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872 lines
17 KiB
872 lines
17 KiB
/* |
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mathlib.c - internal mathlib |
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Copyright (C) 2010 Uncle Mike |
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|
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This program is free software: you can redistribute it and/or modify |
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it under the terms of the GNU General Public License as published by |
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the Free Software Foundation, either version 3 of the License, or |
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(at your option) any later version. |
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|
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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. See the |
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GNU General Public License for more details. |
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*/ |
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#include <math.h> |
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#include "common.h" |
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#include "mathlib.h" |
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#include "eiface.h" |
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#define NUM_HULL_ROUNDS ARRAYSIZE( hull_table ) |
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#define HULL_PRECISION 4 |
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vec3_t vec3_origin = { 0, 0, 0 }; |
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static word hull_table[] = { 2, 4, 6, 8, 12, 16, 18, 24, 28, 32, 36, 40, 48, 54, 56, 60, 64, 72, 80, 112, 120, 128, 140, 176 }; |
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int boxpnt[6][4] = |
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{ |
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{ 0, 4, 6, 2 }, // +X |
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{ 0, 1, 5, 4 }, // +Y |
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{ 0, 2, 3, 1 }, // +Z |
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{ 7, 5, 1, 3 }, // -X |
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{ 7, 3, 2, 6 }, // -Y |
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{ 7, 6, 4, 5 }, // -Z |
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}; |
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// pre-quantized table normals from Quake1 |
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const float m_bytenormals[NUMVERTEXNORMALS][3] = |
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{ |
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#include "anorms.h" |
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}; |
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/* |
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================= |
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anglemod |
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================= |
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*/ |
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float anglemod( float a ) |
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{ |
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a = (360.0 / 65536) * ((int)(a*(65536/360.0)) & 65535); |
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return a; |
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} |
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/* |
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================= |
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SimpleSpline |
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NOTE: ripped from hl2 source |
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hermite basis function for smooth interpolation |
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Similar to Gain() above, but very cheap to call |
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value should be between 0 & 1 inclusive |
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================= |
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*/ |
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float SimpleSpline( float value ) |
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{ |
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float valueSquared = value * value; |
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// nice little ease-in, ease-out spline-like curve |
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return (3.0f * valueSquared - 2.0f * valueSquared * value); |
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} |
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word FloatToHalf( float v ) |
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{ |
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unsigned int i = *((unsigned int *)&v); |
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unsigned int e = (i >> 23) & 0x00ff; |
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unsigned int m = i & 0x007fffff; |
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unsigned short h; |
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if( e <= 127 - 15 ) |
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h = ((m | 0x00800000) >> (127 - 14 - e)) >> 13; |
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else h = (i >> 13) & 0x3fff; |
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h |= (i >> 16) & 0xc000; |
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return h; |
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} |
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float HalfToFloat( word h ) |
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{ |
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unsigned int f = (h << 16) & 0x80000000; |
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unsigned int em = h & 0x7fff; |
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if( em > 0x03ff ) |
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{ |
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f |= (em << 13) + ((127 - 15) << 23); |
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} |
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else |
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{ |
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unsigned int m = em & 0x03ff; |
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if( m != 0 ) |
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{ |
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unsigned int e = (em >> 10) & 0x1f; |
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while(( m & 0x0400 ) == 0 ) |
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{ |
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m <<= 1; |
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e--; |
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} |
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m &= 0x3ff; |
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f |= ((e + (127 - 14)) << 23) | (m << 13); |
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} |
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} |
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return *((float *)&f); |
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} |
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/* |
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================= |
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RoundUpHullSize |
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round the hullsize to nearest 'right' value |
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================= |
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*/ |
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void RoundUpHullSize( vec3_t size ) |
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{ |
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int i, j; |
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for( i = 0; i < 3; i++) |
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{ |
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qboolean negative = false; |
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float result, value; |
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value = size[i]; |
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if( value < 0.0f ) negative = true; |
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value = Q_ceil( fabs( value )); |
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result = Q_ceil( size[i] ); |
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// lookup hull table to find nearest supposed value |
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for( j = 0; j < NUM_HULL_ROUNDS; j++ ) |
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{ |
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if( value > hull_table[j] ) |
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continue; // ceil only |
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if( negative ) |
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{ |
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result = ( value - hull_table[j] ); |
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if( result <= HULL_PRECISION ) |
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{ |
