min(a,b) ((a) < (b) ? (a) : (b))
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#endif
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#ifndef bound
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# define bound(a,b,c) (max(a, min(b, c)))
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#endif
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#ifndef M_PI
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# define M_PI 3.14159265358979323846 // matches value in gcc v2 math.h
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#endif
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extern int nanmask;
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extern const vec_t *const vec3_origin;
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extern const vec_t *const quat_origin;
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#define EQUAL_EPSILON 0.001
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#define RINT(x) (floor ((x) + 0.5))
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#define IS_NAN(x) (((*(int *) (char *) &x) & nanmask) == nanmask)
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#define DotProduct(a,b) ((a)[0] * (b)[0] + (a)[1] * (b)[1] + (a)[2] * (b)[2])
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#define VectorSubtract(a,b,c) \
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do { \
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(c)[0] = (a)[0] - (b)[0]; \
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(c)[1] = (a)[1] - (b)[1]; \
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(c)[2] = (a)[2] - (b)[2]; \
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} while (0)
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#define VectorNegate(a,b) \
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do { \
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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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} while (0)
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#define VectorAdd(a,b,c) \
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do { \
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(c)[0] = (a)[0] + (b)[0]; \
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(c)[1] = (a)[1] + (b)[1]; \
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(c)[2] = (a)[2] + (b)[2]; \
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} while (0)
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#define VectorCopy(a,b) \
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do { \
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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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} while (0)
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#define VectorMultAdd(a,s,b,c) \
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do { \
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(c)[0] = (a)[0] + (s) * (b)[0]; \
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(c)[1] = (a)[1] + (s) * (b)[1]; \
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(c)[2] = (a)[2] + (s) * (b)[2]; \
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} while (0)
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#define VectorMultSub(a,s,b,c) \
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do { \
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(c)[0] = (a)[0] - (s) * (b)[0]; \
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(c)[1] = (a)[1] - (s) * (b)[1]; \
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(c)[2] = (a)[2] - (s) * (b)[2]; \
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} while (0)
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#define VectorLength(a) sqrt(DotProduct(a, a))
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#define VectorScale(a,b,c) \
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do { \
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(c)[0] = (a)[0] * (b); \
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(c)[1] = (a)[1] * (b); \
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(c)[2] = (a)[2] * (b); \
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} while (0)
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/** Shear vector \a b by vector \a a.
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Vector a represents the shear factors XY, XZ, YZ, ie in matrix form:
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[ 1 0 0 ] [ b0 ]
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[ a0 1 0 ] [ b1 ]
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[ a1 a2 1 ] [ b2 ]
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The reason for this particular scheme is that is how Mat4Decompose
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calculates the shear from a matrix.
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\note The order of calculations is important for when b and c refer to
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the same vector.
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*/
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#define VectorShear(a,b,c) \
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do { \
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(c)[2] = (b)[0] * (a)[1] + (b)[1] * (a)[2] + (b)[2]; \
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(c)[1] = (b)[0] * (a)[0] + (b)[1]; \
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(c)[0] = (b)[0]; \
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} while (0)
