858 lines
20 KiB
C++
858 lines
20 KiB
C++
/*
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* Copyright 2011-2018 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/math.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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bx::memSet(_obb.m_mtx, 0, sizeof(_obb.m_mtx) );
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_obb.m_mtx[ 0] = (_aabb.m_max.x - _aabb.m_min.x) * 0.5f;
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_obb.m_mtx[ 5] = (_aabb.m_max.y - _aabb.m_min.y) * 0.5f;
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_obb.m_mtx[10] = (_aabb.m_max.z - _aabb.m_min.z) * 0.5f;
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_obb.m_mtx[12] = (_aabb.m_min.x + _aabb.m_max.x) * 0.5f;
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_obb.m_mtx[13] = (_aabb.m_min.y + _aabb.m_max.y) * 0.5f;
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_obb.m_mtx[14] = (_aabb.m_min.z + _aabb.m_max.z) * 0.5f;
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_obb.m_mtx[15] = 1.0f;
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}
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void toAabb(Aabb& _aabb, const Obb& _obb)
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{
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bx::Vec3 xyz = { 1.0f, 1.0f, 1.0f };
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bx::Vec3 tmp = bx::mul(xyz, _obb.m_mtx);
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_aabb.m_min = tmp;
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_aabb.m_max = tmp;
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for (uint32_t ii = 1; ii < 8; ++ii)
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{
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xyz.x = ii & 1 ? -1.0f : 1.0f;
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xyz.y = ii & 2 ? -1.0f : 1.0f;
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xyz.z = ii & 4 ? -1.0f : 1.0f;
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tmp = bx::mul(xyz, _obb.m_mtx);
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_aabb.m_min = bx::min(_aabb.m_min, tmp);
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_aabb.m_max = bx::max(_aabb.m_max, tmp);
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}
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}
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void toAabb(Aabb& _aabb, const Sphere& _sphere)
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{
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const float radius = _sphere.m_radius;
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_aabb.m_min = bx::sub(_sphere.m_center, radius);
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_aabb.m_max = bx::add(_sphere.m_center, radius);
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}
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void toAabb(Aabb& _aabb, const Disk& _disk)
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{
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// Reference(s):
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// - https://web.archive.org/web/20181113055756/http://iquilezles.org/www/articles/diskbbox/diskbbox.htm
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//
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const bx::Vec3 nsq = bx::mul(_disk.m_normal, _disk.m_normal);
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const bx::Vec3 one = { 1.0f, 1.0f, 1.0f };
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const bx::Vec3 tmp = bx::sub(one, nsq);
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const float inv = 1.0f / (tmp.x*tmp.y*tmp.z);
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const bx::Vec3 extent =
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{
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_disk.m_radius * tmp.x * bx::sqrt((nsq.x + nsq.y * nsq.z) * inv),
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_disk.m_radius * tmp.y * bx::sqrt((nsq.y + nsq.z * nsq.x) * inv),
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_disk.m_radius * tmp.z * bx::sqrt((nsq.z + nsq.x * nsq.y) * inv),
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};
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_aabb.m_min = bx::sub(_disk.m_center, extent);
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_aabb.m_max = bx::add(_disk.m_center, extent);
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}
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void toAabb(Aabb& _aabb, const Cylinder& _cylinder)
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{
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// Reference(s):
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// - https://web.archive.org/web/20181113055756/http://iquilezles.org/www/articles/diskbbox/diskbbox.htm
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//
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const bx::Vec3 axis = bx::sub(_cylinder.m_end, _cylinder.m_pos);
