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cocos_lib/cocos/core/geometry/Intersect.cpp

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/****************************************************************************
Copyright (c) 2022-2023 Xiamen Yaji Software Co., Ltd.
https://www.cocos.com/
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights to
use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
of the Software, and to permit persons to whom the Software is furnished to do so,
subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
****************************************************************************/
#include "core/geometry/Intersect.h"
#include <cmath>
#include <limits>
#include "3d/assets/Mesh.h"
#include "base/TemplateUtils.h"
#include "base/std/container/array.h"
#include "core/TypedArray.h"
#include "core/geometry/AABB.h"
#include "core/geometry/Capsule.h"
#include "core/geometry/Line.h"
#include "core/geometry/Obb.h"
#include "core/geometry/Plane.h"
#include "core/geometry/Ray.h"
#include "core/geometry/Spec.h"
#include "core/geometry/Sphere.h"
#include "core/geometry/Triangle.h"
#include "math/Mat3.h"
#include "math/Math.h"
#include "math/Vec3.h"
#include "renderer/gfx-base/GFXDef.h"
#include "scene/Model.h"
namespace cc {
namespace geometry {
float rayPlane(const Ray &ray, const Plane &plane) {
auto denom = Vec3::dot(ray.d, plane.n);
if (abs(denom) < math::EPSILON) {
return 0;
}
auto t = (plane.n * plane.d - ray.o).dot(plane.n) / denom;
return t < 0 ? 0 : t;
}
// based on http://fileadmin.cs.lth.se/cs/Personal/Tomas_Akenine-Moller/raytri/
float rayTriangle(const Ray &ray, const Triangle &triangle, bool doubleSided) {
Vec3 pvec{};
Vec3 qvec{};
auto ab = triangle.b - triangle.a;
auto ac = triangle.c - triangle.a;
Vec3::cross(ray.d, ac, &pvec);
float det = Vec3::dot(ab, pvec);
if (det < math::EPSILON && (!doubleSided || det > -math::EPSILON)) {
return 0;
}
float invDet = 1.0F / det;
auto ao = ray.o - triangle.a;
auto u = Vec3::dot(ao, pvec) * invDet;
if (u < 0 || u > 1) {
return 0;
}
Vec3::cross(ao, ab, &qvec);
auto v = Vec3::dot(ray.d, qvec) * invDet;
if (v < 0 || u + v > 1) {
return 0;
}
auto t = Vec3::dot(ac, qvec) * invDet;
return t < 0 ? 0 : t;
}
float raySphere(const Ray &ray, const Sphere &sphere) {
auto rSq = sphere.getRadius() * sphere.getRadius();
auto e = sphere.getCenter() - ray.o;
auto eSq = e.lengthSquared();
auto aLength = Vec3::dot(e, ray.d); // assume ray direction already normalized
auto fSq = rSq - (eSq - aLength * aLength);
if (fSq < 0) {
return 0;
}
auto f = sqrt(fSq);
auto t = eSq < rSq ? aLength + f : aLength - f;
return t < 0 ? 0 : t;
}
float rayAABB2(const Ray &ray, const Vec3 &min, const Vec3 &max) {
const auto &o = ray.o;
auto d = ray.d;
auto ix = 1.0F / d.x;
auto iy = 1.0F / d.y;
auto iz = 1.0F / d.z;
auto tx1 = (min.x - o.x) * ix;
auto tx2 = (max.x - o.x) * ix;
auto ty1 = (min.y - o.y) * iy;
auto ty2 = (max.y - o.y) * iy;
auto tz1 = (min.z - o.z) * iz;
auto tz2 = (max.z - o.z) * iz;
auto tmin = std::max(std::max(std::min(tx1, tx2), std::min(ty1, ty2)), std::min(tz1, tz2));
auto tmax = std::min(std::min(std::max(tx1, tx2), std::max(ty1, ty2)), std::max(tz1, tz2));
if (tmax < 0 || tmin > tmax) {
return 0;
}
return tmin > 0 ? tmin : tmax; // ray origin inside aabb
}
float rayAABB(const Ray &ray, const AABB &aabb) {
auto minV = aabb.getCenter() - aabb.getHalfExtents();
auto maxV = aabb.getCenter() + aabb.getHalfExtents();
return rayAABB2(ray, minV, maxV);
}
float rayOBB(const Ray &ray, const OBB &obb) {
ccstd::array<float, 6> t;
ccstd::array<float, 3> size = {obb.halfExtents.x, obb.halfExtents.y, obb.halfExtents.z};
const auto &center = obb.center;
auto const &d = ray.d;
Vec3 x = {obb.orientation.m[0], obb.orientation.m[1], obb.orientation.m[2]};
Vec3 y = {obb.orientation.m[3], obb.orientation.m[4], obb.orientation.m[5]};
Vec3 z = {obb.orientation.m[6], obb.orientation.m[7], obb.orientation.m[8]};
Vec3 p = center - ray.o;
// The cos values of the ray on the X, Y, Z
ccstd::array<float, 3> f = {Vec3::dot(x, d), Vec3::dot(y, d), Vec3::dot(z, d)};
// The projection length of P on X, Y, Z
ccstd::array<float, 3> e{Vec3::dot(x, p), Vec3::dot(y, p), Vec3::dot(z, p)};
for (auto i = 0; i < 3; ++i) {
if (f[i] == 0) {
if (-e[i] - size[i] > 0 || -e[i] + size[i] < 0) {
return 0;
}
// Avoid div by 0!
