493 lines
14 KiB
C++
493 lines
14 KiB
C++
/* Copyright (C) 1996-1997 Id Software, Inc.
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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 2 of the License, or
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(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. See the
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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 the Free Software
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Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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See file, 'COPYING', for details.
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*/
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#ifndef __COMMON_MATHLIB_H__
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#define __COMMON_MATHLIB_H__
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#include <float.h>
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#include <math.h>
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#include <common/cmdlib.hh>
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#include <vector>
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#include <set>
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#include <array>
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#include <utility>
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#include <memory> // for unique_ptr
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#include <string>
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#include <common/qvec.hh>
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#ifdef DOUBLEVEC_T
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#define vec_t double
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#define VECT_MAX DBL_MAX
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#else
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#define vec_t float
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#define VECT_MAX FLT_MAX
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#endif
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typedef vec_t vec3_t[3];
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typedef struct {
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vec3_t normal;
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vec_t dist;
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} plane_t;
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#define SIDE_FRONT 0
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#define SIDE_ON 2
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#define SIDE_BACK 1
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#define SIDE_CROSS -2
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#define Q_PI 3.14159265358979323846
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#define DEG2RAD( a ) ( ( a ) * ( ( 2 * Q_PI ) / 360.0 ) )
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extern const vec3_t vec3_origin;
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#define ZERO_TRI_AREA_EPSILON 0.05f
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#define POINT_EQUAL_EPSILON 0.05f
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#define NORMAL_EPSILON 0.000001
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#define DEGREES_EPSILON 0.001
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qboolean VectorCompare(const vec3_t v1, const vec3_t v2, vec_t epsilon);
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static inline bool
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GLMVectorCompare(const qvec3f &v1, const qvec3f &v2, float epsilon)
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{
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for (int i = 0; i < 3; i++)
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if (fabs(v1[i] - v2[i]) > epsilon)
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return false;
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return true;
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}
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static inline vec_t
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DotProduct(const vec3_t x, const vec3_t y)
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{
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return x[0] * y[0] + x[1] * y[1] + x[2] * y[2];
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}
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static inline void
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VectorSubtract(const vec3_t x, const vec3_t y, vec3_t out)
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{
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out[0] = x[0] - y[0];
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out[1] = x[1] - y[1];
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out[2] = x[2] - y[2];
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}
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static inline void
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VectorAdd(const vec3_t x, const vec3_t y, vec3_t out)
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{
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out[0] = x[0] + y[0];
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out[1] = x[1] + y[1];
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out[2] = x[2] + y[2];
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}
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static inline void
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VectorCopy(const vec3_t in, vec3_t out)
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{
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out[0] = in[0];
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out[1] = in[1];
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out[2] = in[2];
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}
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static inline void
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VectorScale(const vec3_t v, vec_t scale, vec3_t out)
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{
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out[0] = v[0] * scale;
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out[1] = v[1] * scale;
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out[2] = v[2] * scale;
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}
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static inline void
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VectorInverse(vec3_t v)
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{
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v[0] = -v[0];
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v[1] = -v[1];
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v[2] = -v[2];
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}
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static inline void
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VectorSet(vec3_t out, vec_t x, vec_t y, vec_t z)
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{
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out[0] = x;
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out[1] = y;
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out[2] = z;
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}
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static inline void
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VectorClear(vec3_t out)
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{
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out[0] = 0;
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out[1] = 0;
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out[2] = 0;
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}
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static inline void
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VectorCopyFromGLM(const qvec3f &in, vec3_t out)
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{
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out[0] = in[0];
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out[1] = in[1];
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out[2] = in[2];
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}
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void ClearBounds(vec3_t mins, vec3_t maxs);
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void AddPointToBounds(const vec3_t v, vec3_t mins, vec3_t maxs);
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plane_t FlipPlane(plane_t input);
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static inline qvec3f
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VectorToGLM(const vec3_t in)
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{
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return qvec3f(in[0], in[1], in[2]);
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}
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static inline vec_t
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Q_rint(vec_t in)
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{
