add octree to improve rendering performance by reducing the number of ray-sphere-intersection calculations
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253
src/main/java/eu/jonahbauer/raytracing/math/Octree.java
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253
src/main/java/eu/jonahbauer/raytracing/math/Octree.java
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@ -0,0 +1,253 @@
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package eu.jonahbauer.raytracing.math;
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import org.jetbrains.annotations.NotNull;
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import org.jetbrains.annotations.Nullable;
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import java.util.*;
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import java.util.function.Consumer;
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import java.util.stream.Collectors;
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public final class Octree<T> {
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private final @NotNull NodeStorage<T> storage;
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public Octree(@NotNull Vec3 center, double dimension) {
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this.storage = new NodeStorage<>(center, dimension);
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}
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public void add(@NotNull BoundingBox bbox, T object) {
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storage.add(new Entry<>(bbox, object));
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}
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/**
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* Use HERO algorithms to find all elements that could possibly be hit by the given ray.
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* @see <a href="https://diglib.eg.org/server/api/core/bitstreams/33fe8d58-1101-40ff-878a-79d689a4607d/content">The HERO Algorithm for Ray-Tracing Octrees</a>
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*/
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public void hit(@NotNull Ray ray, @NotNull Consumer<T> action) {
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storage.hit(ray, action);
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}
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@Override
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public @NotNull String toString() {
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return storage.toString();
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}
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public static int getOctantIndex(@NotNull Vec3 center, @NotNull Vec3 pos) {
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return (pos.x() < center.x() ? 0 : 1)
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| (pos.y() < center.y() ? 0 : 2)
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| (pos.z() < center.z() ? 0 : 4);
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}
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private sealed interface Storage<T> {
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int LIST_SIZE_LIMIT = 32;
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@NotNull Storage<T> add(@NotNull Entry<T> entry);
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}
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private static final class ListStorage<T> implements Storage<T> {
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private final @NotNull Vec3 center;
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private final double dimension;
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private final @NotNull List<Entry<T>> list = new ArrayList<>();
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public ListStorage(@NotNull Vec3 center, double dimension) {
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this.center = Objects.requireNonNull(center);
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this.dimension = dimension;
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}
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@Override
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public @NotNull Storage<T> add(@NotNull Entry<T> entry) {
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if (list.size() >= LIST_SIZE_LIMIT) {
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var node = new NodeStorage<T>(center, dimension);
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list.forEach(node::add);
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node.add(entry);
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return node;
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} else {
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list.add(entry);
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return this;
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}
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}
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@Override
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public String toString() {
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return list.toString();
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}
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}
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private static final class NodeStorage<T> implements Storage<T> {
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private final @NotNull Vec3 center;
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private final double dimension;
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@SuppressWarnings("unchecked")
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private final @Nullable Storage<T> @NotNull[] octants = new Storage[8];
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private final @NotNull List<Entry<T>> list = new ArrayList<>(); // track elements spanning multiple octants separately
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public NodeStorage(@NotNull Vec3 center, double dimension) {
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this.center = Objects.requireNonNull(center);
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this.dimension = dimension;
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}
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@Override
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public @NotNull Storage<T> add(@NotNull Entry<T> entry) {
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var index = getOctantIndex(center, entry.bbox().min());
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if (index != getOctantIndex(center, entry.bbox().max())) {
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list.add(entry);
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} else {
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var subnode = octants[index];
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if (subnode == null) {
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subnode = newOctant(index);
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}
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octants[index] = subnode.add(entry);
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}
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return this;
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}
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private @NotNull Storage<T> newOctant(int index) {
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var newSize = 0.5 * dimension;
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var newCenter = this.center
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.plus(new Vec3(
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(index & 1) == 0 ? -newSize : newSize,
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(index & 2) == 0 ? -newSize : newSize,
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(index & 4) == 0 ? -newSize : newSize
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));
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return new ListStorage<>(newCenter, newSize);
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}
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public void hit(@NotNull Ray ray, @NotNull Consumer<T> action) {
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int vmask = (ray.direction().x() < 0 ? 1 : 0)
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| (ray.direction().y() < 0 ? 2 : 0)
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| (ray.direction().z() < 0 ? 4 : 0);
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var min = center.minus(dimension, dimension, dimension);
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var max = center.plus(dimension, dimension, dimension);
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// calculate t values for intersection points of ray with planes through min
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var tmin = calculatePlaneIntersections(min, ray);
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// calculate t values for intersection points of ray with planes through max
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var tmax = calculatePlaneIntersections(max, ray);
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// determine range of t for which the ray is inside this voxel
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double tlmax = Double.NEGATIVE_INFINITY; // lower limit maximum
