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/*
*AABB bounding box
*Bouding Volume Hierarchy
*/
class BoundingBox {
float min_x, min_y, min_z, max_x, max_y, max_z;
PVector center;
BoundingBox() {
min_x = Float.POSITIVE_INFINITY;
min_y = Float.POSITIVE_INFINITY;
min_z = Float.POSITIVE_INFINITY;
max_x = Float.NEGATIVE_INFINITY;
max_y = Float.NEGATIVE_INFINITY;
max_z = Float.NEGATIVE_INFINITY;
center = new PVector();
}
// build a bounding box for a triangle
void create(Triangle t) {
min_x = min(t.p1.x, min(t.p2.x, t.p3.x));
max_x = max(t.p1.x, max(t.p2.x, t.p3.x));
min_y = min(t.p1.y, min(t.p2.y, t.p3.y));
max_y = max(t.p1.y, max(t.p2.y, t.p3.y));
min_z = min(t.p1.z, min(t.p2.z, t.p3.z));
max_z = max(t.p1.z, max(t.p2.z, t.p3.z));
center.x = (max_x + min_x) / 2;
center.y = (max_y + min_y) / 2;
center.z = (max_z + min_z) / 2;
}
// merge two bounding boxes
void add(BoundingBox bbx) {
min_x = min(min_x, bbx.min_x);
min_y = min(min_y, bbx.min_y);
min_z = min(min_z, bbx.min_z);
max_x = max(max_x, bbx.max_x);
max_y = max(max_y, bbx.max_y);
max_z = max(max_z, bbx.max_z);
center.x = (max_x + min_x) / 2;
center.y = (max_y + min_y) / 2;
center.z = (max_z + min_z) / 2;
}
// get bounding box center axis value
float getCenterAxisValue(int axis) {
if (axis == 1) {
return center.x;
} else if (axis == 2) {
return center.y;
}
// when axis == 3
return center.z;
}
// check if a ray is intersected with the bounding box
boolean intersect(Ray r) {
float tmin, tmax;
if (r.dir.x >= 0) {
tmin = (min_x - r.ori.x) * (1.0f / r.dir.x);
tmax = (max_x - r.ori.x) * (1.0f / r.dir.x);
} else {
tmin = (max_x - r.ori.x) * (1.0f / r.dir.x);
tmax = (min_x - r.ori.x) * (1.0f / r.dir.x);
}
float tymin, tymax;
if (r.dir.y >= 0) {
tymin = (min_y - r.ori.y) * (1.0f / r.dir.y);
tymax = (max_y - r.ori.y) * (1.0f / r.dir.y);
} else {
tymin = (max_y - r.ori.y) * (1.0f / r.dir.y);
tymax = (min_y - r.ori.y) * (1.0f / r.dir.y);
}
if (tmax < tymin || tymax < tmin) {
return false;
}
tmin = tmin < tymin ? tymin : tmin;
tmax = tmax > tymax ? tymax : tmax;
float tzmin, tzmax;
if (r.dir.z >= 0) {
tzmin = (min_z - r.ori.z) * (1.0f / r.dir.z);
tzmax = (max_z - r.ori.z) * (1.0f / r.dir.z);
} else {
tzmin = (max_z - r.ori.z) * (1.0f / r.dir.z);
tzmax = (min_z - r.ori.z) * (1.0f / r.dir.z);
}
if (tmax < tzmin || tmin > tzmax) {
return false;
}
return true;
}
}
// Bounding Volume Hierarchy
class BVH {
// Binary Tree
BVH left, right;
BoundingBox overall_bbx;
ArrayList<Triangle> mesh;
BVH(ArrayList<Triangle> mesh) {
this.mesh = mesh;
overall_bbx = new BoundingBox();
left = null;
right = null;
int mesh_size = this.mesh.size();
if (mesh_size <= 1) {
return;
}
// random select an axis
int axis = int(random(100)) % 3 + 1;
// build bounding box and save the selected center component
float[] axis_values = new float[mesh_size];
for (int i = 0; i < mesh_size; i++) {
Triangle t = this.mesh.get(i);
overall_bbx.add(t.bbx);
axis_values[i] = t.bbx.getCenterAxisValue(axis);
}
// find the median value of selected center component as pivot
axis_values = sort(axis_values);
float pivot;
if (mesh_size % 2 == 1) {
pivot = axis_values[mesh_size / 2];
} else {
pivot =
0.5f * (axis_values[mesh_size / 2 - 1] + axis_values[mesh_size / 2]);
}
// Build left node and right node by partitioning the mesh based on triangle
// bounding box center component value
ArrayList<Triangle> left_mesh = new ArrayList<Triangle>();
ArrayList<Triangle> right_mesh = new ArrayList<Triangle>();
for (int i = 0; i < mesh_size; i++) {
Triangle t = this.mesh.get(i);
if (t.bbx.getCenterAxisValue(axis) < pivot) {
left_mesh.add(t);
} else if (t.bbx.getCenterAxisValue(axis) > pivot) {
right_mesh.add(t);
} else if (left_mesh.size() < right_mesh.size()) {
left_mesh.add(t);
} else {
right_mesh.add(t);
}
}
left = new BVH(left_mesh);
right = new BVH(right_mesh);
}
// check if a ray intersect with current volume
boolean intersect(Ray r, float[] param) {
if (mesh.size() == 0) {
return false;
}
if (mesh.size() == 1) {
Triangle t = mesh.get(0);
return t.intersect(r, param);
}
if (!overall_bbx.intersect(r)) {
return false;
}
boolean left_res = left.intersect(r, param);
boolean right_res = right.intersect(r, param);
return left_res || right_res;
}
}
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