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return (vec_t)(floor(in + 0.5));
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}
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/*
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Random()
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returns a pseudorandom number between 0 and 1
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*/
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static inline vec_t
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Random( void )
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{
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return (vec_t) rand() / RAND_MAX;
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}
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static inline void
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VectorMA(const vec3_t va, vec_t scale, const vec3_t vb, vec3_t vc)
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{
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vc[0] = va[0] + scale * vb[0];
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vc[1] = va[1] + scale * vb[1];
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vc[2] = va[2] + scale * vb[2];
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}
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void CrossProduct(const vec3_t v1, const vec3_t v2, vec3_t cross);
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static inline double
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VectorLengthSq(const vec3_t v)
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{
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double length = 0;
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for (int i = 0; i < 3; i++)
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length += v[i] * v[i];
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return length;
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}
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static inline double
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VectorLength(const vec3_t v)
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{
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double length = VectorLengthSq(v);
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length = sqrt(length);
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return length;
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}
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static inline vec_t
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VectorNormalize(vec3_t v)
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{
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int i;
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double length;
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length = 0;
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for (i = 0; i < 3; i++)
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length += v[i] * v[i];
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length = sqrt(length);
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if (length == 0)
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return 0;
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for (i = 0; i < 3; i++)
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v[i] /= (vec_t)length;
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return (vec_t)length;
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}
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// returns the normalized direction from `start` to `stop` in the `dir` param
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// returns the distance from `start` to `stop`
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static inline vec_t
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GetDir(const vec3_t start, const vec3_t stop, vec3_t dir)
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{
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VectorSubtract(stop, start, dir);
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return VectorNormalize(dir);
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}
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static inline vec_t
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DistanceAbovePlane(const vec3_t normal, const vec_t dist, const vec3_t point)
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{
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return DotProduct(normal, point) - dist;
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}
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static inline void
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ProjectPointOntoPlane(const vec3_t normal, const vec_t dist, vec3_t point)
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{
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vec_t distAbove = DistanceAbovePlane(normal, dist, point);
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vec3_t move;
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VectorScale(normal, -distAbove, move);
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VectorAdd(point, move, point);
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}
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bool SetPlanePts(const vec3_t planepts[3], vec3_t normal, vec_t *dist);
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/* Shortcut for output of warnings/errors */
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std::string VecStr(const vec3_t vec);
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std::string VecStrf(const vec3_t vec);
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std::string VecStr(const qvec3f vec); //mxd
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std::string VecStrf(const qvec3f vec); //mxd
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// Maps uniform random variables U and V in [0, 1] to uniformly distributed points on a sphere
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void UniformPointOnSphere(vec3_t dir, float u, float v);
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void RandomDir(vec3_t dir);
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qvec3f CosineWeightedHemisphereSample(float u1, float u2);
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qvec3f vec_from_mangle(const qvec3f &m);
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qvec3f mangle_from_vec(const qvec3f &v);
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qmat3x3d RotateAboutX(double radians);
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qmat3x3d RotateAboutY(double radians);
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qmat3x3d RotateAboutZ(double radians);
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qmat3x3f RotateFromUpToSurfaceNormal(const qvec3f &surfaceNormal);
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bool AABBsDisjoint(const vec3_t minsA, const vec3_t maxsA, const vec3_t minsB, const vec3_t maxsB);
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void AABB_Init(vec3_t mins, vec3_t maxs, const vec3_t pt);
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void AABB_Expand(vec3_t mins, vec3_t maxs, const vec3_t pt);
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void AABB_Size(const vec3_t mins, const vec3_t maxs, vec3_t size_out);
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void AABB_Grow(vec3_t mins, vec3_t maxs, const vec3_t size);
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using tri_t = std::tuple<qvec3f, qvec3f, qvec3f>;
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/// abc - clockwise ordered triangle
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/// p - point to get the barycentric coords of
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qvec3f Barycentric_FromPoint(const qvec3f &p, const tri_t &tri);
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qvec3f Barycentric_Random(const float r1, const float r2);
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/// Evaluates the given barycentric coord for the given triangle
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qvec3f Barycentric_ToPoint(const qvec3f &bary,
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const tri_t &tri);
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vec_t TriangleArea(const vec3_t v0, const vec3_t v1, const vec3_t v2);
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// noramlizes the given pdf so it sums to 1, then converts to a cdf
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std::vector<float> MakeCDF(const std::vector<float> &pdf);
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int SampleCDF(const std::vector<float> &cdf, float sample);
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// filtering
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// width (height) are the filter "radius" (not "diameter")
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float Filter_Gaussian(float width, float height, float x, float y);
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// sqrt(x^2 + y^2) should be <= a, returns 0 outside that range.