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#define VectorUnshear(a,b,c) \
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do { \
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(c)[2] = (b)[2] - (b)[1] * (a)[2] - (b)[0] * ((a)[1]-(a)[0]*(a)[2]); \
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(c)[1] = (b)[1] - (b)[0] * (a)[0]; \
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(c)[0] = (b)[0]; \
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} while (0)
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#define VectorCompMult(a,b,c) \
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do { \
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(c)[0] = (a)[0] * (b)[0]; \
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(c)[1] = (a)[1] * (b)[1]; \
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(c)[2] = (a)[2] * (b)[2]; \
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} while (0)
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#define VectorCompDiv(a,b,c) \
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do { \
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(c)[0] = (a)[0] / (b)[0]; \
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(c)[1] = (a)[1] / (b)[1]; \
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(c)[2] = (a)[2] / (b)[2]; \
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} while (0)
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#define VectorCompCompare(x, op, y) \
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(((x)[0] op (y)[0]) && ((x)[1] op (y)[1]) && ((x)[2] op (y)[2]))
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#define VectorCompare(x, y) VectorCompCompare (x, ==, y)
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#define VectorCompMin(a, b, c) \
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do { \
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(c)[0] = min ((a)[0], (b)[0]); \
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(c)[1] = min ((a)[1], (b)[1]); \
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(c)[2] = min ((a)[2], (b)[2]); \
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} while (0)
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#define VectorCompMax(a, b, c) \
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do { \
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(c)[0] = max ((a)[0], (b)[0]); \
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(c)[1] = max ((a)[1], (b)[1]); \
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(c)[2] = max ((a)[2], (b)[2]); \
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} while (0)
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#define VectorCompBound(a, b, c, d) \
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do { \
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(d)[0] = bound ((a)[0], (b)[0], (c)[0]); \
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(d)[1] = bound ((a)[1], (b)[1], (c)[1]); \
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(d)[2] = bound ((a)[2], (b)[2], (c)[2]); \
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} while (0)
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#define VectorIsZero(a) (!(a)[0] && !(a)[1] && !(a)[2])
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#define VectorZero(a) ((a)[2] = (a)[1] = (a)[0] = 0);
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#define VectorSet(a,b,c,d) \
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do { \
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(d)[0] = a; \
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(d)[1] = b; \
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(d)[2] = c; \
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} while (0)
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#define VectorBlend(v1,v2,b,v) \
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do { \
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(v)[0] = (v1)[0] * (1 - (b)) + (v2)[0] * (b); \
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(v)[1] = (v1)[1] * (1 - (b)) + (v2)[1] * (b); \
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(v)[2] = (v1)[2] * (1 - (b)) + (v2)[2] * (b); \
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} while (0)
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//For printf etc
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#define VectorExpand(v) (v)[0], (v)[1], (v)[2]
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/*
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* VectorDistance, the distance between two points.
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* Yes, this is the same as sqrt(VectorSubtract then DotProduct),
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* however that way would involve more vars, this is cheaper.
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*/
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#define VectorDistance_fast(a, b) \
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((((a)[0] - (b)[0]) * ((a)[0] - (b)[0])) + \
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(((a)[1] - (b)[1]) * ((a)[1] - (b)[1])) + \
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(((a)[2] - (b)[2]) * ((a)[2] - (b)[2])))
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#define VectorDistance(a, b) sqrt(VectorDistance_fast(a, b))
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#define QDotProduct(a,b) ((a)[0] * (b)[0] + (a)[1] * (b)[1] \
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+ (a)[2] * (b)[2] + (a)[3] * (b)[3])