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const bx::Vec3 asq = bx::mul(axis, axis);
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const bx::Vec3 nsq = bx::mul(asq, 1.0f/bx::dot(axis, axis) );
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const bx::Vec3 one = { 1.0f, 1.0f, 1.0f };
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const bx::Vec3 tmp = bx::sub(one, nsq);
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const float inv = 1.0f / (tmp.x*tmp.y*tmp.z);
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const bx::Vec3 extent =
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{
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_cylinder.m_radius * tmp.x * bx::sqrt( (nsq.x + nsq.y * nsq.z) * inv),
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_cylinder.m_radius * tmp.y * bx::sqrt( (nsq.y + nsq.z * nsq.x) * inv),
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_cylinder.m_radius * tmp.z * bx::sqrt( (nsq.z + nsq.x * nsq.y) * inv),
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};
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const bx::Vec3 minP = bx::sub(_cylinder.m_pos, extent);
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const bx::Vec3 minE = bx::sub(_cylinder.m_end, extent);
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const bx::Vec3 maxP = bx::add(_cylinder.m_pos, extent);
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const bx::Vec3 maxE = bx::add(_cylinder.m_end, extent);
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_aabb.m_min = bx::min(minP, minE);
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_aabb.m_max = bx::max(maxP, maxE);
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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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bx::memCopy(_obb.m_mtx, result, sizeof(result) );
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}
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void toAabb(Aabb& _aabb, const void* _vertices, uint32_t _numVertices, uint32_t _stride)
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{
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bx::Vec3 min, max;
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uint8_t* vertex = (uint8_t*)_vertices;
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float* position = (float*)vertex;
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min.x = max.x = position[0];
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min.y = max.y = position[1];
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min.z = max.z = 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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bx::Vec3 pos =
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{
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position[0],
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position[1],
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position[2],
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};
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min = bx::min(pos, min);
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max = bx::max(pos, max);
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}
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_aabb.m_min = min;
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_aabb.m_max = max;
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}
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void toAabb(Aabb& _aabb, const float* _mtx, const void* _vertices, uint32_t _numVertices, uint32_t _stride)
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{
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bx::Vec3 min, max;
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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.x = max.x = position[0];
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min.y = max.y = position[1];
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min.z = max.z = 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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bx::Vec3 pos =
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{
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position[0],
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position[1],
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position[2],
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};
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min = bx::min(pos, min);
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max = bx::max(pos, max);
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}
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_aabb.m_min = min;
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_aabb.m_max = max;
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}
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float calcAreaAabb(const Aabb& _aabb)
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{