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result = -hull_table[j]; |
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break; |
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} |
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} |
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else |
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{ |
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result = ( value - hull_table[j] ); |
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if( result <= HULL_PRECISION ) |
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{ |
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result = hull_table[j]; |
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break; |
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} |
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} |
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} |
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size[i] = result; |
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} |
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} |
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/* |
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================= |
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SignbitsForPlane |
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fast box on planeside test |
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================= |
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*/ |
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int SignbitsForPlane( const vec3_t normal ) |
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{ |
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int bits, i; |
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for( bits = i = 0; i < 3; i++ ) |
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if( normal[i] < 0.0f ) bits |= 1<<i; |
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return bits; |
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} |
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/* |
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================= |
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PlaneTypeForNormal |
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================= |
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*/ |
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int PlaneTypeForNormal( const vec3_t normal ) |
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{ |
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if( normal[0] == 1.0f ) |
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return PLANE_X; |
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if( normal[1] == 1.0f ) |
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return PLANE_Y; |
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if( normal[2] == 1.0f ) |
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return PLANE_Z; |
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return PLANE_NONAXIAL; |
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} |
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/* |
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================= |
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PlanesGetIntersectionPoint |
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================= |
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*/ |
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qboolean PlanesGetIntersectionPoint( const mplane_t *plane1, const mplane_t *plane2, const mplane_t *plane3, vec3_t out ) |
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{ |
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vec3_t n1, n2, n3; |
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vec3_t n1n2, n2n3, n3n1; |
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float denom; |
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VectorNormalize2( plane1->normal, n1 ); |
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VectorNormalize2( plane2->normal, n2 ); |
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VectorNormalize2( plane3->normal, n3 ); |
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CrossProduct( n1, n2, n1n2 ); |
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CrossProduct( n2, n3, n2n3 ); |
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CrossProduct( n3, n1, n3n1 ); |
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denom = DotProduct( n1, n2n3 ); |
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VectorClear( out ); |
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// check if the denominator is zero (which would mean that no intersection is to be found |
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if( denom == 0.0f ) |
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{ |
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// no intersection could be found, return <0,0,0> |
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return false; |
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} |
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// compute intersection point |
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#if 0 |
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VectorMAMAM( plane1->dist, n2n3, plane2->dist, n3n1, plane3->dist, n1n2, out ); |
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#else |
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VectorMA( out, plane1->dist, n2n3, out ); |
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VectorMA( out, plane2->dist, n3n1, out ); |
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VectorMA( out, plane3->dist, n1n2, out ); |
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#endif |
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VectorScale( out, ( 1.0f / denom ), out ); |
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return true; |
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} |
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/* |
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================= |
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NearestPOW |
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================= |
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*/ |
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int NearestPOW( int value, qboolean roundDown ) |
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{ |
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int n = 1; |
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if( value <= 0 ) return 1; |
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while( n < value ) n <<= 1; |
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if( roundDown ) |
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{ |
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if( n > value ) n >>= 1; |
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} |
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return n; |
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} |
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// remap a value in the range [A,B] to [C,D]. |
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float RemapVal( float val, float A, float B, float C, float D ) |
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{ |
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return C + (D - C) * (val - A) / (B - A); |
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} |
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float ApproachVal( float target, float value, float speed ) |
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{ |
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float delta = target - value; |
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if( delta > speed ) |
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value += speed; |
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else if( delta < -speed ) |
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value -= speed; |
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else value = target; |
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return value; |
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} |
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/* |
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================= |
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rsqrt |
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================= |
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*/ |
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float rsqrt( float number ) |
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{ |
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int i; |
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float x, y; |
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if( number == 0.0f ) |
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return 0.0f; |
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x = number * 0.5f; |
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i = *(int *)&number; // evil floating point bit level hacking |
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i = 0x5f3759df - (i >> 1); // what the fuck? |
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y = *(float *)&i; |
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y = y * (1.5f - (x * y * y)); // first iteration |
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return y; |
