703 lines
16 KiB
C++
703 lines
16 KiB
C++
/*
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* Copyright 2011-2016 Branimir Karadzic. All rights reserved.
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* License: https://github.com/bkaradzic/bgfx#license-bsd-2-clause
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*/
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#include <bx/rng.h>
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#include <bx/fpumath.h>
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#include "bounds.h"
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void aabbToObb(Obb& _obb, const Aabb& _aabb)
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{
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memset(_obb.m_mtx, 0, sizeof(_obb.m_mtx) );
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_obb.m_mtx[ 0] = (_aabb.m_max[0] - _aabb.m_min[0]) * 0.5f;
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_obb.m_mtx[ 5] = (_aabb.m_max[1] - _aabb.m_min[1]) * 0.5f;
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_obb.m_mtx[10] = (_aabb.m_max[2] - _aabb.m_min[2]) * 0.5f;
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_obb.m_mtx[12] = (_aabb.m_min[0] + _aabb.m_max[0]) * 0.5f;
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_obb.m_mtx[13] = (_aabb.m_min[1] + _aabb.m_max[1]) * 0.5f;
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_obb.m_mtx[14] = (_aabb.m_min[2] + _aabb.m_max[2]) * 0.5f;
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_obb.m_mtx[15] = 1.0f;
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}
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void sphereToAabb(Aabb& _aabb, const Sphere& _sphere)
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{
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float radius = _sphere.m_radius;
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bx::vec3Sub(_aabb.m_min, _sphere.m_center, radius);
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bx::vec3Add(_aabb.m_max, _sphere.m_center, radius);
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}
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void aabbTransformToObb(Obb& _obb, const Aabb& _aabb, const float* _mtx)
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{
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aabbToObb(_obb, _aabb);
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float result[16];
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bx::mtxMul(result, _obb.m_mtx, _mtx);
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memcpy(_obb.m_mtx, result, sizeof(result) );
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}
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float calcAreaAabb(Aabb& _aabb)
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{
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float ww = _aabb.m_max[0] - _aabb.m_min[0];
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float hh = _aabb.m_max[1] - _aabb.m_min[1];
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float dd = _aabb.m_max[2] - _aabb.m_min[2];
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return 2.0f * (ww*hh + ww*dd + hh*dd);
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}
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void calcAabb(Aabb& _aabb, const void* _vertices, uint32_t _numVertices, uint32_t _stride)
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{
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float min[3], max[3];
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uint8_t* vertex = (uint8_t*)_vertices;
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float* position = (float*)vertex;
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min[0] = max[0] = position[0];
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min[1] = max[1] = position[1];
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min[2] = max[2] = position[2];
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vertex += _stride;
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for (uint32_t ii = 1; ii < _numVertices; ++ii)
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{
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position = (float*)vertex;
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vertex += _stride;
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float xx = position[0];
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float yy = position[1];
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float zz = position[2];
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min[0] = bx::fmin(xx, min[0]);
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min[1] = bx::fmin(yy, min[1]);
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min[2] = bx::fmin(zz, min[2]);
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max[0] = bx::fmax(xx, max[0]);
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max[1] = bx::fmax(yy, max[1]);
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max[2] = bx::fmax(zz, max[2]);
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}
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_aabb.m_min[0] = min[0];
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_aabb.m_min[1] = min[1];
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_aabb.m_min[2] = min[2];
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_aabb.m_max[0] = max[0];
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_aabb.m_max[1] = max[1];
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_aabb.m_max[2] = max[2];
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}
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void calcAabb(Aabb& _aabb, const float* _mtx, const void* _vertices, uint32_t _numVertices, uint32_t _stride)
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{
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float min[3], max[3];
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uint8_t* vertex = (uint8_t*)_vertices;