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const float ww = _aabb.m_max.x - _aabb.m_min.x;
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const float hh = _aabb.m_max.y - _aabb.m_min.y;
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const float dd = _aabb.m_max.z - _aabb.m_min.z;
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return 2.0f * (ww*hh + ww*dd + hh*dd);
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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.x -= _factor;
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_aabb.m_min.y -= _factor;
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_aabb.m_min.z -= _factor;
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_aabb.m_max.x += _factor;
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_aabb.m_max.y += _factor;
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_aabb.m_max.z += _factor;
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}
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void aabbExpand(Aabb& _aabb, const float* _pos)
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{
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const bx::Vec3 pos = { _pos[0], _pos[1], _pos[2] };
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_aabb.m_min = bx::min(_aabb.m_min, pos);
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_aabb.m_max = bx::max(_aabb.m_max, pos);
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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.x < _aabb1.m_min.x;
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const uint32_t gtMaxX = _aabb0.m_min.x > _aabb1.m_max.x;
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const uint32_t ltMinY = _aabb0.m_max.y < _aabb1.m_min.y;
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const uint32_t gtMaxY = _aabb0.m_min.y > _aabb1.m_max.y;
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const uint32_t ltMinZ = _aabb0.m_max.z < _aabb1.m_min.z;
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const uint32_t gtMaxZ = _aabb0.m_min.z > _aabb1.m_max.z;
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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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toAabb(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::kPiHalf/_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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toAabb(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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bx::memCopy(&_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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toAabb(aabb, _vertices, _numVertices, _stride);
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bx::Vec3 center =
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{
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(aabb.m_min.x + aabb.m_max.x) * 0.5f,
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(aabb.m_min.y + aabb.m_max.y) * 0.5f,
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(aabb.m_min.z + aabb.m_max.z) * 0.5f,
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};
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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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const float xx = position[0] - center.x;
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const float yy = position[1] - center.y;
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const float zz = position[2] - center.z;
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const float distSq = xx*xx + yy*yy + zz*zz;
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maxDistSq = bx::max(distSq, maxDistSq);
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}
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_sphere.m_center = center;
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_sphere.m_radius = bx::sqrt(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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bx::Vec3 center;
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float* position = (float*)&vertex[0];
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center.x = position[0];
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center.y = position[1];
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center.z = position[2];
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position = (float*)&vertex[1*_stride];
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center.x += position[0];
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center.y += position[1];
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center.z += position[2];
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center.x *= 0.5f;
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center.y *= 0.5f;
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center.z *= 0.5f;
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float xx = position[0] - center.x;
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float yy = position[1] - center.y;