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#define QuatSubtract(a,b,c) \
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do { \
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(c)[0] = (a)[0] - (b)[0]; \
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(c)[1] = (a)[1] - (b)[1]; \
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(c)[2] = (a)[2] - (b)[2]; \
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(c)[3] = (a)[3] - (b)[3]; \
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} while (0)
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#define QuatNegate(a,b) \
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do { \
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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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} while (0)
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#define QuatConj(a,b) \
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do { \
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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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} while (0)
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#define QuatAdd(a,b,c) \
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do { \
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(c)[0] = (a)[0] + (b)[0]; \
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(c)[1] = (a)[1] + (b)[1]; \
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(c)[2] = (a)[2] + (b)[2]; \
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(c)[3] = (a)[3] + (b)[3]; \
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} while (0)
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#define QuatCopy(a,b) \
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do { \
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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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} while (0)
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#define QuatMultAdd(a,s,b,c) \
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do { \
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(c)[0] = (a)[0] + (s) * (b)[0]; \
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(c)[1] = (a)[1] + (s) * (b)[1]; \
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(c)[2] = (a)[2] + (s) * (b)[2]; \
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(c)[3] = (a)[3] + (s) * (b)[3]; \
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} while (0)
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#define QuatMultSub(a,s,b,c) \
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do { \
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(c)[0] = (a)[0] - (s) * (b)[0]; \
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(c)[1] = (a)[1] - (s) * (b)[1]; \
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(c)[2] = (a)[2] - (s) * (b)[2]; \
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(c)[3] = (a)[3] - (s) * (b)[3]; \
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} while (0)
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#define QuatLength(a) sqrt(QDotProduct(a, a))
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#define QuatScale(a,b,c) \
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do { \
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(c)[0] = (a)[0] * (b); \
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(c)[1] = (a)[1] * (b); \
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(c)[2] = (a)[2] * (b); \
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(c)[3] = (a)[3] * (b); \
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} while (0)
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#define QuatCompMult(a,b,c) \
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do { \
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(c)[0] = (a)[0] * (b)[0]; \
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(c)[1] = (a)[1] * (b)[1]; \
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(c)[2] = (a)[2] * (b)[2]; \
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(c)[3] = (a)[3] * (b)[3]; \
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} while (0)
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#define QuatCompDiv(a,b,c) \
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do { \
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(c)[0] = (a)[0] / (b)[0]; \
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(c)[1] = (a)[1] / (b)[1]; \
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(c)[2] = (a)[2] / (b)[2]; \
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(c)[3] = (a)[3] / (b)[3]; \
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} while (0)
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#define QuatCompCompare(x, op, y) \
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(((x)[0] op (y)[0]) && ((x)[1] op (y)[1]) \
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&& ((x)[2] op (y)[2]) && ((x)[3] op (y)[3]))
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#define QuatCompare(x, y) QuatCompCompare (x, ==, y)
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#define QuatCompMin(a, b, c) \
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do { \
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(c)[0] = min ((a)[0], (b)[0]); \
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(c)[1] = min ((a)[1], (b)[1]); \
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(c)[2] = min ((a)[2], (b)[2]); \
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(c)[3] = min ((a)[3], (b)[3]); \