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double tumin = Double.POSITIVE_INFINITY; // upper limit minimum
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for (int i = 0; i < 3; i++) {
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// classify t values as lower or upper limit based on vmask
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if ((vmask & (1 << i)) == 0) {
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// min is lower limit and max is upper limit
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tlmax = Math.max(tlmax, tmin[i]);
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tumin = Math.min(tumin, tmax[i]);
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} else {
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// max is lower limit and min is upper limit
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tlmax = Math.max(tlmax, tmax[i]);
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tumin = Math.min(tumin, tmin[i]);
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}
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}
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var hit = tlmax < tumin;
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if (!hit) return;
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hit0(ray, vmask, tlmax, tumin, action);
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}
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private void hit0(@NotNull Ray ray, int vmask, double tmin, double tmax, @NotNull Consumer<T> action) {
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if (tmax < 0) return;
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for (Entry<T> entry : list) {
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action.accept(entry.object());
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}
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// t values for intersection points of ray with planes through center
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var tmid = calculatePlaneIntersections(center, ray);
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// masks of planes in the order of intersection, e.g. [2, 1, 4] for a ray intersection y = center.y() then x = center.x() then z = center.z()
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var masklist = calculateMastlist(tmid);
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var childmask = (tmid[0] < tmin ? 1 : 0)
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| (tmid[1] < tmin ? 2 : 0)
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| (tmid[2] < tmin ? 4 : 0);
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var lastmask = (tmid[0] < tmax ? 1 : 0)
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| (tmid[1] < tmax ? 2 : 0)
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| (tmid[2] < tmax ? 4 : 0);
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var childTmin = tmin;
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int i = 0;
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while (true) {
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var child = octants[childmask ^ vmask];
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double childTmax;
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if (childmask == lastmask) {
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childTmax = tmax;
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} else {
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while ((masklist[i] & childmask) != 0) {
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i++;
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}
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childmask = childmask | masklist[i];
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childTmax = tmid[Integer.numberOfTrailingZeros(masklist[i])];
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}
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if (child instanceof ListStorage<T> list) {
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for (Entry<T> entry : list.list) {
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action.accept(entry.object);
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}
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} else if (child instanceof NodeStorage<T> node) {
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node.hit0(ray, vmask, childTmin, childTmax, action);
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}
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if (childTmax == tmax) break;
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childTmin = childTmax;
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}
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}
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private double @NotNull [] calculatePlaneIntersections(@NotNull Vec3 position, @NotNull Ray ray) {
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return new double[] {
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(position.x() - ray.origin().x()) / ray.direction().x(),
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(position.y() - ray.origin().y()) / ray.direction().y(),
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(position.z() - ray.origin().z()) / ray.direction().z(),
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};
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}
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private int @NotNull [] calculateMastlist(double @NotNull[] tmid) {
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var masklist = new int[3];
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if (tmid[0] < tmid[1] && tmid[0] < tmid[2]) {
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masklist[0] = 1;
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if (tmid[1] < tmid[2]) {
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masklist[1] = 2;
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masklist[2] = 4;
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} else {
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masklist[1] = 4;
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masklist[2] = 2;
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}
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} else if (tmid[1] < tmid[2]) {
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masklist[0] = 2;
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if (tmid[0] < tmid[2]) {
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masklist[1] = 1;
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masklist[2] = 4;
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} else {
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masklist[1] = 4;
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masklist[2] = 1;
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}
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} else {
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masklist[0] = 4;
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if (tmid[0] < tmid[1]) {
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masklist[1] = 1;
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masklist[2] = 2;
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} else {
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masklist[1] = 2;
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masklist[2] = 1;
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}
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}
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return masklist;
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}
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@Override
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public String toString() {
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var out = new StringBuilder("Octree centered on " + center + " with dimension " + dimension + "\n");
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for (int i = 0; i < 8; i++) {
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out.append(i == 7 ? "\\- [" : "|- [").append(i).append("]: ");
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var prefix = i == 7 ? " " : "| ";
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out.append(Objects.toString(octants[i]).lines().map(str -> prefix + str).collect(Collectors.joining("\n")).substring(8));
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out.append("\n");
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}
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return out.toString();
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}
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}
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private record Entry<T>(@NotNull BoundingBox bbox, T object) { }
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}
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@ -6,6 +6,8 @@ import java.util.Optional;
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public record Vec3(double x, double y, double z) {
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public static final Vec3 ZERO = new Vec3(0, 0, 0);
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public static final Vec3 MAX = new Vec3(Double.MAX_VALUE, Double.MAX_VALUE, Double.MAX_VALUE);
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public static final Vec3 MIN = new Vec3(-Double.MAX_VALUE, -Double.MAX_VALUE, -Double.MAX_VALUE);