f[i] = 0.000001F;
}
// min
t[i * 2 + 0] = (e[i] + size[i]) / f[i];
// max
t[i * 2 + 1] = (e[i] - size[i]) / f[i];
}
auto tmin = std::max(std::max(std::min(t[0], t[1]), std::min(t[2], t[3])), std::min(t[4], t[5]));
auto tmax = std::min(std::min(std::max(t[0], t[1]), std::max(t[2], t[3])), std::max(t[4], t[5]));
if (tmax < 0 || tmin > tmax) {
return 0;
}
return tmin > 0 ? tmin : tmax; // ray origin inside aabb
}
float rayCapsule(const Ray &ray, const Capsule &capsule) {
Sphere sphere;
auto radiusSqr = capsule.radius * capsule.radius;
auto vRayNorm = ray.d.getNormalized();
auto aa = capsule.ellipseCenter0;
auto bb = capsule.ellipseCenter1;
auto ba = bb - aa;
if (ba == Vec3::ZERO) {
sphere.setRadius(capsule.radius);
sphere.setCenter(capsule.ellipseCenter0);
return raySphere(ray, sphere);
}
auto oa = ray.o - aa;
Vec3 VxBA; //NOLINT(readability-identifier-naming)
Vec3::cross(vRayNorm, ba, &VxBA);
auto a = VxBA.lengthSquared();
if (a == 0.0F) {
sphere.setRadius(capsule.radius);
auto bo = bb - ray.o;
if (oa.lengthSquared() < bo.lengthSquared()) {
sphere.setCenter(capsule.ellipseCenter0);
} else {
sphere.setCenter(capsule.ellipseCenter1);
}
return raySphere(ray, sphere);
}
Vec3 OAxBA; //NOLINT(readability-identifier-naming)
Vec3::cross(oa, ba, &OAxBA);
auto ab2 = ba.lengthSquared();
auto b = 2.0F * Vec3::dot(VxBA, OAxBA);
auto c = OAxBA.lengthSquared() - (radiusSqr * ab2);
auto d = b * b - 4 * a * c;
if (d < 0) {
return 0;
}
auto t = (-b - std::sqrt(d)) / (2.0F * a);
if (t < 0.0F) {
sphere.setRadius(capsule.radius);
auto bo = bb - ray.o;
if (oa.lengthSquared() < bo.lengthSquared()) {
sphere.setCenter(capsule.ellipseCenter0);
} else {
sphere.setCenter(capsule.ellipseCenter1);
}
return raySphere(ray, sphere);
}
// Limit intersection between the bounds of the cylinder's end caps.
auto iPos = ray.o + vRayNorm * t;
auto iPosLen = iPos - aa;
auto tLimit = Vec3::dot(iPosLen, ba) / ab2;
if (tLimit >= 0 && tLimit <= 1) {
return t;
}
if (tLimit < 0) {
sphere.setRadius(capsule.radius);
sphere.setCenter(capsule.ellipseCenter0);
return raySphere(ray, sphere);
}
if (tLimit > 1) {
sphere.setRadius(capsule.radius);
sphere.setCenter(capsule.ellipseCenter1);
return raySphere(ray, sphere);
}
return 0;
}
namespace {
void fillResult(float *minDis, ERaycastMode m, float d, float i0, float i1, float i2, ccstd::optional<ccstd::vector<IRaySubMeshResult>> &r) {
if (m == ERaycastMode::CLOSEST) {
if (*minDis > d || *minDis == 0.0F) {
*minDis = d;
if (r) {
if (r->empty()) {
r->emplace_back(IRaySubMeshResult{d, static_cast<uint32_t>(i0 / 3), static_cast<uint32_t>(i1 / 3), static_cast<uint32_t>(i2 / 3)});
} else {
(*r)[0].distance = d;
(*r)[0].vertexIndex0 = static_cast<uint32_t>(i0 / 3);
(*r)[0].vertexIndex1 = static_cast<uint32_t>(i1 / 3);
(*r)[0].vertexIndex2 = static_cast<uint32_t>(i2 / 3);
}
}
}
} else {
*minDis = d;
if (r) r->emplace_back(IRaySubMeshResult{d, static_cast<uint32_t>(i0 / 3), static_cast<uint32_t>(i1 / 3), static_cast<uint32_t>(i2 / 3)});
}
}
float narrowphase(float *minDis, const Float32Array &vb, const IBArray &ib, gfx::PrimitiveMode pm, const Ray &ray, IRaySubMeshOptions *opt) {
Triangle tri;
auto ibSize = ccstd::visit(overloaded{
[](const auto &arr) {
return arr.length();
},
[](const ccstd::monostate & /*unused*/) {
return static_cast<uint32_t>(0);
}},
ib);
return ccstd::visit(overloaded{[&](const auto &ib) {
if (pm == gfx::PrimitiveMode::TRIANGLE_LIST) {
auto cnt = ibSize;
for (auto j = 0; j < cnt; j += 3) {
auto i0 = ib[j] * 3;
auto i1 = ib[j + 1] * 3;
auto i2 = ib[j + 2] * 3;
tri.a = {vb[i0], vb[i0 + 1], vb[i0 + 2]};
tri.b = {vb[i1], vb[i1 + 1], vb[i1 + 2]};
tri.c = {vb[i2], vb[i2 + 1], vb[i2 + 2]};
auto dist = rayTriangle(ray, tri, opt->doubleSided);
if (dist == 0.0F || dist > opt->distance) continue;
fillResult(minDis, opt->mode, dist, static_cast<float>(i0), static_cast<float>(i1), static_cast<float>(i2), opt->result);