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float position[3];
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bx::vec3MulMtx(position, (float*)vertex, _mtx);
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min[0] = max[0] = position[0];
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min[1] = max[1] = position[1];
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min[2] = max[2] = position[2];
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vertex += _stride;
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for (uint32_t ii = 1; ii < _numVertices; ++ii)
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{
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bx::vec3MulMtx(position, (float*)vertex, _mtx);
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vertex += _stride;
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float xx = position[0];
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float yy = position[1];
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float zz = position[2];
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min[0] = bx::fmin(xx, min[0]);
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min[1] = bx::fmin(yy, min[1]);
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min[2] = bx::fmin(zz, min[2]);
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max[0] = bx::fmax(xx, max[0]);
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max[1] = bx::fmax(yy, max[1]);
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max[2] = bx::fmax(zz, max[2]);
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}
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_aabb.m_min[0] = min[0];
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_aabb.m_min[1] = min[1];
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_aabb.m_min[2] = min[2];
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_aabb.m_max[0] = max[0];
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_aabb.m_max[1] = max[1];
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_aabb.m_max[2] = max[2];
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}
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void aabbExpand(Aabb& _aabb, float _factor)
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{
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_aabb.m_min[0] -= _factor;
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_aabb.m_min[1] -= _factor;
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_aabb.m_min[2] -= _factor;
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_aabb.m_max[0] += _factor;
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_aabb.m_max[1] += _factor;
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_aabb.m_max[2] += _factor;
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}
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uint32_t aabbOverlapTest(const Aabb& _aabb0, const Aabb& _aabb1)
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{
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const uint32_t ltMinX = _aabb0.m_max[0] < _aabb1.m_min[0];
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const uint32_t gtMaxX = _aabb0.m_min[0] > _aabb1.m_max[0];
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const uint32_t ltMinY = _aabb0.m_max[1] < _aabb1.m_min[1];
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const uint32_t gtMaxY = _aabb0.m_min[1] > _aabb1.m_max[1];
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const uint32_t ltMinZ = _aabb0.m_max[2] < _aabb1.m_min[2];
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const uint32_t gtMaxZ = _aabb0.m_min[2] > _aabb1.m_max[2];
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return 0
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| (ltMinX<<0)
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| (gtMaxX<<1)
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| (ltMinY<<2)
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| (gtMaxY<<3)
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| (ltMinZ<<4)
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| (gtMaxZ<<5)
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;
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}
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void calcObb(Obb& _obb, const void* _vertices, uint32_t _numVertices, uint32_t _stride, uint32_t _steps)
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{
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Aabb aabb;
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calcAabb(aabb, _vertices, _numVertices, _stride);
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float minArea = calcAreaAabb(aabb);
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Obb best;
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aabbToObb(best, aabb);
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float angleStep = float(bx::piHalf/_steps);
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float ax = 0.0f;
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float mtx[16];
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for (uint32_t ii = 0; ii < _steps; ++ii)
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{
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float ay = 0.0f;
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for (uint32_t jj = 0; jj < _steps; ++jj)
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{
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float az = 0.0f;
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for (uint32_t kk = 0; kk < _steps; ++kk)
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{
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bx::mtxRotateXYZ(mtx, ax, ay, az);
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float mtxT[16];
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bx::mtxTranspose(mtxT, mtx);
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calcAabb(aabb, mtxT, _vertices, _numVertices, _stride);