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} while (0)
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#define QuatCompMax(a, b, c) \
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do { \
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(c)[0] = max ((a)[0], (b)[0]); \
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(c)[1] = max ((a)[1], (b)[1]); \
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(c)[2] = max ((a)[2], (b)[2]); \
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(c)[3] = max ((a)[3], (b)[3]); \
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} while (0)
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#define QuatCompBound(a, b, c, d) \
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do { \
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(d)[0] = bound ((a)[0], (b)[0], (c)[0]); \
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(d)[1] = bound ((a)[1], (b)[1], (c)[1]); \
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(d)[2] = bound ((a)[2], (b)[2], (c)[2]); \
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(d)[3] = bound ((a)[3], (b)[3], (c)[3]); \
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} while (0)
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#define QuatIsZero(a) (!(a)[0] && !(a)[1] && !(a)[2] && !(a)[3])
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#define QuatZero(a) ((a)[3] = (a)[2] = (a)[1] = (a)[0] = 0);
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#define QuatSet(a,b,c,d,e) \
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do { \
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(e)[0] = a; \
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(e)[1] = b; \
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(e)[2] = c; \
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(e)[3] = d; \
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} while (0)
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#define QuatBlend(q1,q2,b,q) \
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do { \
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(q)[0] = (q1)[0] * (1 - (b)) + (q2)[0] * (b); \
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(q)[1] = (q1)[1] * (1 - (b)) + (q2)[1] * (b); \
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(q)[2] = (q1)[2] * (1 - (b)) + (q2)[2] * (b); \
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(q)[3] = (q1)[3] * (1 - (b)) + (q2)[3] * (b); \
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} while (0)
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//For printf etc
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#define QuatExpand(q) (q)[0], (q)[1], (q)[2], (q)[3]
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#define DualAdd(a,b,c) \
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do { \
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(c).r = (a).r + (b).r; \
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(c).e = (a).e + (b).e; \
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} while (0)
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#define DualSubtract(a,b,c) \
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do { \
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(c).r = (a).r - (b).r; \
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(c).e = (a).e - (b).e; \
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} while (0)
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#define DualNegate(a,b) \
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do { \
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(b).r = -(a).r; \
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(b).e = -(a).e; \
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} while (0)
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#define DualConj(a,b) \
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do { \
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(b).r = (a).r; \
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(b).e = -(a).e; \
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} while (0)
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#define DualMult(a,b,c) \
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do { \
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(c).e = (a).r * (b).e + (a).e * (b).r; \
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(c).r = (a).r * (b).r; \
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} while (0)
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#define DualMultAdd(a,s,b,c) \
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do { \
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(c).r = (a).r + (s) * (b).r; \
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(c).e = (a).e + (s) * (b).e; \
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} while (0)
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#define DualMultSub(a,s,b,c) \
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do { \
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(c).r = (a).r - (s) * (b).r; \
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(c).e = (a).e - (s) * (b).e; \
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} while (0)
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#define DualNorm(a) ((a).r)
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#define DualScale(a,b,c) \
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do { \
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(c).r = (a).r * (b); \