if (opt->mode == ERaycastMode::ANY) return dist;
}
} else if (pm == gfx::PrimitiveMode::TRIANGLE_STRIP) {
auto cnt = ibSize - 2;
int32_t rev = 0;
for (auto j = 0; j < cnt; j += 1) {
auto i0 = ib[j - rev] * 3;
auto i1 = ib[j + rev + 1] * 3;
auto i2 = ib[j + 2] * 3;
tri.a = {vb[i0], vb[i0 + 1], vb[i0 + 2]};
tri.b = {vb[i1], vb[i1 + 1], vb[i1 + 2]};
tri.c = {vb[i2], vb[i2 + 1], vb[i2 + 2]};
rev = ~rev;
auto dist = rayTriangle(ray, tri, opt->doubleSided);
if (dist == 0.0F || dist > opt->distance) continue;
fillResult(minDis, opt->mode, dist, static_cast<float>(i0), static_cast<float>(i1), static_cast<float>(i2), opt->result);
if (opt->mode == ERaycastMode::ANY) return dist;
}
} else if (pm == gfx::PrimitiveMode::TRIANGLE_FAN) {
auto cnt = ibSize - 1;
auto i0 = ib[0] * 3;
tri.a = {vb[i0], vb[i0 + 1], vb[i0 + 2]};
for (auto j = 1; j < cnt; j += 1) {
auto i1 = ib[j] * 3;
auto i2 = ib[j + 1] * 3;
tri.b = {vb[i1], vb[i1 + 1], vb[i1 + 2]};
tri.c = {vb[i2], vb[i2 + 1], vb[i2 + 2]};
auto dist = rayTriangle(ray, tri, opt->doubleSided);
if (dist == 0.0 || dist > opt->distance) continue;
fillResult(minDis, opt->mode, dist, static_cast<float>(i0), static_cast<float>(i1), static_cast<float>(i2), opt->result);
if (opt->mode == ERaycastMode::ANY) return dist;
}
}
return *minDis;
},
[](const ccstd::monostate & /*unused*/) { return 0.F; }},
ib);
}
} // namespace
float raySubMesh(const Ray &ray, const RenderingSubMesh &submesh, IRaySubMeshOptions *options) {
Triangle tri;
IRaySubMeshOptions deOpt;
deOpt.mode = ERaycastMode::ANY;
deOpt.distance = FLT_MAX;
deOpt.doubleSided = false;
float minDis = 0.0F;
auto &mesh = const_cast<RenderingSubMesh &>(submesh);
if (mesh.getGeometricInfo().positions.empty()) return minDis;
IRaySubMeshOptions *opt = options ? options : &deOpt;
auto min = mesh.getGeometricInfo().boundingBox.min;
auto max = mesh.getGeometricInfo().boundingBox.max;
if (rayAABB2(ray, min, max) != 0.0F) {
const auto &pm = mesh.getPrimitiveMode();
const auto &info = mesh.getGeometricInfo();
narrowphase(&minDis, info.positions, info.indices.value(), pm, ray, opt);
}
return minDis;
}
float rayMesh(const Ray &ray, const Mesh &mesh, IRayMeshOptions *option) {
float minDis = 0.0F;
IRayMeshOptions deOpt;
deOpt.distance = std::numeric_limits<float>::max();
deOpt.doubleSided = false;
deOpt.mode = ERaycastMode::ANY;
IRayMeshOptions *opt = option ? option : &deOpt;
auto length = mesh.getSubMeshCount();
auto min = mesh.getStruct().minPosition;
auto max = mesh.getStruct().maxPosition;
if (min.has_value() && max.has_value() && rayAABB2(ray, min.value(), max.value()) == 0.0F) return minDis;
for (uint32_t i = 0; i < length; i++) {
const auto &sm = const_cast<Mesh &>(mesh).getRenderingSubMeshes()[i];
float dis = raySubMesh(ray, *sm, opt);
if (dis != 0.0F) {
if (opt->mode == ERaycastMode::CLOSEST) {
if (minDis == 0.0F || minDis > dis) {
minDis = dis;
if (opt->subIndices.has_value()) {
if (opt->subIndices->empty()) {
opt->subIndices->resize(1);
}
opt->subIndices.value()[0] = i;
}
}
} else {
minDis = dis;
if (opt->subIndices.has_value()) opt->subIndices->emplace_back(i);
if (opt->mode == ERaycastMode::ANY) {
return dis;
}
}
}
}
if (minDis != 0.0F && opt->mode == ERaycastMode::CLOSEST) {
if (opt->result.has_value()) {
opt->result.value()[0].distance = minDis;
opt->result.value().resize(1);
}
if (opt->subIndices.has_value()) opt->subIndices.value().resize(1);
}
return minDis;
}
float rayModel(const Ray &ray, const scene::Model &model, IRayModelOptions *option) {
float minDis = 0.0F;
IRayModelOptions deOpt;
deOpt.distance = std::numeric_limits<float>::max();
deOpt.doubleSided = false;
deOpt.mode = ERaycastMode::ANY;
IRayModelOptions *opt = option ? option : &deOpt;
const auto *wb = model.getWorldBounds();
if (wb && rayAABB(ray, *wb) == 0.0F) {
return minDis;
}
Ray modelRay{ray};
if (model.getNode()) {
Mat4 m4 = model.getNode()->getWorldMatrix().getInversed();