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} |
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/* |
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================= |
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SinCos |
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================= |
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*/ |
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void SinCos( float radians, float *sine, float *cosine ) |
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{ |
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#if _MSC_VER == 1200 |
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_asm |
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{ |
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fld dword ptr [radians] |
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fsincos |
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mov edx, dword ptr [cosine] |
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mov eax, dword ptr [sine] |
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fstp dword ptr [edx] |
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fstp dword ptr [eax] |
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} |
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#else |
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*sine = sinf(radians); |
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*cosine = cosf(radians); |
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#endif |
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} |
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/* |
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============== |
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VectorCompareEpsilon |
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============== |
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*/ |
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qboolean VectorCompareEpsilon( const vec3_t vec1, const vec3_t vec2, vec_t epsilon ) |
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{ |
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vec_t ax, ay, az; |
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ax = fabs( vec1[0] - vec2[0] ); |
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ay = fabs( vec1[1] - vec2[1] ); |
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az = fabs( vec1[2] - vec2[2] ); |
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if(( ax <= epsilon ) && ( ay <= epsilon ) && ( az <= epsilon )) |
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return true; |
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return false; |
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} |
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float VectorNormalizeLength2( const vec3_t v, vec3_t out ) |
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{ |
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float length, ilength; |
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length = v[0] * v[0] + v[1] * v[1] + v[2] * v[2]; |
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length = sqrt( length ); |
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if( length ) |
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{ |
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ilength = 1.0f / length; |
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out[0] = v[0] * ilength; |
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out[1] = v[1] * ilength; |
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out[2] = v[2] * ilength; |
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} |
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return length; |
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} |
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void VectorVectors( const vec3_t forward, vec3_t right, vec3_t up ) |
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{ |
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float d; |
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right[0] = forward[2]; |
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right[1] = -forward[0]; |
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right[2] = forward[1]; |
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d = DotProduct( forward, right ); |
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VectorMA( right, -d, forward, right ); |
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VectorNormalize( right ); |
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CrossProduct( right, forward, up ); |
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VectorNormalize( up ); |
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} |
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/* |
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================= |
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AngleVectors |
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================= |
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*/ |
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void AngleVectors( const vec3_t angles, vec3_t forward, vec3_t right, vec3_t up ) |
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{ |
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float sr, sp, sy, cr, cp, cy; |
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SinCos( DEG2RAD( angles[YAW] ), &sy, &cy ); |
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SinCos( DEG2RAD( angles[PITCH] ), &sp, &cp ); |
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SinCos( DEG2RAD( angles[ROLL] ), &sr, &cr ); |
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if( forward ) |
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{ |
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forward[0] = cp * cy; |
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forward[1] = cp * sy; |
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forward[2] = -sp; |
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} |
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if( right ) |
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{ |
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right[0] = (-1.0f * sr * sp * cy + -1.0f * cr * -sy ); |
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right[1] = (-1.0f * sr * sp * sy + -1.0f * cr * cy ); |
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right[2] = (-1.0f * sr * cp); |
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} |
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if( up ) |
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{ |
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up[0] = (cr * sp * cy + -sr * -sy ); |
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up[1] = (cr * sp * sy + -sr * cy ); |
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up[2] = (cr * cp); |
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} |
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} |
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/* |
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================= |
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VectorAngles |
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================= |
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*/ |
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void VectorAngles( const float *forward, float *angles ) |
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{ |
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float tmp, yaw, pitch; |
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if( !forward || !angles ) |
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{ |
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if( angles ) VectorClear( angles ); |
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return; |
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} |
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if( forward[1] == 0 && forward[0] == 0 ) |
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{ |
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// fast case |
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yaw = 0; |
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if( forward[2] > 0 ) |
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pitch = 90.0f; |
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else pitch = 270.0f; |
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} |
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else |
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{ |
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yaw = ( atan2( forward[1], forward[0] ) * 180 / M_PI ); |
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if( yaw < 0 ) yaw += 360; |
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tmp = sqrt( forward[0] * forward[0] + forward[1] * forward[1] ); |
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pitch = ( atan2( forward[2], tmp ) * 180 / M_PI ); |
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if( pitch < 0 ) pitch += 360; |
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} |
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VectorSet( angles, pitch, yaw, 0 ); |
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} |
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/* |
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================= |
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VectorsAngles |