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(c).e = (a).e * (b); \
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} while (0)
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#define DualCompCompare(x, op, y) ((x).r op (y).r) && ((x).e op (y).e)
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#define DualCompare(x, y) DualCompCompare (x, ==, y)
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#define DualIsZero(a) ((a).r == 0 && (a).e == 0)
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#define DualIsUnit(a) (((a).r - 1) * ((a).r - 1) < 1e-6 && (a).e * (a).e < 1e-6)
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#define DualSet(ar,ae,a) \
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do { \
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(a).ar = r; \
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|
(a).er = r; \
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} while (0)
|
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#define DualZero(a) \
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do { \
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(a).e = (a).r = 0; \
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} while (0)
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#define DualBlend(d1,d2,b,d) \
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do { \
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(d).r = (d1).r * (1 - (b)) + (d2).r * (b); \
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(d).e = (d1).e * (1 - (b)) + (d2).e * (b); \
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} while (0)
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#define DualExpand(d) (d).r, (d).e
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#define DualQuatAdd(a,b,c) \
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do { \
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QuatAdd ((a).q0.q, (b).q0.q, (c).q0.q); \
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QuatAdd ((a).qe.q, (b).qe.q, (c).qe.q); \
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} while (0)
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#define DualQuatSubtract(a,b,c) \
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do { \
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QuatSub ((a).q0.q, (b).q0.q, (c).q0.q); \
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QuatSub ((a).qe.q, (b).qe.q, (c).qe.q); \
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} while (0)
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#define DualQuatNegate(a,b) \
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do { \
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QuatNegate ((a).q0.q, (b).q0.q); \
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QuatNegate ((a).qe.q, (b).qe.q); \
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} while (0)
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#define DualQuatConjQ(a,b) \
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do { \
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QuatConj ((a).q0.q, (b).q0.q); \
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QuatConj ((a).qe.q, (b).qe.q); \
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} while (0)
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|
#define DualQuatConjE(a,b) \
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do { \
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(b).q0 = (a).q0; \
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QuatNegate ((a).qe.q, (b).qe.q); \
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} while (0)
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|
#define DualQuatConjQE(a,b) \
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do { \
|
|
QuatConj ((a).q0.q, (b).q0.q); \
|
|
(b).qe.sv.s = -(a).qe.sv.s; \
|
|
VectorCopy ((a).qe.sv.v, (b).qe.sv.v); \
|
|
} while (0)
|
|
#define DualQuatMult(a,b,c) \
|
|
do { \
|
|
Quat_t t; \
|
|
QuatMult ((a).q0.q, (b).qe.q, t.q); \
|
|
QuatMult ((a).qe.q, (b).q0.q, (c).qe.q); \
|
|
QuatAdd (t.q, (c).qe.q, (c).qe.q); \
|
|
QuatMult ((a).q0.q, (b).q0.q, (c).q0.q); \
|
|
} while (0);
|
|
#define DualQuatMultAdd(a,s,b,c) \
|
|
do { \
|
|
QuatMultAdd ((a).q0.q, s, (b).q0.q, (c).q0.q); \
|
|
QuatMultAdd ((a).qe.q, s, (b).qe.q, (c).qe.q); \
|
|
} while (0)
|
|
#define DualQuatMultSub(a,s,b,c) \
|
|
do { \
|
|
QuatMultSub ((a).q0.q, s, (b).q0.q, (c).q0.q); \
|
|
QuatMultSub ((a).qe.q, s, (b).qe.q, (c).qe.q); \
|
|
} while (0)
|
|
#define DualQuatNorm(a,b) \
|
|
do { \
|
|
(b).r = QuatLength ((a).q0.q); \
|
|
(b).e = 2 * QDotProduct ((a).q0.q, (a).qe.q); \
|
|
} while (0)
|
|
#define DualQuatScale(a,b,c) \
|
|
do { \
|
|
QuatSub ((a).q0.q, (b), (c).q0.q); \
|
|
QuatSub ((a).qe.q, (b), (c).qe.q); \
|
|
} while (0)
|
|
#define DualQuatCompCompare(x, op, y) \
|
|
(QuatCompCompare ((x).q0.q, op, (y).q0.q) \
|
|
&&QuatCompCompare ((x).qe.q, op, (y).qe.q))
|
|
#define DualQuatCompare(x, y) DualQuatCompCompare (x, ==, y)
|
|
#define DualQuatIsZero(a) (QuatIsZero ((a).q0.q) && QuatIsZero ((a).qe.q))
|
|
#define DualQuatSetVect(vec, a) \
|
|
do { \
|
|
(a).q0.sv.s = 1; \
|
|
VectorZero ((a).q0.sv.v); \
|
|
(a).qe.sv.s = 0; \
|
|
VectorCopy (vec, (a).qe.sv.v); \
|
|
} while (0)
|
|
#define DualQuatRotTrans(rot, trans, dq) \
|
|
do { \
|
|
QuatCopy (rot, (dq).q0.q); \
|
|
(dq).qe.sv.s = 0; \
|
|
VectorScale (trans, 0.5, (dq).qe.sv.v); \
|
|
QuatMult ((dq).qe.q, (dq).q0.q, (dq).qe.q); \
|
|
} while (0)
|
|
#define DualQuatZero(a) \
|
|
do { \
|
|
QuatZero ((a).q0.q); \
|
|
QuatZero ((a).qe.q); \
|
|
} while (0)
|
|
#define DualQuatBlend(dq1,dq2,b,dq) \