Vec3::transformMat4(ray.o, m4, &modelRay.o);
Vec3::transformMat4Normal(ray.d, m4, &modelRay.d);
}
const auto &subModels = model.getSubModels();
for (auto i = 0; i < subModels.size(); i++) {
const auto &subMesh = subModels[i]->getSubMesh();
float dis = raySubMesh(modelRay, *subMesh, opt);
if (dis != 0.0F) {
if (opt->mode == ERaycastMode::CLOSEST) {
if (minDis == 0.0F || minDis > dis) {
minDis = dis;
if (opt->subIndices.has_value()) {
if (opt->subIndices->empty()) {
opt->subIndices->resize(1);
}
opt->subIndices.value()[0] = i;
}
}
} else {
minDis = dis;
if (opt->subIndices.has_value()) opt->subIndices->emplace_back(i);
if (opt->mode == ERaycastMode::ANY) {
return dis;
}
}
}
}
if (minDis != 0.0F && opt->mode == ERaycastMode::CLOSEST) {
if (opt->result.has_value()) {
opt->result.value()[0].distance = minDis;
opt->result.value().resize(1);
}
if (opt->subIndices.has_value()) opt->subIndices->resize(1);
}
return minDis;
}
float linePlane(const Line &line, const Plane &plane) {
auto ab = line.e - line.s;
auto t = (plane.d - Vec3::dot(line.s, plane.n)) / Vec3::dot(ab, plane.n);
return (t < 0 || t > 1) ? 0 : t;
}
int lineTriangle(const Line &line, const Triangle &triangle, Vec3 *outPt) {
Vec3 n;
Vec3 e;
auto ab = triangle.b - triangle.a;
auto ac = triangle.c - triangle.a;
auto qp = line.s - line.e;
Vec3::cross(ab, ac, &n);
auto det = Vec3::dot(qp, n);
if (det <= 0.0F) {
return 0;
}
auto ap = line.s - triangle.a;
auto t = Vec3::dot(ap, n);
if (t < 0 || t > det) {
return 0;
}
Vec3::cross(qp, ap, &e);
auto v = Vec3::dot(ac, e);
if (v < 0.0F || v > det) {
return 0;
}
auto w = -Vec3::dot(ab, e);
if (w < 0.0F || v + w > det) {
return 0;
}
if (outPt) {
auto invDet = 1.0F / det;
v *= invDet;
w *= invDet;
auto u = 1.0F - v - w;
// outPt = u*a + v*d + w*c;
*outPt = {triangle.a.x * u + triangle.b.x * v + triangle.c.x * w,
triangle.a.y * u + triangle.b.y * v + triangle.c.y * w,
triangle.a.z * u + triangle.b.z * v + triangle.c.z * w};
}
return 1;
}
float lineAABB(const Line &line, const AABB &aabb) {
Ray ray;
ray.o.set(line.s);
ray.d = line.e - line.s;
ray.d.normalize();
auto min = rayAABB(ray, aabb);
return min < line.length() ? min : 0.0F;
}
float lineOBB(const Line &line, const OBB &obb) {
Ray ray;
ray.o.set(line.s);
ray.d = line.e - line.s;
ray.d.normalize();
auto min = rayOBB(ray, obb);
return min < line.length() ? min : 0.0F;
}
float lineSphere(const Line &line, const Sphere &sphere) {
Ray ray;
ray.o.set(line.s);
ray.d = line.e - line.s;
ray.d.normalize();
auto min = raySphere(ray, sphere);
return min < line.length() ? min : 0.0F;
}
bool aabbWithAABB(const AABB &aabb1, const AABB &aabb2) {
auto aMin = aabb1.getCenter() - aabb1.getHalfExtents();
auto aMax = aabb1.getCenter() + aabb1.getHalfExtents();
auto bMin = aabb2.getCenter() - aabb2.getHalfExtents();
auto bMax = aabb2.getCenter() + aabb2.getHalfExtents();
return (aMin.x <= bMax.x && aMax.x >= bMin.x) && (aMin.y <= bMax.y && aMax.y >= bMin.y) && (aMin.z <= bMax.z && aMax.z >= bMin.z);
}
static void getAABBVertices(const Vec3 &min, const Vec3 &max, ccstd::array<Vec3, 8> *out) {
*out = {
Vec3{min.x, max.y, max.z},
Vec3{min.x, max.y, min.z},
Vec3{min.x, min.y, max.z},
Vec3{min.x, min.y, min.z},
Vec3{max.x, max.y, max.z},
Vec3{max.x, max.y, min.z},
Vec3{max.x, min.y, max.z},
Vec3{max.x, min.y, min.z},
};
}
static void getOBBVertices(const Vec3 &c, const Vec3 &e,
const Vec3 &a1, const Vec3 &a2, const Vec3 &a3,
ccstd::array<Vec3, 8> *out) {
*out = {Vec3{
c.x + a1.x * e.x + a2.x * e.y + a3.x * e.z,
c.y + a1.y * e.x + a2.y * e.y + a3.y * e.z,
c.z + a1.z * e.x + a2.z * e.y + a3.z * e.z},
Vec3{
c.x - a1.x * e.x + a2.x * e.y + a3.x * e.z,
c.y - a1.y * e.x + a2.y * e.y + a3.y * e.z,
c.z - a1.z * e.x + a2.z * e.y + a3.z * e.z},
Vec3{
c.x + a1.x * e.x - a2.x * e.y + a3.x * e.z,
c.y + a1.y * e.x - a2.y * e.y + a3.y * e.z,
c.z + a1.z * e.x - a2.z * e.y + a3.z * e.z},
Vec3{
c.x + a1.x * e.x + a2.x * e.y - a3.x * e.z,