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float Lanczos2D(float x, float y, float a);
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// glm geometry
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static inline qvec3f vec3_t_to_glm(const vec3_t vec) {
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return qvec3f(vec[0], vec[1], vec[2]);
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}
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static inline qvec3d qvec3d_from_vec3(const vec3_t vec) {
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return qvec3d(vec[0], vec[1], vec[2]);
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}
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static inline void glm_to_vec3_t(const qvec3f &glm, vec3_t out) {
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out[0] = glm[0];
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out[1] = glm[1];
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out[2] = glm[2];
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}
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static inline void glm_to_vec3_t(const qvec3d &glm, vec3_t out) {
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out[0] = glm[0];
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out[1] = glm[1];
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out[2] = glm[2];
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}
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// Returns (0 0 0) if we couldn't determine the normal
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qvec3f GLM_FaceNormal(std::vector<qvec3f> points);
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std::pair<bool, qvec4f> GLM_MakeInwardFacingEdgePlane(const qvec3f &v0, const qvec3f &v1, const qvec3f &faceNormal);
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std::vector<qvec4f> GLM_MakeInwardFacingEdgePlanes(const std::vector<qvec3f> &points);
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bool GLM_EdgePlanes_PointInside(const std::vector<qvec4f> &edgeplanes, const qvec3f &point);
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float GLM_EdgePlanes_PointInsideDist(const std::vector<qvec4f> &edgeplanes, const qvec3f &point);
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qvec3f GLM_TriangleCentroid(const qvec3f &v0, const qvec3f &v1, const qvec3f &v2);
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float GLM_TriangleArea(const qvec3f &v0, const qvec3f &v1, const qvec3f &v2);
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qvec4f GLM_MakePlane(const qvec3f &normal, const qvec3f &point);
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float GLM_DistAbovePlane(const qvec4f &plane, const qvec3f &point);
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qvec3f GLM_ProjectPointOntoPlane(const qvec4f &plane, const qvec3f &point);
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float GLM_PolyArea(const std::vector<qvec3f> &points);
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qvec3f GLM_PolyCentroid(const std::vector<qvec3f> &points);
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qvec4f GLM_PolyPlane(const std::vector<qvec3f> &points);
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/// Returns the index of the polygon edge, and the closest point on that edge, to the given point
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std::pair<int, qvec3f> GLM_ClosestPointOnPolyBoundary(const std::vector<qvec3f> &poly, const qvec3f &point);
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/// Returns `true` and the interpolated normal if `point` is in the polygon, otherwise returns false.
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std::pair<bool, qvec3f> GLM_InterpolateNormal(const std::vector<qvec3f> &points,
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const std::vector<qvec3f> &normals,
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const qvec3f &point);
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std::vector<qvec3f> GLM_ShrinkPoly(const std::vector<qvec3f> &poly, const float amount);
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/// Returns (front part, back part)
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std::pair<std::vector<qvec3f>,std::vector<qvec3f>> GLM_ClipPoly(const std::vector<qvec3f> &poly, const qvec4f &plane);
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class poly_random_point_state_t {
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public:
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std::vector<qvec3f> points;
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std::vector<float> triareas;
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std::vector<float> triareas_cdf;
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};
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poly_random_point_state_t GLM_PolyRandomPoint_Setup(const std::vector<qvec3f> &points);
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qvec3f GLM_PolyRandomPoint(const poly_random_point_state_t &state, float r1, float r2, float r3);
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/// projects p onto the vw line.
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/// returns 0 for p==v, 1 for p==w
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float FractionOfLine(const qvec3f &v, const qvec3f &w, const qvec3f& p);
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/**
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* Distance from `p` to the line v<->w (extending infinitely in either direction)
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*/
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float DistToLine(const qvec3f &v, const qvec3f &w, const qvec3f& p);
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qvec3f ClosestPointOnLine(const qvec3f &v, const qvec3f &w, const qvec3f &p);
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/**
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* Distance from `p` to the line segment v<->w.
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* i.e., 0 if `p` is between v and w.