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================= |
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*/ |
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void VectorsAngles( const vec3_t forward, const vec3_t right, const vec3_t up, vec3_t angles ) |
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{ |
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float pitch, cpitch, yaw, roll; |
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pitch = -asin( forward[2] ); |
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cpitch = cos( pitch ); |
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if( fabs( cpitch ) > EQUAL_EPSILON ) // gimball lock? |
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{ |
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cpitch = 1.0f / cpitch; |
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pitch = RAD2DEG( pitch ); |
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yaw = RAD2DEG( atan2( forward[1] * cpitch, forward[0] * cpitch )); |
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roll = RAD2DEG( atan2( -right[2] * cpitch, up[2] * cpitch )); |
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} |
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else |
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{ |
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pitch = forward[2] > 0 ? -90.0f : 90.0f; |
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yaw = RAD2DEG( atan2( right[0], -right[1] )); |
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roll = 180.0f; |
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} |
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angles[PITCH] = pitch; |
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angles[YAW] = yaw; |
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angles[ROLL] = roll; |
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} |
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// |
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// bounds operations |
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// |
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/* |
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================= |
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ClearBounds |
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================= |
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*/ |
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void ClearBounds( vec3_t mins, vec3_t maxs ) |
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{ |
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// make bogus range |
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mins[0] = mins[1] = mins[2] = 999999.0f; |
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maxs[0] = maxs[1] = maxs[2] = -999999.0f; |
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} |
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/* |
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================= |
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AddPointToBounds |
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================= |
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*/ |
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void AddPointToBounds( const vec3_t v, vec3_t mins, vec3_t maxs ) |
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{ |
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float val; |
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int i; |
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for( i = 0; i < 3; i++ ) |
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{ |
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val = v[i]; |
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if( val < mins[i] ) mins[i] = val; |
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if( val > maxs[i] ) maxs[i] = val; |
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} |
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} |
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/* |
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================= |
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ExpandBounds |
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================= |
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*/ |
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void ExpandBounds( vec3_t mins, vec3_t maxs, float offset ) |
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{ |
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mins[0] -= offset; |
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mins[1] -= offset; |
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mins[2] -= offset; |
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maxs[0] += offset; |
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maxs[1] += offset; |
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maxs[2] += offset; |
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} |
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|
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/* |
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================= |
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BoundsIntersect |
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================= |
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*/ |
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qboolean BoundsIntersect( const vec3_t mins1, const vec3_t maxs1, const vec3_t mins2, const vec3_t maxs2 ) |
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{ |
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if( mins1[0] > maxs2[0] || mins1[1] > maxs2[1] || mins1[2] > maxs2[2] ) |
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return false; |
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if( maxs1[0] < mins2[0] || maxs1[1] < mins2[1] || maxs1[2] < mins2[2] ) |
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return false; |
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return true; |
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} |
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|
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/* |
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================= |
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BoundsAndSphereIntersect |
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================= |
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*/ |
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qboolean BoundsAndSphereIntersect( const vec3_t mins, const vec3_t maxs, const vec3_t origin, float radius ) |
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{ |
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if( mins[0] > origin[0] + radius || mins[1] > origin[1] + radius || mins[2] > origin[2] + radius ) |
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return false; |
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if( maxs[0] < origin[0] - radius || maxs[1] < origin[1] - radius || maxs[2] < origin[2] - radius ) |
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return false; |
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return true; |
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} |
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|
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/* |
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================= |
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SphereIntersect |
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================= |
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*/ |
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qboolean SphereIntersect( const vec3_t vSphereCenter, float fSphereRadiusSquared, const vec3_t vLinePt, const vec3_t vLineDir ) |
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{ |
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float a, b, c, insideSqr; |
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vec3_t p; |
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// translate sphere to origin. |
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VectorSubtract( vLinePt, vSphereCenter, p ); |
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a = DotProduct( vLineDir, vLineDir ); |
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b = 2.0f * DotProduct( p, vLineDir ); |
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c = DotProduct( p, p ) - fSphereRadiusSquared; |
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insideSqr = b * b - 4.0f * a * c; |
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if( insideSqr <= 0.000001f ) |
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return false; |
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return true; |
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} |
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|
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/* |
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================= |
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PlaneIntersect |
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|
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find point where ray |
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was intersect with plane |
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================= |
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*/ |