c.y + a1.y * e.x + a2.y * e.y - a3.y * e.z,
c.z + a1.z * e.x + a2.z * e.y - a3.z * e.z},
Vec3{
c.x - a1.x * e.x - a2.x * e.y - a3.x * e.z,
c.y - a1.y * e.x - a2.y * e.y - a3.y * e.z,
c.z - a1.z * e.x - a2.z * e.y - a3.z * e.z},
Vec3{
c.x + a1.x * e.x - a2.x * e.y - a3.x * e.z,
c.y + a1.y * e.x - a2.y * e.y - a3.y * e.z,
c.z + a1.z * e.x - a2.z * e.y - a3.z * e.z},
Vec3{
c.x - a1.x * e.x + a2.x * e.y - a3.x * e.z,
c.y - a1.y * e.x + a2.y * e.y - a3.y * e.z,
c.z - a1.z * e.x + a2.z * e.y - a3.z * e.z},
Vec3{
c.x - a1.x * e.x - a2.x * e.y + a3.x * e.z,
c.y - a1.y * e.x - a2.y * e.y + a3.y * e.z,
c.z - a1.z * e.x - a2.z * e.y + a3.z * e.z}};
}
struct Interval {
float min;
float max;
};
static Interval getInterval(const ccstd::array<Vec3, 8> &vertices, const Vec3 &axis) {
auto min = std::numeric_limits<float>::max();
auto max = std::numeric_limits<float>::min();
for (auto i = 0; i < 8; ++i) {
auto projection = Vec3::dot(axis, vertices[i]);
min = std::min(projection, min);
max = std::max(projection, max);
}
return Interval{min, max};
}
int aabbWithOBB(const AABB &aabb, const OBB &obb) {
ccstd::array<Vec3, 15> test;
ccstd::array<Vec3, 8> vertices;
ccstd::array<Vec3, 8> vertices2;
test[0] = {1, 0, 0};
test[1] = {0, 1, 0};
test[2] = {0, 0, 1};
test[3] = {obb.orientation.m[0], obb.orientation.m[1], obb.orientation.m[2]};
test[4] = {obb.orientation.m[3], obb.orientation.m[4], obb.orientation.m[5]};
test[5] = {obb.orientation.m[6], obb.orientation.m[7], obb.orientation.m[8]};
for (auto i = 0; i < 3; ++i) { // Fill out rest of axis
Vec3::cross(test[i], test[3], &test[6 + i * 3 + 0]);
Vec3::cross(test[i], test[4], &test[6 + i * 3 + 1]);
Vec3::cross(test[i], test[5], &test[6 + i * 3 + 2]);
}
auto min = aabb.getCenter() - aabb.getHalfExtents();
auto max = aabb.getCenter() + aabb.getHalfExtents();
getAABBVertices(min, max, &vertices);
getOBBVertices(obb.center, obb.halfExtents, test[3], test[4], test[5], &vertices2);
for (auto j = 0; j < 15; ++j) {
auto a = getInterval(vertices, test[j]);
auto b = getInterval(vertices2, test[j]);
if (b.min > a.max || a.min > b.max) {
return 0; // Seperating axis found
}
}
return 1;
}
int aabbPlane(const AABB &aabb, const Plane &plane) {
auto r = aabb.getHalfExtents().x * std::abs(plane.n.x) + aabb.getHalfExtents().y * std::abs(plane.n.y) + aabb.getHalfExtents().z * std::abs(plane.n.z);
auto dot = Vec3::dot(plane.n, aabb.getCenter());
if (dot + r < plane.d) {
return -1;
}
if (dot - r > plane.d) {
return 0;
}
return 1;
}
int aabbFrustum(const AABB &aabb, const Frustum &frustum) {
for (const auto &plane : frustum.planes) {
// frustum plane normal points to the inside
if (aabbPlane(aabb, *plane) == -1) {
return 0;
}
} // completely outside
return 1;
}
int aabbFrustumCompletelyInside(const AABB &aabb, const Frustum &frustum) {
for (const auto &plane : frustum.planes) {
// frustum plane normal points to the inside
if (aabbPlane(aabb, *plane) != 0) {
return 0;
}
} // completely inside
return 1;
}
// https://cesium.com/blog/2017/02/02/tighter-frustum-culling-and-why-you-may-want-to-disregard-it/
int aabbFrustumAccurate(const AABB &aabb, const Frustum &frustum) {
ccstd::array<Vec3, 8> tmp;
int out1 = 0;
int out2 = 0;
int result = 0;
bool intersects = false;
// 1. aabb inside/outside frustum test
for (const auto &plane : frustum.planes) {
result = aabbPlane(aabb, *plane);
// frustum plane normal points to the inside
if (result == -1) {
return 0; // completely outside
}
if (result == 1) {
intersects = true;
}
}
if (!intersects) {
return 1;
} // completely inside
// in case of false positives
// 2. frustum inside/outside aabb test
for (auto i = 0; i < frustum.vertices.size(); i++) {
tmp[i] = frustum.vertices[i] - aabb.getCenter();
}
out1 = 0;
out2 = 0;
for (auto i = 0; i < frustum.vertices.size(); i++) {
if (tmp[i].x > aabb.getHalfExtents().x) {
out1++;
} else if (tmp[i].x < -aabb.getHalfExtents().x) {