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float zz = position[2] - center.z;
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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.x;
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yy = position[1] - center.y;
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zz = position[2] - center.z;
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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.x += xx * radiusStep;
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center.y += yy * radiusStep;
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center.z += zz * radiusStep;
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maxDistSq = bx::lerp(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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_sphere.m_center = center;
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_sphere.m_radius = bx::sqrt(maxDistSq);
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}
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void calcPlaneUv(const Plane& _plane, bx::Vec3& _udir, bx::Vec3& _vdir)
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{
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bx::calcTangentFrame(_udir, _vdir, _plane.m_normal);
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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.x = xw - xz;
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near.m_normal.y = yw - yz;
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near.m_normal.z = zw - zz;
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near.m_dist = ww - wz;
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far.m_normal.x = xw + xz;
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far.m_normal.y = yw + yz;
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far.m_normal.z = 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.x = xw - xx;
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left.m_normal.y = yw - yx;
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left.m_normal.z = zw - zx;
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left.m_dist = ww - wx;
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right.m_normal.x = xw + xx;
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right.m_normal.y = yw + yx;
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right.m_normal.z = 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.x = xw + xy;
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top.m_normal.y = yw + yy;
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top.m_normal.z = zw + zy;
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top.m_dist = ww + wy;
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bottom.m_normal.x = xw - xy;
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bottom.m_normal.y = yw - yy;
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bottom.m_normal.z = 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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const float len = bx::length(plane->m_normal);
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plane->m_normal = bx::normalize(plane->m_normal);
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float invLen = 1.0f / len;
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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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bx::Vec3 intersectPlanes(const Plane& _pa, const Plane& _pb, const Plane& _pc)
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{
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const bx::Vec3 axb = bx::cross(_pa.m_normal, _pb.m_normal);
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const bx::Vec3 bxc = bx::cross(_pb.m_normal, _pc.m_normal);
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const bx::Vec3 cxa = bx::cross(_pc.m_normal, _pa.m_normal);
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const bx::Vec3 tmp0 = bx::mul(bxc, _pa.m_dist);
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const bx::Vec3 tmp1 = bx::mul(cxa, _pb.m_dist);
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const bx::Vec3 tmp2 = bx::mul(axb, _pc.m_dist);
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const bx::Vec3 tmp3 = bx::add(tmp0, tmp1);
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const bx::Vec3 tmp4 = bx::add(tmp3, tmp2);
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const float denom = bx::dot(_pa.m_normal, bxc);
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const bx::Vec3 result = bx::mul(tmp4, -1.0f/denom);
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return result;
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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 bx::Vec3 near = { _x, _y, 0.0f };
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ray.m_pos = bx::mulH(near, _invVp);
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const bx::Vec3 far = { _x, _y, 1.0f };
