452 lines
13 KiB
C++
452 lines
13 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 <array>
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#include <glm/vec4.hpp>
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#include <glm/vec3.hpp>
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#include <glm/vec2.hpp>
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#include <glm/glm.hpp>
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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 EQUAL_EPSILON 0.001
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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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qboolean VectorCompare(const vec3_t v1, const vec3_t v2);
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static inline bool
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GLMVectorCompare(const glm::vec3 &v1, const glm::vec3 &v2)
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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]) > EQUAL_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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VectorCopyFromGLM(const glm::vec3 &in, vec3_t out)
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{
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out[0] = in.x;
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out[1] = in.y;
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out[2] = in.z;
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}
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static inline glm::vec3
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VectorToGLM(const vec3_t in)
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{
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return glm::vec3(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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VectorLength(const 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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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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/* Shortcut for output of warnings/errors */
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//FIXME: change from static buffers to returning std::string for thread safety
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const char *VecStr(const vec3_t vec);
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const char *VecStrf(const vec3_t vec);
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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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glm::vec3 CosineWeightedHemisphereSample(float u1, float u2);
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glm::mat3x3 RotateFromUpToSurfaceNormal(const glm::vec3 &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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template <class V>
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class aabb {
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private:
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V m_mins, m_maxs;
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public:
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aabb() : m_mins(FLT_MAX), m_maxs(-FLT_MAX) {}
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aabb(const V &mins, const V &maxs) : m_mins(mins), m_maxs(maxs) {}
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aabb(const aabb<V> &other) : m_mins(other.m_mins), m_maxs(other.m_maxs) {}
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int length() const { return m_mins.length(); }
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bool disjoint(const aabb<V> &other) const {
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for (int i=0; i<length(); i++) {
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if (m_maxs[i] < other.m_mins[i]) return true;
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if (m_mins[i] > other.m_maxs[i]) return true;
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}
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return false;
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}
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bool contains(const V &p) const {
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for (int i=0; i<length(); i++) {
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if (!(p[i] >= m_mins[i] && p[i] <= m_maxs[i])) return false;
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}
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return true;
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}
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aabb<V> expand(const V &pt) const {
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V mins, maxs;
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for (int i=0; i<length(); i++) {
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mins[i] = qmin(m_mins[i], pt[i]);
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maxs[i] = qmax(m_maxs[i], pt[i]);
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}
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return aabb<V>(mins, maxs);
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}
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V size() const {
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V result;
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for (int i=0; i<length(); i++) {
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result[i] = m_maxs[i] - m_mins[i];
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}
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return result;
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}
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aabb<V> grow(const V &size) const {
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V mins = m_mins;
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V maxs = m_maxs;
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for (int i=0; i<length(); i++) {
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mins[i] -= size[i];
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maxs[i] += size[i];
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}
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return aabb<V>(mins, maxs);
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}
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};
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using aabb3 = aabb<glm::vec3>;
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using aabb2 = aabb<glm::vec2>;
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using tri_t = std::tuple<glm::vec3, glm::vec3, glm::vec3>;
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/// abc - clockwise ordered triangle
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/// p - point to get the barycentric coords of
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glm::vec3 Barycentric_FromPoint(const glm::vec3 &p, const tri_t &tri);
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glm::vec3 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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glm::vec3 Barycentric_ToPoint(const glm::vec3 &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 glm::vec3 vec3_t_to_glm(const vec3_t vec) {