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void PlaneIntersect( const mplane_t *plane, const vec3_t p0, const vec3_t p1, vec3_t out ) |
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{ |
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float distToPlane = PlaneDiff( p0, plane ); |
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float planeDotRay = DotProduct( plane->normal, p1 ); |
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float sect = -(distToPlane) / planeDotRay; |
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VectorMA( p0, sect, p1, out ); |
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} |
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|
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/* |
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================= |
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RadiusFromBounds |
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================= |
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*/ |
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float RadiusFromBounds( const vec3_t mins, const vec3_t maxs ) |
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{ |
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vec3_t corner; |
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int i; |
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for( i = 0; i < 3; i++ ) |
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{ |
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corner[i] = fabs( mins[i] ) > fabs( maxs[i] ) ? fabs( mins[i] ) : fabs( maxs[i] ); |
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} |
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return VectorLength( corner ); |
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} |
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// |
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// studio utils |
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// |
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/* |
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==================== |
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AngleQuaternion |
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|
|
==================== |
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*/ |
|
void AngleQuaternion( const vec3_t angles, vec4_t q, qboolean studio ) |
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{ |
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float sr, sp, sy, cr, cp, cy; |
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|
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if( studio ) |
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{ |
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SinCos( angles[ROLL] * 0.5f, &sy, &cy ); |
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SinCos( angles[YAW] * 0.5f, &sp, &cp ); |
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SinCos( angles[PITCH] * 0.5f, &sr, &cr ); |
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} |
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else |
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{ |
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SinCos( DEG2RAD( angles[YAW] ) * 0.5f, &sy, &cy ); |
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SinCos( DEG2RAD( angles[PITCH] ) * 0.5f, &sp, &cp ); |
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SinCos( DEG2RAD( angles[ROLL] ) * 0.5f, &sr, &cr ); |
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} |
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|
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q[0] = sr * cp * cy - cr * sp * sy; // X |
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q[1] = cr * sp * cy + sr * cp * sy; // Y |
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q[2] = cr * cp * sy - sr * sp * cy; // Z |
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q[3] = cr * cp * cy + sr * sp * sy; // W |
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} |
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|
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/* |
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==================== |
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QuaternionAngle |
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==================== |
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*/ |
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void QuaternionAngle( const vec4_t q, vec3_t angles ) |
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{ |
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matrix3x4 mat; |
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Matrix3x4_FromOriginQuat( mat, q, vec3_origin ); |
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Matrix3x4_AnglesFromMatrix( mat, angles ); |
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} |
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/* |
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==================== |
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QuaternionAlign |
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make sure quaternions are within 180 degrees of one another, |
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if not, reverse q |
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==================== |
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*/ |
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void QuaternionAlign( const vec4_t p, const vec4_t q, vec4_t qt ) |
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{ |
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// decide if one of the quaternions is backwards |
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float a = 0.0f; |
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float b = 0.0f; |
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int i; |
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for( i = 0; i < 4; i++ ) |
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{ |
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a += (p[i] - q[i]) * (p[i] - q[i]); |
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b += (p[i] + q[i]) * (p[i] + q[i]); |
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} |
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if( a > b ) |
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{ |
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for( i = 0; i < 4; i++ ) |
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qt[i] = -q[i]; |
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} |
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else |
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{ |
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for( i = 0; i < 4; i++ ) |
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qt[i] = q[i]; |
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} |
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} |
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/* |
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==================== |
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QuaternionSlerpNoAlign |
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==================== |
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*/ |
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void QuaternionSlerpNoAlign( const vec4_t p, const vec4_t q, float t, vec4_t qt ) |
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{ |
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float omega, cosom, sinom, sclp, sclq; |
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int i; |
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// 0.0 returns p, 1.0 return q. |
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cosom = p[0] * q[0] + p[1] * q[1] + p[2] * q[2] + p[3] * q[3]; |
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if(( 1.0f + cosom ) > 0.000001f ) |
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{ |
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if(( 1.0f - cosom ) > 0.000001f ) |
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{ |
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omega = acos( cosom ); |
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sinom = sin( omega ); |
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sclp = sin( (1.0f - t) * omega) / sinom; |
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sclq = sin( t * omega ) / sinom; |
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} |
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else |
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{ |
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sclp = 1.0f - t; |
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sclq = t; |
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} |
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for( i = 0; i < 4; i++ ) |
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{ |
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qt[i] = sclp * p[i] + sclq * q[i]; |
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} |
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} |
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else |
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{ |
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qt[0] = -q[1]; |
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qt[1] = q[0]; |
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qt[2] = -q[3]; |