out2++;
}
}
if (out1 == frustum.vertices.size() || out2 == frustum.vertices.size()) {
return 0;
}
out1 = 0;
out2 = 0;
for (auto i = 0; i < frustum.vertices.size(); i++) {
if (tmp[i].y > aabb.getHalfExtents().y) {
out1++;
} else if (tmp[i].y < -aabb.getHalfExtents().y) {
out2++;
}
}
if (out1 == frustum.vertices.size() || out2 == frustum.vertices.size()) {
return 0;
}
out1 = 0;
out2 = 0;
for (auto i = 0; i < frustum.vertices.size(); i++) {
if (tmp[i].z > aabb.getHalfExtents().z) {
out1++;
} else if (tmp[i].z < -aabb.getHalfExtents().z) {
out2++;
}
}
if (out1 == frustum.vertices.size() || out2 == frustum.vertices.size()) {
return 0;
}
return 1;
}
bool obbPoint(const OBB &obb, const Vec3 &point) {
Mat3 m3;
auto lessThan = [](const Vec3 &a, const Vec3 &b) -> bool {
return std::abs(a.x) < b.x && std::abs(a.y) < b.y && std::abs(a.z) < b.z;
};
auto tmp = point - obb.center;
Mat3::transpose(obb.orientation, &m3);
tmp.transformMat3(tmp, m3);
return lessThan(tmp, obb.halfExtents);
};
int obbPlane(const OBB &obb, const Plane &plane) {
auto absDot = [](const Vec3 &n, float x, float y, float z) -> float {
return std::abs(n.x * x + n.y * y + n.z * z);
};
// Real-Time Collision Detection, Christer Ericson, p. 163.
auto r = obb.halfExtents.x * absDot(plane.n, obb.orientation.m[0], obb.orientation.m[1], obb.orientation.m[2]) +
obb.halfExtents.y * absDot(plane.n, obb.orientation.m[3], obb.orientation.m[4], obb.orientation.m[5]) +
obb.halfExtents.z * absDot(plane.n, obb.orientation.m[6], obb.orientation.m[7], obb.orientation.m[8]);
auto dot = Vec3::dot(plane.n, obb.center);
if (dot + r < plane.d) {
return -1;
}
if (dot - r > plane.d) {
return 0;
}
return 1;
}
int obbFrustum(const OBB &obb, const Frustum &frustum) {
for (const auto &plane : frustum.planes) {
// frustum plane normal points to the inside
if (obbPlane(obb, *plane) == -1) {
return 0;
}
} // completely outside
return 1;
};
// https://cesium.com/blog/2017/02/02/tighter-frustum-culling-and-why-you-may-want-to-disregard-it/
int obbFrustumAccurate(const OBB &obb, const Frustum &frustum) {
ccstd::array<Vec3, 8> tmp = {};
float dist = 0.0F;
size_t out1 = 0;
size_t out2 = 0;
auto dot = [](const Vec3 &n, float x, float y, float z) -> float {
return n.x * x + n.y * y + n.z * z;
};
int result = 0;
auto intersects = false;
// 1. obb inside/outside frustum test
for (const auto &plane : frustum.planes) {
result = obbPlane(obb, *plane);
// frustum plane normal points to the inside
if (result == -1) {
return 0; // completely outside
}
if (result == 1) {
intersects = true;
}
}
if (!intersects) {
return 1;
} // completely inside
// in case of false positives
// 2. frustum inside/outside obb test
for (auto i = 0; i < frustum.vertices.size(); i++) {
tmp[i] = frustum.vertices[i] - obb.center;
}
out1 = 0;
out2 = 0;
for (auto i = 0; i < frustum.vertices.size(); i++) {
dist = dot(tmp[i], obb.orientation.m[0], obb.orientation.m[1], obb.orientation.m[2]);
if (dist > obb.halfExtents.x) {
out1++;
} else if (dist < -obb.halfExtents.x) {
out2++;
}
}
if (out1 == frustum.vertices.size() || out2 == frustum.vertices.size()) {
return 0.0F;
}
out1 = 0;
out2 = 0;
for (auto i = 0; i < frustum.vertices.size(); i++) {
dist = dot(tmp[i], obb.orientation.m[3], obb.orientation.m[4], obb.orientation.m[5]);
if (dist > obb.halfExtents.y) {
out1++;
} else if (dist < -obb.halfExtents.y) {
out2++;
}
}
if (out1 == frustum.vertices.size() || out2 == frustum.vertices.size()) {
return 0;
}
out1 = 0;
out2 = 0;
for (auto i = 0; i < frustum.vertices.size(); i++) {
dist = dot(tmp[i], obb.orientation.m[6], obb.orientation.m[7], obb.orientation.m[8]);
if (dist > obb.halfExtents.z) {
out1++;
} else if (dist < -obb.halfExtents.z) {
out2++;
}
}
if (out1 == frustum.vertices.size() || out2 == frustum.vertices.size()) {
return 0;
}
return 1;
}
int obbWithOBB(const OBB &obb1, const OBB &obb2) {
ccstd::array<Vec3, 8> vertices;