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float area = calcAreaAabb(aabb);
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if (area < minArea)
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{
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minArea = area;
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aabbTransformToObb(best, aabb, mtx);
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}
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az += angleStep;
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}
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ay += angleStep;
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}
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ax += angleStep;
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}
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memcpy(&_obb, &best, sizeof(Obb) );
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}
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void calcMaxBoundingSphere(Sphere& _sphere, const void* _vertices, uint32_t _numVertices, uint32_t _stride)
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{
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Aabb aabb;
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calcAabb(aabb, _vertices, _numVertices, _stride);
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float center[3];
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center[0] = (aabb.m_min[0] + aabb.m_max[0]) * 0.5f;
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center[1] = (aabb.m_min[1] + aabb.m_max[1]) * 0.5f;
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center[2] = (aabb.m_min[2] + aabb.m_max[2]) * 0.5f;
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float maxDistSq = 0.0f;
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uint8_t* vertex = (uint8_t*)_vertices;
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for (uint32_t ii = 0; ii < _numVertices; ++ii)
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{
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float* position = (float*)vertex;
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vertex += _stride;
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float xx = position[0] - center[0];
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float yy = position[1] - center[1];
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float zz = position[2] - center[2];
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float distSq = xx*xx + yy*yy + zz*zz;
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maxDistSq = bx::fmax(distSq, maxDistSq);
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}
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bx::vec3Move(_sphere.m_center, center);
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_sphere.m_radius = sqrtf(maxDistSq);
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}
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void calcMinBoundingSphere(Sphere& _sphere, const void* _vertices, uint32_t _numVertices, uint32_t _stride, float _step)
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{
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bx::RngMwc rng;
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uint8_t* vertex = (uint8_t*)_vertices;
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float center[3];
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float* position = (float*)&vertex[0];
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bx::vec3Move(center, position);
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position = (float*)&vertex[1*_stride];
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center[0] += position[0];
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center[1] += position[1];
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center[2] += position[2];
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center[0] *= 0.5f;
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center[1] *= 0.5f;
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center[2] *= 0.5f;
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float xx = position[0] - center[0];
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float yy = position[1] - center[1];
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float zz = position[2] - center[2];
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float maxDistSq = xx*xx + yy*yy + zz*zz;
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float radiusStep = _step * 0.37f;
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bool done;
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do
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{
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done = true;
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for (uint32_t ii = 0, index = rng.gen()%_numVertices; ii < _numVertices; ++ii, index = (index + 1)%_numVertices)
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{
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position = (float*)&vertex[index*_stride];
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xx = position[0] - center[0];
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yy = position[1] - center[1];
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zz = position[2] - center[2];
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float distSq = xx*xx + yy*yy + zz*zz;
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if (distSq > maxDistSq)
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{
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done = false;
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center[0] += xx * radiusStep;
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center[1] += yy * radiusStep;
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center[2] += zz * radiusStep;
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maxDistSq = bx::flerp(maxDistSq, distSq, _step);