|
|
do { \
|
|
QuatBlend ((dq1).q0.q, (dq2).q0.q, (b), (dq).q0.q); \
|
|
QuatBlend ((dq1).qe.q, (dq2).qe.q, (b), (dq).qe.q); \
|
|
} while (0)
|
|
#define DualQuatExpand(dq) QuatExpand ((dq).q0.q), QuatExpand ((dq).qe.q)
|
|
|
|
#define Mat4Copy(a, b) \
|
|
do { \
|
|
QuatCopy ((a) + 0, (b) + 0); \
|
|
QuatCopy ((a) + 4, (b) + 4); \
|
|
QuatCopy ((a) + 8, (b) + 8); \
|
|
QuatCopy ((a) + 12, (b) + 12); \
|
|
} while (0)
|
|
#define Mat4Add(a, b, c) \
|
|
do { \
|
|
QuatAdd ((a) + 0, (b) + 0, (c) + 0); \
|
|
QuatAdd ((a) + 4, (b) + 4, (c) + 4); \
|
|
QuatAdd ((a) + 8, (b) + 8, (c) + 8); \
|
|
QuatAdd ((a) + 12, (b) + 12, (c) + 12); \
|
|
} while (0)
|
|
#define Mat4Subtract(a, b, c) \
|
|
do { \
|
|
QuatSubtract ((a) + 0, (b) + 0, (c) + 0); \
|
|
QuatSubtract ((a) + 4, (b) + 4, (c) + 4); \
|
|
QuatSubtract ((a) + 8, (b) + 8, (c) + 8); \
|
|
QuatSubtract ((a) + 12, (b) + 12, (c) + 12); \
|
|
} while (0)
|
|
#define Mat4Scale(a, b, c) \
|
|
do { \
|
|
QuatScale ((a) + 0, (b), (c) + 0); \
|
|
QuatScale ((a) + 4, (b), (c) + 4); \
|
|
QuatScale ((a) + 8, (b), (c) + 8); \
|
|
QuatScale ((a) + 12, (b), (c) + 12); \
|
|
} while (0)
|
|
#define Mat4CompMult(a, b, c) \
|
|
do { \
|
|
QuatCompMult ((a) + 0, (b) + 0, (c) + 0); \
|
|
QuatCompMult ((a) + 4, (b) + 4, (c) + 4); \
|
|
QuatCompMult ((a) + 8, (b) + 8, (c) + 8); \
|
|
QuatCompMult ((a) + 12, (b) + 12, (c) + 12); \
|
|
} while (0)
|
|
#define Mat4Zero(a) \
|
|
memset (a, 0, 16 * sizeof a[0])
|
|
#define Mat4Identity(a) \
|
|
do { \
|
|
Mat4Zero (a); \
|
|
a[15] = a[10] = a[5] = a[0] = 1; \
|
|
} while (0)
|
|
#define Mat4Expand(a) \
|
|
QuatExpand (a + 0), \
|
|
QuatExpand (a + 4), \
|
|
QuatExpand (a + 8), \
|
|
QuatExpand (a + 12)
|
|
|
|
#define qfrandom(MAX) ((float) MAX * (rand() * (1.0 / (RAND_MAX + 1.0))))
|
|
|
|
// up / down
|
|
#define PITCH 0
|
|
// left / right
|
|
#define YAW 1
|
|
// fall over
|
|
#define ROLL 2
|
|
|
|
vec_t _DotProduct (const vec3_t v1, const vec3_t v2);
|
|
void _VectorAdd (const vec3_t veca, const vec3_t vecb, vec3_t out);
|
|
void _VectorCopy (const vec3_t in, vec3_t out);
|
|
int _VectorCompare (const vec3_t v1, const vec3_t v2); // uses EQUAL_EPSILON
|
|
vec_t _VectorLength (const vec3_t v);
|
|
void _VectorMA (const vec3_t veca, float scale, const vec3_t vecb,
|
|
vec3_t vecc);
|
|
void _VectorScale (const vec3_t in, vec_t scale, vec3_t out);
|
|
void _VectorSubtract (const vec3_t veca, const vec3_t vecb, vec3_t out);
|
|
void CrossProduct (const vec3_t v1, const vec3_t v2, vec3_t cross);
|
|
vec_t _VectorNormalize (vec3_t v); // returns vector length
|
|
int Q_log2(int val);
|
|
|
|
void R_ConcatRotations (float in1[3][3], float in2[3][3], float out[3][3]);
|
|
void R_ConcatTransforms (float in1[3][4], float in2[3][4], float out[3][4]);
|
|
|
|
void FloorDivMod (double numer, double denom, int *quotient, int *rem);
|
|
fixed16_t Invert24To16(fixed16_t val);
|
|
fixed16_t Mul16_30(fixed16_t multiplier, fixed16_t multiplicand);
|
|
int GreatestCommonDivisor (int i1, int i2);
|
|
|
|
/** Convert quake angles to basis vectors.
|
|
|
|
The basis vectors form a left handed system (although the world is
|
|
right handed). When all angles are 0, \a forward points along the world
|
|
X axis, \a right along the <em>negative</em> Y axis, and \a up along
|
|
the Z axis.
|
|
|
|
Rotation is done by:
|
|
-# Rotating YAW degrees counterclockwise around the local Z axis
|
|
-# Rotating PITCH degrees clockwise around the new local negative Y axis
|
|
(or counterclockwise around the new local Y axis).
|
|
-# Rotating ROLL degrees counterclockwise around the local X axis
|
|
|
|
Thus when used for the player from the first person perspective,
|
|
positive YAW turns to the left, positive PITCH looks down, and positive
|
|
ROLL leans to the right.
|
|
|
|
\f[
|
|
YAW=\begin{array}{ccc}
|
|
c_{y} & s_{y} & 0\\
|
|
-s_{y} & c_{y} & 0\\
|
|
0 & 0 & 1
|
|
\end{array}
|
|
\f]
|
|
\f[
|
|
PITCH=\begin{array}{ccc}
|
|
c_{p} & 0 & -s_{p}\\
|
|
0 & 1 & 0\\
|
|
s_{p} & 0 & c_{p}
|
|
\end{array}
|
|
\f]
|
|
\f[
|
|
ROLL=\begin{array}{ccc}
|
|
1 & 0 & 0\\
|
|
0 & c_{r} & -s_{r}\\
|
|
0 & s_{r} & c_{r}
|
|
\end{array}
|
|
\f]
|
|
\f[
|
|
ROLL\,(PITCH\,YAW)=\begin{array}{c}
|
|
forward\\
|
|
-right\\
|
|
up
|
|
\end{array}
|
|
\f]
|
|
|
|
\param angles The rotation angles.
|
|
\param forward The vector pointing forward.
|
|
\param right The vector pointing to the right.
|
|
\param up The vector pointing up.
|
|
*/
|
|
void AngleVectors (const vec3_t angles, vec3_t forward, vec3_t right,
|
|
vec3_t up);
|
|
void AngleQuat (const vec3_t angles, quat_t q);
|
|
void VectorVectors (const vec3_t forward, vec3_t right, vec3_t up);
|
|
int BoxOnPlaneSide (const vec3_t emins, const vec3_t emaxs,
|
|
struct plane_s *plane);
|
|
float anglemod (float a);
|
|
|
|
void RotatePointAroundVector (vec3_t dst, const vec3_t axis,
|
|
const vec3_t point, float degrees);
|
|
|
|
void QuatMult (const quat_t q1, const quat_t q2, quat_t out);
|
|
void QuatMultVec (const quat_t q, const vec3_t v, vec3_t out);
|
|
void QuatInverse (const quat_t in, quat_t out);
|
|
void QuatExp (const quat_t a, quat_t b);
|
|
void QuatToMatrix (const quat_t q, vec_t *m, int homogenous, int vertical);
|
|
|
|
void Mat4Init (const quat_t rot, const vec3_t scale, const vec3_t trans,
|
|
mat4_t mat);
|
|
void Mat4Transpose (const mat4_t a, mat4_t b);
|
|
int Mat4Inverse (const mat4_t a, mat4_t b);
|
|
void Mat4Mult (const mat4_t a, const mat4_t b, mat4_t c);
|
|
void Mat4MultVec (const mat4_t a, const vec3_t b, vec3_t c);
|
|
/** Decompose a column major matrix into its component transformations.