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|
bx::Vec3 tmp = bx::mulH(far, _invVp);
|
|
|
|
const bx::Vec3 dir = bx::sub(tmp, ray.m_pos);
|
|
ray.m_dir = bx::normalize(dir);
|
|
|
|
return ray;
|
|
}
|
|
|
|
inline bx::Vec3 getPointAt(const Ray& _ray, float _t)
|
|
{
|
|
return bx::add(bx::mul(_ray.m_dir, _t), _ray.m_pos);
|
|
}
|
|
|
|
bool intersect(const Ray& _ray, const Aabb& _aabb, Hit* _hit)
|
|
{
|
|
const bx::Vec3 invDir = bx::rcp(_ray.m_dir);
|
|
const bx::Vec3 tmp0 = bx::sub(_aabb.m_min, _ray.m_pos);
|
|
const bx::Vec3 t0 = bx::mul(tmp0, invDir);
|
|
const bx::Vec3 tmp1 = bx::sub(_aabb.m_max, _ray.m_pos);
|
|
const bx::Vec3 t1 = bx::mul(tmp1, invDir);
|
|
|
|
const bx::Vec3 min = bx::min(t0, t1);
|
|
const bx::Vec3 max = bx::max(t0, t1);
|
|
|
|
const float tmin = bx::max(min.x, min.y, min.z);
|
|
const float tmax = bx::min(max.x, max.y, max.z);
|
|
|
|
if (tmax < 0.0f
|
|
|| tmin > tmax)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
if (NULL != _hit)
|
|
{
|
|
_hit->m_normal.x = float( (t1.x == tmin) - (t0.x == tmin) );
|
|
_hit->m_normal.y = float( (t1.y == tmin) - (t0.y == tmin) );
|
|
_hit->m_normal.z = float( (t1.z == tmin) - (t0.z == tmin) );
|
|
|
|
_hit->m_dist = tmin;
|
|
_hit->m_pos = getPointAt(_ray, tmin);
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
static const Aabb s_kUnitAabb =
|
|
{
|
|
{ -1.0f, -1.0f, -1.0f },
|
|
{ 1.0f, 1.0f, 1.0f },
|
|
};
|
|
|
|
bool intersect(const Ray& _ray, const Obb& _obb, Hit* _hit)
|
|
{
|
|
Aabb aabb;
|
|
toAabb(aabb, _obb);
|
|
|
|
if (!intersect(_ray, aabb) )
|
|
{
|
|
return false;
|
|
}
|
|
|
|
float mtxInv[16];
|
|
bx::mtxInverse(mtxInv, _obb.m_mtx);
|
|
|
|
Ray obbRay;
|
|
obbRay.m_pos = bx::mul(_ray.m_pos, mtxInv);
|
|
obbRay.m_dir = bx::mulXyz0(_ray.m_dir, mtxInv);
|
|
|
|
if (intersect(obbRay, s_kUnitAabb, _hit) )
|
|
{
|
|
if (NULL != _hit)
|
|
{
|
|
_hit->m_pos = bx::mul(_hit->m_pos, _obb.m_mtx);
|
|
|
|
const bx::Vec3 tmp = bx::mulXyz0(_hit->m_normal, _obb.m_mtx);
|
|
_hit->m_normal = bx::normalize(tmp);
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
bool intersect(const Ray& _ray, const Disk& _disk, Hit* _hit)
|
|
{
|
|
Plane plane;
|
|
plane.m_normal = _disk.m_normal;
|
|
plane.m_dist = -bx::dot(_disk.m_center, _disk.m_normal);
|
|
|
|
Hit tmpHit;
|
|
_hit = NULL != _hit ? _hit : &tmpHit;
|
|
|
|
if (intersect(_ray, plane, _hit) )
|
|
{
|
|
const bx::Vec3 tmp = bx::sub(_disk.m_center, _hit->m_pos);
|
|
return bx::dot(tmp, tmp) <= bx::square(_disk.m_radius);
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
static bool intersect(const Ray& _ray, const Cylinder& _cylinder, bool _capsule, Hit* _hit)
|
|
{
|
|
bx::Vec3 axis = bx::sub(_cylinder.m_end, _cylinder.m_pos);
|
|
const bx::Vec3 rc = bx::sub(_ray.m_pos, _cylinder.m_pos);
|
|
const bx::Vec3 dxa = bx::cross(_ray.m_dir, axis);
|
|
|
|
const float len = bx::length(dxa);
|
|
const bx::Vec3 normal = bx::normalize(dxa);
|
|
const float dist = bx::abs(bx::dot(rc, normal) );
|
|
|
|
if (dist > _cylinder.m_radius)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
bx::Vec3 vo = bx::cross(rc, axis);
|
|
const float t0 = -bx::dot(vo, normal) / len;
|
|
|
|
vo = bx::normalize(bx::cross(normal, axis) );
|
|
|
|
const float rsq = bx::square(_cylinder.m_radius);
|
|
const float ddoto = bx::dot(_ray.m_dir, vo);
|
|
const float ss = t0 - bx::abs(bx::sqrt(rsq - bx::square(dist) ) / ddoto);
|
|
|
|
if (0.0f > ss)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
const bx::Vec3 point = getPointAt(_ray, ss);
|
|
|
|
const float axisLen = bx::length(axis);
|
|
axis = bx::normalize(axis);
|
|
const float pdota = bx::dot(_cylinder.m_pos, axis);
|
|
const float height = bx::dot(point, axis) - pdota;
|
|
|
|
if (height > 0.0f
|
|
&& height < axisLen)
|
|
{
|
|
if (NULL != _hit)
|
|
{
|
|
const float t1 = height / axisLen;
|
|
const bx::Vec3 pointOnAxis = bx::lerp(_cylinder.m_pos, _cylinder.m_end, t1);
|
|
|
|
_hit->m_pos = point;
|
|
|
|
const bx::Vec3 tmp = bx::sub(point, pointOnAxis);
|
|
_hit->m_normal = bx::normalize(tmp);
|
|
|
|
_hit->m_dist = ss;
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
if (_capsule)
|
|
{
|
|
const float rdota = bx::dot(_ray.m_pos, axis);
|
|
const float pp = rdota - pdota;
|
|
const float t1 = pp / axisLen;
|
|
|
|
const bx::Vec3 pointOnAxis = bx::lerp(_cylinder.m_pos, _cylinder.m_end, t1);
|
|
const bx::Vec3 axisToRay = bx::sub(_ray.m_pos, pointOnAxis);
|
|
|
|
if (_cylinder.m_radius < bx::length(axisToRay)
|
|
&& 0.0f > ss)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
Sphere sphere;
|
|
sphere.m_radius = _cylinder.m_radius;
|
|
|
|
sphere.m_center = 0.0f >= height
|
|
? _cylinder.m_pos
|
|
: _cylinder.m_end
|
|
;
|
|
|
|
return intersect(_ray, sphere, _hit);
|
|
}
|
|
|
|
Plane plane;
|
|
bx::Vec3 pos;
|
|
|
|
if (0.0f >= height)
|
|
{
|
|
plane.m_normal = bx::neg(axis);
|
|
pos = _cylinder.m_pos;
|
|
}
|
|
else
|
|
{
|
|
plane.m_normal = axis;
|
|
pos = _cylinder.m_end;
|
|
}
|
|
|
|
plane.m_dist = -bx::dot(pos, plane.m_normal);
|
|
|
|
Hit tmpHit;
|
|
_hit = NULL != _hit ? _hit : &tmpHit;
|
|
|
|