ccstd::array<Vec3, 8> vertices2;
ccstd::array<Vec3, 15> test;
test[0] = {obb1.orientation.m[0], obb1.orientation.m[1], obb1.orientation.m[2]};
test[1] = {obb1.orientation.m[3], obb1.orientation.m[4], obb1.orientation.m[5]};
test[2] = {obb1.orientation.m[6], obb1.orientation.m[7], obb1.orientation.m[8]};
test[3] = {obb2.orientation.m[0], obb2.orientation.m[1], obb2.orientation.m[2]};
test[4] = {obb2.orientation.m[3], obb2.orientation.m[4], obb2.orientation.m[5]};
test[5] = {obb2.orientation.m[6], obb2.orientation.m[7], obb2.orientation.m[8]};
for (auto i = 0; i < 3; ++i) { // Fill out rest of axis
Vec3::cross(test[i], test[3], &test[6 + i * 3 + 0]);
Vec3::cross(test[i], test[4], &test[6 + i * 3 + 1]);
Vec3::cross(test[i], test[5], &test[6 + i * 3 + 2]);
}
getOBBVertices(obb1.center, obb1.halfExtents, test[0], test[1], test[2], &vertices);
getOBBVertices(obb2.center, obb2.halfExtents, test[3], test[4], test[5], &vertices2);
for (auto i = 0; i < 15; ++i) {
auto a = getInterval(vertices, test[i]);
auto b = getInterval(vertices2, test[i]);
if (b.min > a.max || a.min > b.max) {
return 0; // Seperating axis found
}
}
return 1;
}
// https://github.com/diku-dk/bvh-tvcg18/blob/1fd3348c17bc8cf3da0b4ae60fdb8f2aa90a6ff0/FOUNDATION/GEOMETRY/GEOMETRY/include/overlap/geometry_overlap_obb_capsule.h
int obbCapsule(const OBB &obb, const Capsule &capsule) {
Sphere sphere{};
ccstd::array<Vec3, 8> v3Verts8{};
ccstd::array<Vec3, 8> v3Axis8{};
auto h = capsule.ellipseCenter0.distanceSquared(capsule.ellipseCenter1);
if (h == 0.0F) {
sphere.setRadius(capsule.radius);
sphere.setCenter(capsule.ellipseCenter0);
return sphereOBB(sphere, obb);
}
Vec3 v3Tmp0 = {
obb.orientation.m[0],
obb.orientation.m[1],
obb.orientation.m[2]};
Vec3 v3Tmp1 = {
obb.orientation.m[3],
obb.orientation.m[4],
obb.orientation.m[5]};
Vec3 v3Tmp2 = {
obb.orientation.m[6],
obb.orientation.m[7],
obb.orientation.m[8]};
getOBBVertices(obb.center, obb.halfExtents, v3Tmp0, v3Tmp1, v3Tmp2, &v3Verts8);
auto axes = v3Axis8;
auto a0 = axes[0] = v3Tmp0;
auto a1 = axes[1] = v3Tmp1;
auto a2 = axes[2] = v3Tmp2;
auto cc = axes[3] = capsule.center - obb.center;
auto bb = axes[4] = capsule.ellipseCenter0 - capsule.ellipseCenter1;
cc.normalize();
bb.normalize();
Vec3::cross(a0, bb, &axes[5]);
Vec3::cross(a1, bb, &axes[6]);
Vec3::cross(a2, bb, &axes[7]);
for (auto i = 0; i < 8; ++i) {
auto a = getInterval(v3Verts8, axes[i]);
auto d0 = Vec3::dot(axes[i], capsule.ellipseCenter0);
auto d1 = Vec3::dot(axes[i], capsule.ellipseCenter1);
auto dMin = std::min(d0, d1) - capsule.radius;
auto dMax = std::max(d0, d1) + capsule.radius;
if (dMin > a.max || a.min > dMax) {
return 0; // Seperating axis found
}
}
return 1;
}
int spherePlane(const Sphere &sphere, const Plane &plane) {
auto dot = Vec3::dot(plane.n, sphere.getCenter());
auto r = sphere.getRadius() * plane.n.length();
if (dot + r < plane.d) {
return -1;
}
if (dot - r > plane.d) {
return 0;
}
return 1;
}
int sphereFrustum(const Sphere &sphere, const Frustum &frustum) {
for (const auto &plane : frustum.planes) {
// frustum plane normal points to the inside
if (spherePlane(sphere, *plane) == -1) {
return 0;
}
} // completely outside
return 1;
}
int sphereFrustumAccurate(const Sphere &sphere, const Frustum &frustum) {
const static ccstd::array<int, 6> MAP = {1, -1, 1, -1, 1, -1};
for (auto i = 0; i < 6; i++) {
const auto &plane = frustum.planes[i];
const auto &n = plane->n;
const auto &d = plane->d;
auto r = sphere.getRadius();
const auto &c = sphere.getCenter();
auto dot = Vec3::dot(n, c);
// frustum plane normal points to the inside
if (dot + r < d) {
return 0; // completely outside
}
if (dot - r > d) {
continue;
}
// in case of false positives
// has false negatives, still working on it
auto pt = c + n * r;
for (auto j = 0; j < 6; j++) {
if (j == i || j == i + MAP[i]) {
continue;
}
const auto &test = frustum.planes[j];
if (Vec3::dot(test->n, pt) < test->d) {