|
|
|
|
This gives the matrix's rotation as a quaternion, shear, scale
|
|
(XY, XZ, YZ), and translation. Using the following sequence will give the
|
|
same result as multiplying \a v by \a mat.
|
|
|
|
QuatMultVec (rot, v, v);
|
|
VectorShear (shear, v, v);
|
|
VectorCompMult (scale, v, v);
|
|
VectorAdd (trans, v, v);
|
|
*/
|
|
int Mat4Decompose (const mat4_t mat, quat_t rot, vec3_t shear, vec3_t scale,
|
|
vec3_t trans);
|
|
|
|
#define BOX_ON_PLANE_SIDE(emins, emaxs, p) \
|
|
(((p)->type < 3)? \
|
|
( \
|
|
((p)->dist <= (emins)[(p)->type])? \
|
|
1 \
|
|
: \
|
|
( \
|
|
((p)->dist >= (emaxs)[(p)->type])? \
|
|
2 \
|
|
: \
|
|
3 \
|
|
) \
|
|
) \
|
|
: \
|
|
BoxOnPlaneSide( (emins), (emaxs), (p)))
|
|
|
|
#define PlaneDist(point,plane) \
|
|
((plane)->type < 3 ? (point)[(plane)->type] \
|
|
: DotProduct((point), (plane)->normal))
|
|
#define PlaneDiff(point,plane) \
|
|
(PlaneDist (point, plane) - (plane)->dist)
|
|
|
|
#define PlaneFlip(sp, dp) \
|
|
do { \
|
|
(dp)->dist = -(sp)->dist; \
|
|
VectorNegate ((sp)->normal, (dp)->normal); \
|
|
} while (0)
|
|
|
|
int16_t FloatToHalf (float x);
|
|
float HalfToFloat (int16_t x);
|
|
extern plane_t * const frustum;
|
|
extern inline qboolean R_CullBox (const vec3_t mins, const vec3_t maxs);
|
|
extern inline qboolean R_CullSphere (const vec3_t origin, const float radius);
|
|
extern inline float VectorNormalize (vec3_t v); // returns vector length
|
|
#ifndef IMPLEMENT_R_Cull
|
|
extern inline
|
|
#else
|
|
VISIBLE
|
|
#endif
|
|
qboolean
|
|
R_CullBox (const vec3_t mins, const vec3_t maxs)
|
|
{
|
|
int i;
|
|
|
|
for (i=0 ; i < 4 ; i++)
|
|
if (BoxOnPlaneSide (mins, maxs, &frustum[i]) == 2)
|
|
return true;
|
|
return false;
|
|
}
|
|
|
|
#ifndef IMPLEMENT_R_Cull
|
|
extern inline
|
|
#else
|
|
VISIBLE
|
|
#endif
|
|
qboolean
|
|
R_CullSphere (const vec3_t origin, const float radius)
|
|
{
|
|
int i;
|
|
float r;
|
|
|
|
for (i = 0; i < 4; i++)
|
|
{
|
|
r = DotProduct (origin, frustum[i].normal) - frustum[i].dist;
|
|
if (r <= -radius)
|
|
return true;
|
|
}
|
|
return false;
|
|
}
|
|
|
|
#ifndef IMPLEMENT_VectorNormalize
|
|
extern inline
|
|
#else
|
|
VISIBLE
|
|
#endif
|
|
float
|
|
VectorNormalize (vec3_t v)
|
|
{
|
|
float length;
|
|
|
|
length = DotProduct (v, v);
|
|
if (length) {
|
|
float ilength;
|
|
|
|
length = sqrt (length);
|
|
ilength = 1.0 / length;
|
|
v[0] *= ilength;
|
|
v[1] *= ilength;
|
|
v[2] *= ilength;
|
|
}
|
|
|
|
return length;
|
|
}
|
|
|
|
//@}
|
|
|
|
#endif // __mathlib_h
|