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return glm::vec3(vec[0], vec[1], vec[2]);
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}
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static inline void glm_to_vec3_t(const glm::vec3 &glm, vec3_t out) {
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out[0] = glm.x;
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out[1] = glm.y;
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out[2] = glm.z;
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}
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// Returns (0 0 0) if we couldn't determine the normal
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glm::vec3 GLM_FaceNormal(std::vector<glm::vec3> points);
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std::pair<bool, glm::vec4> GLM_MakeInwardFacingEdgePlane(const glm::vec3 &v0, const glm::vec3 &v1, const glm::vec3 &faceNormal);
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std::vector<glm::vec4> GLM_MakeInwardFacingEdgePlanes(const std::vector<glm::vec3> &points);
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bool GLM_EdgePlanes_PointInside(const std::vector<glm::vec4> &edgeplanes, const glm::vec3 &point);
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float GLM_EdgePlanes_PointInsideDist(const std::vector<glm::vec4> &edgeplanes, const glm::vec3 &point);
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glm::vec3 GLM_TriangleCentroid(const glm::vec3 &v0, const glm::vec3 &v1, const glm::vec3 &v2);
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float GLM_TriangleArea(const glm::vec3 &v0, const glm::vec3 &v1, const glm::vec3 &v2);
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float GLM_DistAbovePlane(const glm::vec4 &plane, const glm::vec3 &point);
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glm::vec3 GLM_ProjectPointOntoPlane(const glm::vec4 &plane, const glm::vec3 &point);
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float GLM_PolyArea(const std::vector<glm::vec3> &points);
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glm::vec3 GLM_PolyCentroid(const std::vector<glm::vec3> &points);
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glm::vec4 GLM_PolyPlane(const std::vector<glm::vec3> &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, glm::vec3> GLM_ClosestPointOnPolyBoundary(const std::vector<glm::vec3> &poly, const glm::vec3 &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, glm::vec3> GLM_InterpolateNormal(const std::vector<glm::vec3> &points,
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const std::vector<glm::vec3> &normals,
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const glm::vec3 &point);
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std::vector<glm::vec3> GLM_ShrinkPoly(const std::vector<glm::vec3> &poly, const float amount);
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/// Returns (front part, back part)
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std::pair<std::vector<glm::vec3>,std::vector<glm::vec3>> GLM_ClipPoly(const std::vector<glm::vec3> &poly, const glm::vec4 &plane);
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glm::vec3 GLM_PolyRandomPoint(const std::vector<glm::vec3> &points);
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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 glm::vec4 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 glm::vec4((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<glm::ivec2, float>, 4>
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bilinearWeightsAndCoords(glm::vec2 pos, const glm::ivec2 &size)
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{
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Q_assert(pos.x >= -0.5f && pos.x <= (size.x - 0.5f));
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Q_assert(pos.y >= -0.5f && pos.y <= (size.y - 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.x >= 0.f && pos.x <= (size.x - 1));
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Q_assert(pos.y >= 0.f && pos.y <= (size.y - 1));
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glm::ivec2 integerPart(glm::floor(pos));
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glm::vec2 fractionalPart(pos - glm::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.x + 1 < size.x);
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Q_assert(integerPart.y + 1 < size.y);
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Q_assert(glm::vec2(integerPart) + fractionalPart == pos);
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// f(0,0), f(1,0), f(0,1), f(1,1)
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const glm::vec4 weights = bilinearWeights(fractionalPart.x, fractionalPart.y);
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std::array<std::pair<glm::ivec2, 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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glm::ivec2 pos(integerPart);
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if ((i % 2) == 1)
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pos.x += 1;
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if (i >= 2)
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pos.y += 1;
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Q_assert(pos.x >= 0);
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Q_assert(pos.x < size.x);
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Q_assert(pos.y >= 0);
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Q_assert(pos.y < size.y);
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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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glm::vec4 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] + \
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f11 * weights[3];
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return fxy;
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}
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template <typename V>
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std::vector<V> PointsAlongLine(const V &start, const V &end, const float step)
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{
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const V linesegment = end - start;
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const float len = glm::length(linesegment);
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if (len == 0)
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return {};
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std::vector<V> result;
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const V dir = linesegment / len;
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const int stepCount = static_cast<int>(len / step);
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for (int i=0; i<=stepCount; i++) {
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const V pt = start + (dir * (step * i));
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result.push_back(pt);
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}
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return result;
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}
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#endif /* __COMMON_MATHLIB_H__ */
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