if (intersect(_ray, plane, _hit) )
|
|
{
|
|
const bx::Vec3 tmp = bx::sub(pos, _hit->m_pos);
|
|
return bx::dot(tmp, tmp) <= rsq;
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
bool intersect(const Ray& _ray, const Cylinder& _cylinder, Hit* _hit)
|
|
{
|
|
return intersect(_ray, _cylinder, false, _hit);
|
|
}
|
|
|
|
bool intersect(const Ray& _ray, const Capsule& _capsule, Hit* _hit)
|
|
{
|
|
BX_STATIC_ASSERT(sizeof(Capsule) == sizeof(Cylinder) );
|
|
return intersect(_ray, *( (const Cylinder*)&_capsule), true, _hit);
|
|
}
|
|
|
|
bool intersect(const Ray& _ray, const Cone& _cone, Hit* _hit)
|
|
{
|
|
const bx::Vec3 axis = bx::sub(_cone.m_pos, _cone.m_end);
|
|
|
|
const float len = bx::length(axis);
|
|
const bx::Vec3 normal = bx::normalize(axis);
|
|
|
|
Disk disk;
|
|
disk.m_center = _cone.m_pos;
|
|
disk.m_normal = normal;
|
|
disk.m_radius = _cone.m_radius;
|
|
|
|
Hit tmpInt;
|
|
Hit* out = NULL != _hit ? _hit : &tmpInt;
|
|
bool hit = intersect(_ray, disk, out);
|
|
|
|
const bx::Vec3 ro = bx::sub(_ray.m_pos, _cone.m_end);
|
|
|
|
const float hyp = bx::sqrt(bx::square(_cone.m_radius) + bx::square(len) );
|
|
const float cosaSq = bx::square(len/hyp);
|
|
const float ndoto = bx::dot(normal, ro);
|
|
const float ndotd = bx::dot(normal, _ray.m_dir);
|
|
|
|
const float aa = bx::square(ndotd) - cosaSq;
|
|
const float bb = 2.0f * (ndotd*ndoto - bx::dot(_ray.m_dir, ro)*cosaSq);
|
|
const float cc = bx::square(ndoto) - bx::dot(ro, ro)*cosaSq;
|
|
|
|
float det = bb*bb - 4.0f*aa*cc;
|
|
|
|
if (0.0f > det)
|
|
{
|
|
return hit;
|
|
}
|
|
|
|
det = bx::sqrt(det);
|
|
const float invA2 = 1.0f / (2.0f*aa);
|
|
const float t1 = (-bb - det) * invA2;
|
|
const float t2 = (-bb + det) * invA2;
|
|
|
|
float tt = t1;
|
|
if (0.0f > t1
|
|
|| (0.0f < t2 && t2 < t1) )
|
|
{
|
|
tt = t2;
|
|
}
|
|
|
|
if (0.0f > tt)
|
|
{
|
|
return hit;
|
|
}
|
|
|
|
const bx::Vec3 hitPos = getPointAt(_ray, tt);
|
|
const bx::Vec3 point = bx::sub(hitPos, _cone.m_end);
|
|
|
|
const float hh = bx::dot(normal, point);
|
|
|
|
if (0.0f > hh
|
|
|| len < hh)
|
|
{
|
|
return hit;
|
|
}
|
|
|
|
if (NULL != _hit)
|
|
{
|
|
if (!hit
|
|
|| tt < _hit->m_dist)
|
|
{
|
|
_hit->m_dist = tt;
|
|
_hit->m_pos = hitPos;
|
|
|
|
const float scale = hh / bx::dot(point, point);
|
|
const bx::Vec3 pointScaled = bx::mul(point, scale);
|
|
|
|
const bx::Vec3 tmp = bx::sub(pointScaled, normal);
|
|
_hit->m_normal = bx::normalize(tmp);
|
|
}
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
bool intersect(const Ray& _ray, const Plane& _plane, Hit* _hit)
|
|
{
|
|
float equation = bx::dot(_ray.m_pos, _plane.m_normal) + _plane.m_dist;
|
|
if (0.0f > equation)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
float ndotd = bx::dot(_ray.m_dir, _plane.m_normal);
|
|
if (0.0f < ndotd)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
if (NULL != _hit)
|
|
{
|
|
_hit->m_normal = _plane.m_normal;
|
|
|
|
float tt = -equation/ndotd;
|
|
_hit->m_dist = tt;
|
|
_hit->m_pos = getPointAt(_ray, tt);
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
bool intersect(const Ray& _ray, const Sphere& _sphere, Hit* _hit)
|
|
{
|
|
const bx::Vec3 rs = bx::sub(_ray.m_pos, _sphere.m_center);
|
|
|
|
const float bb = bx::dot(rs, _ray.m_dir);
|
|
if (0.0f < bb)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
const float aa = bx::dot(_ray.m_dir, _ray.m_dir);
|
|
const float cc = bx::dot(rs, rs) - bx::square(_sphere.m_radius);
|
|
|
|
const float discriminant = bb*bb - aa*cc;
|
|
|
|
if (0.0f >= discriminant)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
const float sqrtDiscriminant = bx::sqrt(discriminant);
|
|
const float invA = 1.0f / aa;
|
|
const float tt = -(bb + sqrtDiscriminant)*invA;
|
|
|
|
if (0.0f >= tt)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
if (NULL != _hit)
|
|
{
|
|
_hit->m_dist = tt;
|
|
|
|
const bx::Vec3 point = getPointAt(_ray, tt);
|
|
_hit->m_pos = point;
|
|
|
|
const bx::Vec3 tmp = bx::sub(point, _sphere.m_center);
|
|
_hit->m_normal = bx::normalize(tmp);
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
bool intersect(const Ray& _ray, const Tris& _triangle, Hit* _hit)
|
|
{
|
|
const bx::Vec3 edge10 = bx::sub(_triangle.m_v1, _triangle.m_v0);
|
|
const bx::Vec3 edge02 = bx::sub(_triangle.m_v0, _triangle.m_v2);
|
|
const bx::Vec3 normal = bx::cross(edge02, edge10);
|
|
const bx::Vec3 vo = bx::sub(_triangle.m_v0, _ray.m_pos);
|
|
const bx::Vec3 dxo = bx::cross(_ray.m_dir, vo);
|
|
const float det = bx::dot(normal, _ray.m_dir);
|
|
|
|
if (det > 0.0f)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
const float invDet = 1.0f/det;
|
|
const float bz = bx::dot(dxo, edge02) * invDet;
|
|
const float by = bx::dot(dxo, edge10) * invDet;
|
|
const float bx = 1.0f - by - bz;
|
|
|
|
if (bx < 0.0f || by < 0.0f || bz < 0.0f)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
if (NULL != _hit)
|
|
{
|
|
_hit->m_normal = bx::normalize(normal);
|
|
|
|
const float tt = bx::dot(normal, vo) * invDet;
|
|
_hit->m_dist = tt;
|
|
_hit->m_pos = getPointAt(_ray, tt);
|
|
}
|
|
|
|
return true;
|
|
}
|