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break;
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}
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}
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} while (!done);
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bx::vec3Move(_sphere.m_center, center);
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_sphere.m_radius = bx::fsqrt(maxDistSq);
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}
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void calcPlaneUv(const Plane& _plane, float* _udir, float* _vdir)
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{
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bx::vec3TangentFrame(_plane.m_normal, _udir, _vdir);
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}
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void buildFrustumPlanes(Plane* _result, const float* _viewProj)
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{
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const float xw = _viewProj[ 3];
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const float yw = _viewProj[ 7];
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const float zw = _viewProj[11];
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const float ww = _viewProj[15];
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const float xz = _viewProj[ 2];
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const float yz = _viewProj[ 6];
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const float zz = _viewProj[10];
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const float wz = _viewProj[14];
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Plane& near = _result[0];
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Plane& far = _result[1];
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Plane& left = _result[2];
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Plane& right = _result[3];
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Plane& top = _result[4];
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Plane& bottom = _result[5];
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near.m_normal[0] = xw - xz;
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near.m_normal[1] = yw - yz;
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near.m_normal[2] = zw - zz;
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near.m_dist = ww - wz;
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far.m_normal[0] = xw + xz;
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far.m_normal[1] = yw + yz;
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far.m_normal[2] = zw + zz;
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far.m_dist = ww + wz;
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const float xx = _viewProj[ 0];
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const float yx = _viewProj[ 4];
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const float zx = _viewProj[ 8];
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const float wx = _viewProj[12];
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left.m_normal[0] = xw - xx;
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left.m_normal[1] = yw - yx;
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left.m_normal[2] = zw - zx;
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left.m_dist = ww - wx;
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right.m_normal[0] = xw + xx;
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right.m_normal[1] = yw + yx;
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right.m_normal[2] = zw + zx;
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right.m_dist = ww + wx;
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const float xy = _viewProj[ 1];
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const float yy = _viewProj[ 5];
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const float zy = _viewProj[ 9];
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const float wy = _viewProj[13];
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top.m_normal[0] = xw + xy;
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top.m_normal[1] = yw + yy;
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top.m_normal[2] = zw + zy;
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top.m_dist = ww + wy;
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bottom.m_normal[0] = xw - xy;
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bottom.m_normal[1] = yw - yy;
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bottom.m_normal[2] = zw - zy;
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bottom.m_dist = ww - wy;
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Plane* plane = _result;
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for (uint32_t ii = 0; ii < 6; ++ii)
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{
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float invLen = 1.0f / bx::vec3Norm(plane->m_normal, plane->m_normal);
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plane->m_dist *= invLen;
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++plane;
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}
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}
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void intersectPlanes(float _result[3], const Plane& _pa, const Plane& _pb, const Plane& _pc)
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{
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float axb[3];
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bx::vec3Cross(axb, _pa.m_normal, _pb.m_normal);
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float bxc[3];
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bx::vec3Cross(bxc, _pb.m_normal, _pc.m_normal);
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float cxa[3];
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bx::vec3Cross(cxa, _pc.m_normal, _pa.m_normal);
