视锥体与AABB和OBB包围盒相交判断
1.视锥体与AABB包围盒相交判断
template <class TYPE>
class Frustum
{
public:
Frustum(){
}
Frustum(const Frustum<TYPE>& rhs){
for(int i=0; i<6; i++)
planes[i] = rhs.planes[i];
}
bool ContainsPoint(const Vec3<TYPE>& v){
for (int i = 0; i < 6; i ++ ) {
if (planes[i].DistanceToPoint(v) < 0 ) {
return false;
}
}
return true;
}
CullStatus intersects(const Box3<TYPE>& box){
// https://old.cescg.org/CESCG-2002/DSykoraJJelinek/
CullStatus result = CullStatus::INSIDE;
for (int i = 0; i < 6; i++) {
const auto& plane = planes[i];
Vec3<TYPE> p = box.vMin;
if (plane.nx >= 0) p.x = box.vMax.x;
if (plane.ny >= 0) p.y = box.vMax.y;
if (plane.nz >= 0) p.z = box.vMax.z;
Vec3<TYPE> n = box.vMax;
if (plane.nx >= 0) n.x = box.vMin.x;
if (plane.ny >= 0) n.y = box.vMin.y;
if (plane.nz >= 0) n.z = box.vMin.z;
TYPE nt = (plane.nx * p.x) + (plane.ny * p.y) + (plane.nz * p.z);
if (nt < -plane.d)
{
return CullStatus::OUTSIDE;
}
TYPE mt = (plane.nx * n.x) + (plane.ny * n.y) + (plane.nz * n.z);
if (mt < -plane.d)
{
result = CullStatus::INTERSECT;
}
}
if(result == CullStatus::INTERSECT)
{
for (int axis = 0; axis < 3; axis++)
{
TYPE projectedPoint = corners[0].m[axis] - box.vMin.m[axis];
TYPE projMin = projectedPoint;
TYPE projMax = projectedPoint;
for (int p = 1; p < 8; p++) {
projectedPoint = corners[p].m[axis] - box.vMin.m[axis];
projMin = Math::Min(projMin, projectedPoint);
projMax = Math::Max(projMax, projectedPoint);
}
if (projMax < 0 || projMin > box.vMax.m[axis] - box.vMin.m[axis])
return CullStatus::OUTSIDE;
}
}
return result;
}
public:
Plane<TYPE> planes[6];
Vec3<TYPE> corners[8];
};
template <class TYPE>
Frustum<TYPE> fromClipMatrix(const Mat4<TYPE>& clip, const Mat4<TYPE>& inv_clip)
{
Frustum<TYPE> frustum;
frustum.corners[0] = inv_clip.TransformCoord({-1, +1, -1}); // left top near
frustum.corners[1] = inv_clip.TransformCoord({+1, +1, -1}); // right top near
frustum.corners[2] = inv_clip.TransformCoord({+1, -1, -1}); // right bottom near
frustum.corners[3] = inv_clip.TransformCoord({-1, -1, -1}); // left bottom near
frustum.corners[4] = inv_clip.TransformCoord({-1, +1, +1}); // left top far
frustum.corners[5] = inv_clip.TransformCoord({+1, +1, +1}); // right top far
frustum.corners[6] = inv_clip.TransformCoord({+1, -1, +1}); // right bottom far
frustum.corners[7] = inv_clip.TransformCoord({-1, -1, +1}); // left bottom far
TYPE me0 = clip.m[0], me1 = clip.m[1], me2 = clip.m[2], me3 = clip.m[3];
TYPE me4 = clip.m[4], me5 = clip.m[5], me6 = clip.m[6], me7 = clip.m[7];
TYPE me8 = clip.m[8], me9 = clip.m[9], me10 = clip.m[10], me11 = clip.m[11];
TYPE me12 = clip.m[12], me13 = clip.m[13], me14 = clip.m[14], me15 = clip.m[15];
frustum.planes[0].Set(me3 + me2, me7 + me6, me11 + me10, me15 + me14); // near
frustum.planes[1].Set(me3 - me2, me7 - me6, me11 - me10, me15 - me14); // far
frustum.planes[2].Set(me3 + me0, me7 + me4, me11 + me8, me15 + me12); // left
frustum.planes[3].Set(me3 - me0, me7 - me4, me11 - me8, me15 - me12); // right
frustum.planes[4].Set(me3 + me1, me7 + me5, me11 + me9, me15 + me13); // bottom
frustum.planes[5].Set(me3 - me1, me7 - me5, me11 - me9, me15 - me13); // top
for(int i=0; i<6; i++)
{
frustum.planes[i].Normalize();
}
return frustum;
}
2.视锥体与AABB包围盒相交判断
一般的做法是做保守的剔除，检测OBB是否都在视锥的六个平面之外。
遍历视椎体的6个面判断是否相交：
CullingResult
OrientedBoundingBox::intersectPlane(const Plane& plane) const noexcept {
const glm::dvec3 normal = plane.getNormal();
const glm::dmat3& halfAxes = this->getHalfAxes();
const glm::dvec3& xAxisDirectionAndHalfLength = halfAxes[0];
const glm::dvec3& yAxisDirectionAndHalfLength = halfAxes[1];
const glm::dvec3& zAxisDirectionAndHalfLength = halfAxes[2];
// plane is used as if it is its normal; the first three components are
// assumed to be normalized
const double radEffective = glm::abs(
normal.x * xAxisDirectionAndHalfLength.x +
normal.y * xAxisDirectionAndHalfLength.y +
normal.z * xAxisDirectionAndHalfLength.z) +
glm::abs(
normal.x * yAxisDirectionAndHalfLength.x +
normal.y * yAxisDirectionAndHalfLength.y +
normal.z * yAxisDirectionAndHalfLength.z) +
glm::abs(
normal.x * zAxisDirectionAndHalfLength.x +
normal.y * zAxisDirectionAndHalfLength.y +
normal.z * zAxisDirectionAndHalfLength.z);
const double distanceToPlane =
::glm::dot(normal, this->getCenter()) + plane.getDistance();
if (distanceToPlane <= -radEffective) {
// The entire box is on the negative side of the plane normal
return CullingResult::Outside;
}
if (distanceToPlane >= radEffective) {
// The entire box is on the positive side of the plane normal
return CullingResult::Inside;
}
return CullingResult::Intersecting;
}
Renference：