return 0;
}
}
}
return 1;
}
bool sphereWithSphere(const Sphere &sphere0, const Sphere &sphere1) {
auto r = sphere0.getRadius() + sphere1.getRadius();
return sphere0.getCenter().distanceSquared(sphere1.getCenter()) < r * r;
}
bool sphereAABB(const Sphere &sphere, const AABB &aabb) {
Vec3 pt;
ptPointAabb(&pt, sphere.getCenter(), aabb);
return sphere.getCenter().distanceSquared(pt) < sphere.getRadius() * sphere.getRadius();
}
bool sphereOBB(const Sphere &sphere, const OBB &obb) {
Vec3 pt;
ptPointObb(&pt, sphere.getCenter(), obb);
return sphere.getCenter().distanceSquared(pt) < sphere.getRadius() * sphere.getRadius();
}
bool sphereCapsule(const Sphere &sphere, const Capsule &capsule) {
auto r = sphere.getRadius() + capsule.radius;
auto squaredR = r * r;
auto h = capsule.ellipseCenter0.distanceSquared(capsule.ellipseCenter1);
if (h == 0.0F) {
return sphere.getCenter().distanceSquared(capsule.center) < squaredR;
}
auto v3Tmp0 = sphere.getCenter() - capsule.ellipseCenter0;
auto v3Tmp1 = capsule.ellipseCenter1 - capsule.ellipseCenter0;
auto t = Vec3::dot(v3Tmp0, v3Tmp1) / h;
if (t < 0) {
return sphere.getCenter().distanceSquared(capsule.ellipseCenter0) < squaredR;
}
if (t > 1) {
return sphere.getCenter().distanceSquared(capsule.ellipseCenter1) < squaredR;
}
v3Tmp0 = capsule.ellipseCenter0 + t * v3Tmp1;
return sphere.getCenter().distanceSquared(v3Tmp0) < squaredR;
}
bool capsuleWithCapsule(const Capsule &capsuleA, const Capsule &capsuleB) {
auto u = capsuleA.ellipseCenter1 - capsuleA.ellipseCenter0;
auto v = capsuleB.ellipseCenter1 - capsuleB.ellipseCenter0;
auto w = capsuleA.ellipseCenter0 - capsuleB.ellipseCenter0;
auto a = Vec3::dot(u, u); // always >= 0
auto b = Vec3::dot(u, v);
auto c = Vec3::dot(v, v); // always >= 0
auto d = Vec3::dot(u, w);
auto e = Vec3::dot(v, w);
auto dd = a * c - b * b; // always >= 0
float sN;
float sD = dd; // sc = sN / sD, default sD = dd >= 0
float tN;
float tD = dd; // tc = tN / tD, default tD = dd >= 0
// compute the line parameters of the two closest points
if (dd < math::EPSILON) { // the lines are almost parallel
sN = 0.0F; // force using point P0 on segment S1
sD = 1.0F; // to prevent possible division by 0.0 later
tN = e;
tD = c;
} else { // get the closest points on the infinite lines
sN = (b * e - c * d);
tN = (a * e - b * d);
if (sN < 0.0F) { // sc < 0 => the s=0 edge is visible
sN = 0.0F;
tN = e;
tD = c;
} else if (sN > sD) { // sc > 1 => the s=1 edge is visible
sN = sD;
tN = e + b;
tD = c;
}
}
if (tN < 0.0F) { // tc < 0 => the t=0 edge is visible
tN = 0.0F;
// recompute sc for this edge
if (-d < 0.0F) {
sN = 0.0F;
} else if (-d > a) {
sN = sD;
} else {
sN = -d;
sD = a;
}
} else if (tN > tD) { // tc > 1 => the t=1 edge is visible
tN = tD;
// recompute sc for this edge
if ((-d + b) < 0.0F) {
sN = 0.0F;
} else if ((-d + b) > a) {
sN = sD;
} else {
sN = (-d + b);
sD = a;
}
}
// finally do the division to get sc and tc
auto sc = (std::abs(sN) < math::EPSILON ? 0.0F : sN / sD);
auto tc = (std::abs(tN) < math::EPSILON ? 0.0F : tN / tD);
// get the difference of the two closest points
auto dP = w;
dP = dP + u * sc;
dP = dP - v * tc;
auto radius = capsuleA.radius + capsuleB.radius;
return dP.lengthSquared() < radius * radius;
}
int dynObbFrustum(const OBB &obb, const Frustum &frustum) {
if (frustum.getType() == ShapeEnum::SHAPE_FRUSTUM_ACCURATE) {
return obbFrustumAccurate(obb, frustum);
}
return obbFrustum(obb, frustum);
}
int dynSphereFrustum(const Sphere &sphere, const Frustum &frustum) {
if (frustum.getType() == ShapeEnum::SHAPE_FRUSTUM_ACCURATE) {
return sphereFrustumAccurate(sphere, frustum);
}
return sphereFrustum(sphere, frustum);
}
int dynAabbFrustum(const AABB &aabb, const Frustum &frustum) {
if (frustum.getType() == ShapeEnum::SHAPE_FRUSTUM_ACCURATE) {
return aabbFrustumAccurate(aabb, frustum);
}
return aabbFrustum(aabb, frustum);
}
} // namespace geometry
} // namespace cc