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float tmp0[3];
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bx::vec3Mul(tmp0, bxc, _pa.m_dist);
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float tmp1[3];
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bx::vec3Mul(tmp1, cxa, _pb.m_dist);
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float tmp2[3];
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bx::vec3Mul(tmp2, axb, _pc.m_dist);
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float tmp[3];
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bx::vec3Add(tmp, tmp0, tmp1);
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bx::vec3Add(tmp0, tmp, tmp2);
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float denom = bx::vec3Dot(_pa.m_normal, bxc);
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bx::vec3Mul(_result, tmp0, -1.0f/denom);
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}
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Ray makeRay(float _x, float _y, const float* _invVp)
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{
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Ray ray;
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const float near[3] = { _x, _y, 0.0f };
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bx::vec3MulMtxH(ray.m_pos, near, _invVp);
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float tmp[3];
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const float far[3] = { _x, _y, 1.0f };
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bx::vec3MulMtxH(tmp, far, _invVp);
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float dir[3];
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bx::vec3Sub(dir, tmp, ray.m_pos);
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bx::vec3Norm(ray.m_dir, dir);
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return ray;
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}
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inline void getPointAt(float* _result, const Ray& _ray, float _t)
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{
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float tmp[3];
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bx::vec3Mul(tmp, _ray.m_dir, _t);
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bx::vec3Add(_result, _ray.m_pos, tmp);
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}
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bool intersect(const Ray& _ray, const Aabb& _aabb, Intersection* _intersection)
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{
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float invDir[3];
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bx::vec3Rcp(invDir, _ray.m_dir);
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float tmp[3];
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float t0[3];
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bx::vec3Sub(tmp, _aabb.m_min, _ray.m_pos);
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bx::vec3Mul(t0, tmp, invDir);
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float t1[3];
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bx::vec3Sub(tmp, _aabb.m_max, _ray.m_pos);
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bx::vec3Mul(t1, tmp, invDir);
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float min[3];
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bx::vec3Min(min, t0, t1);
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float max[3];
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bx::vec3Max(max, t0, t1);
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const float tmin = bx::fmax3(min[0], min[1], min[2]);
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const float tmax = bx::fmin3(max[0], max[1], max[2]);
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if (tmax < 0.0f
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|| tmin > tmax)
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{
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return false;
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}
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if (NULL != _intersection)
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{
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_intersection->m_normal[0] = float( (min[0] == tmin) - (max[0] == tmin) );
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_intersection->m_normal[1] = float( (min[1] == tmin) - (max[1] == tmin) );
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_intersection->m_normal[2] = float( (min[2] == tmin) - (max[2] == tmin) );
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_intersection->m_dist = tmin;
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getPointAt(_intersection->m_pos, _ray, tmin);
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}
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return true;
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}
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bool intersect(const Ray& _ray, const Disk& _disk, Intersection* _intersection)
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{
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Plane plane;
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bx::vec3Move(plane.m_normal, _disk.m_normal);
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plane.m_dist = -bx::vec3Dot(_disk.m_center, _disk.m_normal);
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Intersection tmpIntersection;
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_intersection = NULL != _intersection ? _intersection : &tmpIntersection;
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if (intersect(_ray, plane, _intersection) )
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{
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float tmp[3];
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bx::vec3Sub(tmp, _disk.m_center, _intersection->m_pos);