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qt[3] = q[2]; |
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sclp = sin(( 1.0f - t ) * ( 0.5f * M_PI )); |
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sclq = sin( t * ( 0.5f * M_PI )); |
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for( i = 0; i < 3; i++ ) |
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{ |
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qt[i] = sclp * p[i] + sclq * qt[i]; |
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} |
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} |
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} |
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/* |
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==================== |
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QuaternionSlerp |
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Quaternion sphereical linear interpolation |
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==================== |
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*/ |
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void QuaternionSlerp( const vec4_t p, const vec4_t q, float t, vec4_t qt ) |
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{ |
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vec4_t q2; |
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// 0.0 returns p, 1.0 return q. |
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// decide if one of the quaternions is backwards |
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QuaternionAlign( p, q, q2 ); |
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QuaternionSlerpNoAlign( p, q2, t, qt ); |
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} |
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/* |
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==================== |
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V_CalcFov |
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==================== |
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*/ |
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float V_CalcFov( float *fov_x, float width, float height ) |
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{ |
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float x, half_fov_y; |
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if( *fov_x < 1.0f || *fov_x > 179.0f ) |
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*fov_x = 90.0f; // default value |
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x = width / tan( DEG2RAD( *fov_x ) * 0.5f ); |
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half_fov_y = atan( height / x ); |
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return RAD2DEG( half_fov_y ) * 2; |
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} |
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/* |
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==================== |
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V_AdjustFov |
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==================== |
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*/ |
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void V_AdjustFov( float *fov_x, float *fov_y, float width, float height, qboolean lock_x ) |
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{ |
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float x, y; |
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if( width * 3 == 4 * height || width * 4 == height * 5 ) |
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{ |
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// 4:3 or 5:4 ratio |
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return; |
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} |
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if( lock_x ) |
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{ |
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*fov_y = 2 * atan((width * 3) / (height * 4) * tan( *fov_y * M_PI / 360.0 * 0.5 )) * 360 / M_PI; |
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return; |
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} |
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y = V_CalcFov( fov_x, 640, 480 ); |
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x = *fov_x; |
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*fov_x = V_CalcFov( &y, height, width ); |
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if( *fov_x < x ) *fov_x = x; |
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else *fov_y = y; |
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} |
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/* |
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================== |
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BoxOnPlaneSide |
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Returns 1, 2, or 1 + 2 |
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================== |
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*/ |
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int BoxOnPlaneSide( const vec3_t emins, const vec3_t emaxs, const mplane_t *p ) |
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{ |
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float dist1, dist2; |
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int sides = 0; |
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// general case |
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switch( p->signbits ) |
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{ |
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case 0: |
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dist1 = p->normal[0]*emaxs[0] + p->normal[1]*emaxs[1] + p->normal[2]*emaxs[2]; |
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dist2 = p->normal[0]*emins[0] + p->normal[1]*emins[1] + p->normal[2]*emins[2]; |
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break; |
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case 1: |
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dist1 = p->normal[0]*emins[0] + p->normal[1]*emaxs[1] + p->normal[2]*emaxs[2]; |
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dist2 = p->normal[0]*emaxs[0] + p->normal[1]*emins[1] + p->normal[2]*emins[2]; |
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break; |
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case 2: |
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dist1 = p->normal[0]*emaxs[0] + p->normal[1]*emins[1] + p->normal[2]*emaxs[2]; |
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dist2 = p->normal[0]*emins[0] + p->normal[1]*emaxs[1] + p->normal[2]*emins[2]; |
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break; |
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case 3: |
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dist1 = p->normal[0]*emins[0] + p->normal[1]*emins[1] + p->normal[2]*emaxs[2]; |
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dist2 = p->normal[0]*emaxs[0] + p->normal[1]*emaxs[1] + p->normal[2]*emins[2]; |
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break; |
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case 4: |
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dist1 = p->normal[0]*emaxs[0] + p->normal[1]*emaxs[1] + p->normal[2]*emins[2]; |
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dist2 = p->normal[0]*emins[0] + p->normal[1]*emins[1] + p->normal[2]*emaxs[2]; |
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break; |
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case 5: |
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dist1 = p->normal[0]*emins[0] + p->normal[1]*emaxs[1] + p->normal[2]*emins[2]; |
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dist2 = p->normal[0]*emaxs[0] + p->normal[1]*emins[1] + p->normal[2]*emaxs[2]; |
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break; |
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case 6: |
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dist1 = p->normal[0]*emaxs[0] + p->normal[1]*emins[1] + p->normal[2]*emins[2]; |
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dist2 = p->normal[0]*emins[0] + p->normal[1]*emaxs[1] + p->normal[2]*emaxs[2]; |
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break; |
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case 7: |
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dist1 = p->normal[0]*emins[0] + p->normal[1]*emins[1] + p->normal[2]*emins[2]; |
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dist2 = p->normal[0]*emaxs[0] + p->normal[1]*emaxs[1] + p->normal[2]*emaxs[2]; |
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break; |
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default: |
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// shut up compiler |
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dist1 = dist2 = 0; |
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break; |
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} |
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if( dist1 >= p->dist ) |
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sides = 1; |
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if( dist2 < p->dist ) |
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sides |= 2; |
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return sides; |
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}
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