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*/
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float DistToLineSegment(const qvec3f &v, const qvec3f &w, const qvec3f &p);
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qvec3f ClosestPointOnLineSegment(const qvec3f &v, const qvec3f &w, const qvec3f &p);
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float SignedDegreesBetweenUnitVectors(const qvec3f &start, const qvec3f &end, const qvec3f &normal);
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enum class concavity_t {
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Coplanar,
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Concave,
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Convex
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};
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concavity_t FacePairConcavity(const qvec3f &face1Center,
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const qvec3f &face1Normal,
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const qvec3f &face2Center,
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const qvec3f &face2Normal);
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// Returns weights for f(0,0), f(1,0), f(0,1), f(1,1)
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// from: https://en.wikipedia.org/wiki/Bilinear_interpolation#Unit_Square
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static inline qvec4f bilinearWeights(const float x, const float y) {
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Q_assert(x >= 0.0f);
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Q_assert(x <= 1.0f);
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Q_assert(y >= 0.0f);
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Q_assert(y <= 1.0f);
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return qvec4f((1.0f - x) * (1.0f - y), x * (1.0f - y), (1.0f - x) * y, x * y);
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}
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// This uses a coordinate system where the pixel centers are on integer coords.
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// e.g. the corners of a 3x3 pixel bitmap are at (-0.5, -0.5) and (2.5, 2.5).
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static inline std::array<std::pair<qvec2i, float>, 4>
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bilinearWeightsAndCoords(qvec2f pos, const qvec2i &size)
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{
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Q_assert(pos[0] >= -0.5f && pos[0] <= (size[0] - 0.5f));
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Q_assert(pos[1] >= -0.5f && pos[1] <= (size[1] - 0.5f));
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// Handle extrapolation.
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for (int i=0; i<2; i++) {
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if (pos[i] < 0)
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pos[i] = 0;
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if (pos[i] > (size[i] - 1))
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pos[i] = (size[i] - 1);
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}
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Q_assert(pos[0] >= 0.f && pos[0] <= (size[0] - 1));
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Q_assert(pos[1] >= 0.f && pos[1] <= (size[1] - 1));
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qvec2i integerPart{static_cast<int>(qv::floor(pos)[0]),
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static_cast<int>(qv::floor(pos)[1])};
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qvec2f fractionalPart(pos - qv::floor(pos));
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// ensure integerPart + (1, 1) is still in bounds
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for (int i=0; i<2; i++) {
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if (fractionalPart[i] == 0.0f && integerPart[i] > 0) {
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integerPart[i] -= 1;
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fractionalPart[i] = 1.0f;
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}
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}
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Q_assert(integerPart[0] + 1 < size[0]);
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Q_assert(integerPart[1] + 1 < size[1]);
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Q_assert(qvec2f(integerPart) + fractionalPart == pos);
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// f(0,0), f(1,0), f(0,1), f(1,1)
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const qvec4f weights = bilinearWeights(fractionalPart[0], fractionalPart[1]);
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std::array<std::pair<qvec2i, float>, 4> result;
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for (int i=0; i<4; i++) {
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const float weight = weights[i];
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qvec2i pos(integerPart);
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if ((i % 2) == 1)
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pos[0] += 1;
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if (i >= 2)
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pos[1] += 1;
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Q_assert(pos[0] >= 0);
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Q_assert(pos[0] < size[0]);
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Q_assert(pos[1] >= 0);
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Q_assert(pos[1] < size[1]);
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result[i] = std::make_pair(pos, weight);
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}
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return result;
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}
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template <typename V>
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V bilinearInterpolate(const V &f00, const V &f10, const V &f01, const V &f11, const float x, const float y)
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{
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qvec4f weights = bilinearWeights(x,y);
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const V fxy = f00 * weights[0] + \
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f10 * weights[1] + \
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|
f01 * weights[2] + \
|
|
f11 * weights[3];
|
|
|
|
return fxy;
|
|
}
|
|
|
|
template <typename V>
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|
std::vector<V> PointsAlongLine(const V &start, const V &end, const float step)
|
|
{
|
|
const V linesegment = end - start;
|
|
const float len = qv::length(linesegment);
|
|
if (len == 0)
|
|
return {};
|
|
|
|
std::vector<V> result;
|
|
const V dir = linesegment / len;
|
|
const int stepCount = static_cast<int>(len / step);
|
|
for (int i=0; i<=stepCount; i++) {
|
|
const V pt = start + (dir * (step * i));
|
|
result.push_back(pt);
|
|
}
|
|
return result;
|
|
}
|
|
|
|
bool LinesOverlap(const qvec3f p0, const qvec3f p1,
|
|
const qvec3f q0, const qvec3f q1);
|
|
|
|
#endif /* __COMMON_MATHLIB_H__ */
|