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return bx::vec3Dot(tmp, tmp) <= bx::fsq(_disk.m_radius);
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
bool intersect(const Ray& _ray, const Cylinder& _cylinder, bool _capsule, Intersection* _intersection)
|
|
{
|
|
float axis[3];
|
|
bx::vec3Sub(axis, _cylinder.m_end, _cylinder.m_pos);
|
|
|
|
float rc[3];
|
|
bx::vec3Sub(rc, _ray.m_pos, _cylinder.m_pos);
|
|
|
|
float normal[3];
|
|
bx::vec3Cross(normal, _ray.m_dir, axis);
|
|
|
|
const float len = bx::vec3Norm(normal, normal);
|
|
const float dist = bx::fabsolute(bx::vec3Dot(rc, normal) );
|
|
|
|
if (dist > _cylinder.m_radius)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
float vo[3];
|
|
bx::vec3Cross(vo, rc, axis);
|
|
const float t0 = -bx::vec3Dot(vo, normal) / len;
|
|
|
|
bx::vec3Cross(vo, normal, axis);
|
|
bx::vec3Norm(vo, vo);
|
|
|
|
const float rsq = bx::fsq(_cylinder.m_radius);
|
|
const float ddoto = bx::vec3Dot(_ray.m_dir, vo);
|
|
const float ss = t0 - bx::fabsolute(bx::fsqrt(rsq - bx::fsq(dist) ) / ddoto);
|
|
|
|
float point[3];
|
|
getPointAt(point, _ray, ss);
|
|
|
|
const float axisLen = bx::vec3Norm(axis, axis);
|
|
const float pdota = bx::vec3Dot(_cylinder.m_pos, axis);
|
|
const float height = bx::vec3Dot(point, axis) - pdota;
|
|
|
|
if (height > 0.0f
|
|
&& height < axisLen)
|
|
{
|
|
if (NULL != _intersection)
|
|
{
|
|
const float t1 = height / axisLen;
|
|
float pointOnAxis[3];
|
|
bx::vec3Lerp(pointOnAxis, _cylinder.m_pos, _cylinder.m_end, t1);
|
|
|
|
bx::vec3Move(_intersection->m_pos, point);
|
|
|
|
float tmp[3];
|
|
bx::vec3Sub(tmp, point, pointOnAxis);
|
|
bx::vec3Norm(_intersection->m_normal, tmp);
|
|
|
|
_intersection->m_dist = ss;
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
if (_capsule)
|
|
{
|
|
const float rdota = bx::vec3Dot(_ray.m_pos, axis);
|
|
const float pp = rdota - pdota;
|
|
const float t1 = pp / axisLen;
|
|
|
|
float pointOnAxis[3];
|
|
bx::vec3Lerp(pointOnAxis, _cylinder.m_pos, _cylinder.m_end, t1);
|
|
|
|
float axisToRay[3];
|
|
bx::vec3Sub(axisToRay, _ray.m_pos, pointOnAxis);
|
|
|
|
if (_cylinder.m_radius < bx::vec3Length(axisToRay)
|
|
&& 0.0f > ss)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
Sphere sphere;
|
|
sphere.m_radius = _cylinder.m_radius;
|
|
|
|
bx::vec3Move(sphere.m_center, 0.0f >= height
|
|
? _cylinder.m_pos
|
|
: _cylinder.m_end
|
|
);
|
|
|
|
return intersect(_ray, sphere, _intersection);
|
|
}
|
|
|
|
Plane plane;
|
|
float pos[3];
|
|
|
|
if (0.0f >= height)
|
|
{
|
|
bx::vec3Neg(plane.m_normal, axis);
|
|
bx::vec3Move(pos, _cylinder.m_pos);
|
|
}
|
|
else
|
|
{
|
|
bx::vec3Move(plane.m_normal, axis);
|
|
bx::vec3Move(pos, _cylinder.m_end);
|
|
}
|
|
|
|
plane.m_dist = -bx::vec3Dot(pos, plane.m_normal);
|
|
|
|
Intersection tmpIntersection;
|
|
_intersection = NULL != _intersection ? _intersection : &tmpIntersection;
|
|
|
|
if (intersect(_ray, plane, _intersection) )
|
|
{
|
|
float tmp[3];
|
|
bx::vec3Sub(tmp, pos, _intersection->m_pos);
|
|
return bx::vec3Dot(tmp, tmp) <= rsq;
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
bool intersect(const Ray& _ray, const Plane& _plane, Intersection* _intersection)
|
|
{
|
|
float equation = bx::vec3Dot(_ray.m_pos, _plane.m_normal) + _plane.m_dist;
|
|
if (0.0f > equation)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
float ndotd = bx::vec3Dot(_ray.m_dir, _plane.m_normal);
|
|
if (0.0f < ndotd)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
if (NULL != _intersection)
|
|
{
|
|
bx::vec3Move(_intersection->m_normal, _plane.m_normal);
|
|
|
|
float tt = -equation/ndotd;
|
|
_intersection->m_dist = tt;
|
|
|
|
getPointAt(_intersection->m_pos, _ray, tt);
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
bool intersect(const Ray& _ray, const Sphere& _sphere, Intersection* _intersection)
|
|
{
|
|
float rs[3];
|
|
bx::vec3Sub(rs, _ray.m_pos, _sphere.m_center);
|
|
|
|
const float bb = bx::vec3Dot(rs, _ray.m_dir);
|
|
if (0.0f < bb)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
const float aa = bx::vec3Dot(_ray.m_dir, _ray.m_dir);
|
|
const float cc = bx::vec3Dot(rs, rs) - bx::fsq(_sphere.m_radius);
|
|
|
|
const float discriminant = bb*bb - aa*cc;
|
|
|
|
if (0.0f >= discriminant)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
const float sqrtDiscriminant = bx::fsqrt(discriminant);
|
|
const float invA = 1.0f / aa;
|
|
const float tt = -(bb + sqrtDiscriminant)*invA;
|
|
|
|
if (0.0f >= tt)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
if (NULL != _intersection)
|
|
{
|
|
_intersection->m_dist = tt;
|
|
|
|
float point[3];
|
|
getPointAt(point, _ray, tt);
|
|
bx::vec3Move(_intersection->m_pos, point);
|
|
|
|
float tmp[3];
|
|
bx::vec3Sub(tmp, point, _sphere.m_center);
|
|
bx::vec3Norm(_intersection->m_normal, tmp);
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
bool intersect(const Ray& _ray, const Tris& _triangle, Intersection* _intersection)
|
|
{
|
|
float edge10[3];
|
|
bx::vec3Sub(edge10, _triangle.m_v1, _triangle.m_v0);
|
|
|
|
float edge02[3];
|
|
bx::vec3Sub(edge02, _triangle.m_v0, _triangle.m_v2);
|
|
|
|
float normal[3];
|
|
bx::vec3Cross(normal, edge02, edge10);
|
|
|
|
float vo[3];
|
|
bx::vec3Sub(vo, _triangle.m_v0, _ray.m_pos);
|
|
|
|
float dxo[3];
|
|
bx::vec3Cross(dxo, _ray.m_dir, vo);
|
|
|
|
const float det = bx::vec3Dot(normal, _ray.m_dir);
|
|
|
|
if (det > 0.0f)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
const float invDet = 1.0f/det;
|
|
const float bz = bx::vec3Dot(dxo, edge02) * invDet;
|
|
const float by = bx::vec3Dot(dxo, edge10) * invDet;
|
|
const float bx = 1.0f - by - bz;
|
|
|
|
if (bx < 0.0f || by < 0.0f || bz < 0.0f)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
if (NULL != _intersection)
|
|
{
|
|
bx::vec3Norm(_intersection->m_normal, normal);
|
|
|
|
const float tt = bx::vec3Dot(normal, vo) * invDet;
|
|
_intersection->m_dist = tt;
|
|
|
|
getPointAt(_intersection->m_pos, _ray, tt);
|
|
}
|
|
|
|
return true;
|
|
}
|