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public static final Vec3 UNIT_X = new Vec3(1, 0, 0);
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public static final Vec3 UNIT_Y = new Vec3(0, 1, 0);
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public static final Vec3 UNIT_Z = new Vec3(0, 0, 1);
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@ -52,6 +54,38 @@ public record Vec3(double x, double y, double z) {
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return a.minus(b).length();
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}
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public static @NotNull Vec3 average(@NotNull Vec3 current, @NotNull Vec3 next, int index) {
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return new Vec3(
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current.x() + (next.x() - current.x()) / index,
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current.y() + (next.y() - current.y()) / index,
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current.z() + (next.z() - current.z()) / index
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);
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}
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public static @NotNull Vec3 max(@NotNull Vec3 a, @NotNull Vec3 b) {
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return new Vec3(
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Math.max(a.x(), b.x()),
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Math.max(a.y(), b.y()),
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Math.max(a.z(), b.z())
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);
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}
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public static @NotNull Vec3 min(@NotNull Vec3 a, @NotNull Vec3 b) {
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return new Vec3(
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Math.min(a.x(), b.x()),
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Math.min(a.y(), b.y()),
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Math.min(a.z(), b.z())
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);
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}
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public @NotNull Vec3 plus(double x, double y, double z) {
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return new Vec3(this.x + x, this.y + y, this.z + z);
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}
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public @NotNull Vec3 minus(double x, double y, double z) {
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return new Vec3(this.x - x, this.y - y, this.z - z);
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}
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public @NotNull Vec3 plus(@NotNull Vec3 b) {
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return new Vec3(this.x + b.x, this.y + b.y, this.z + b.z);
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}
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@ -1,31 +1,80 @@
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package eu.jonahbauer.raytracing.scene;
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import eu.jonahbauer.raytracing.math.Octree;
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import eu.jonahbauer.raytracing.math.Range;
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import eu.jonahbauer.raytracing.math.Ray;
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import eu.jonahbauer.raytracing.math.Vec3;
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import org.jetbrains.annotations.NotNull;
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import java.util.ArrayList;
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import java.util.Arrays;
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import java.util.List;
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import java.util.Optional;
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public record Scene(@NotNull List<@NotNull Hittable> objects) implements Hittable {
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public final class Scene implements Hittable {
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private final @NotNull Octree<@NotNull Hittable> octree;
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private final @NotNull List<@NotNull Hittable> list;
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public Scene {
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objects = List.copyOf(objects);
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}
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public Scene(@NotNull List<? extends @NotNull Hittable> objects) {
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this.octree = newOctree(objects);
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this.list = new ArrayList<>();
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public Scene(@NotNull Hittable @NotNull ... objects) {
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this(List.of(objects));
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}
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public @NotNull Optional<HitResult> hit(@NotNull Ray ray, @NotNull Range range) {
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var result = (HitResult) null;
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for (var object : objects) {
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var r = object.hit(ray, range);
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if (r.isPresent() && range.surrounds(r.get().t())) {
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result = r.get();
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range = new Range(range.min(), result.t());
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for (Hittable object : objects) {
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var bbox = object.getBoundingBox();
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if (bbox.isPresent()) {
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octree.add(bbox.get(), object);
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} else {
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list.add(object);
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}
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}
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return Optional.ofNullable(result);
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}
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@Override
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public @NotNull Optional<HitResult> hit(@NotNull Ray ray, @NotNull Range range) {
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var state = new State();
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state.range = range;
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octree.hit(ray, object -> hit(state, ray, object));
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list.forEach(object -> hit(state, ray, object));
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return Optional.ofNullable(state.result);
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}
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private void hit(@NotNull State state, @NotNull Ray ray, @NotNull Hittable object) {
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var r = object.hit(ray, state.range);
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if (r.isPresent() && state.range.surrounds(r.get().t())) {
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state.result = r.get();
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state.range = new Range(state.range.min(), state.result.t());
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}
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}
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private static @NotNull Octree<Hittable> newOctree(@NotNull List<? extends Hittable> objects) {
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Vec3 center = Vec3.ZERO, max = Vec3.MIN, min = Vec3.MAX;
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int i = 1;
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for (Hittable object : objects) {
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var bbox = object.getBoundingBox();
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if (bbox.isPresent()) {
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center = Vec3.average(center, bbox.get().center(), i++);
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max = Vec3.max(max, bbox.get().max());
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min = Vec3.min(min, bbox.get().min());
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}
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}
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var dimension = Arrays.stream(new double[] {
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Math.abs(max.x() - center.x()),
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Math.abs(max.y() - center.y()),
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Math.abs(max.z() - center.z()),
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Math.abs(min.x() - center.x()),
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Math.abs(min.y() - center.y()),
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Math.abs(min.z() - center.z())
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}).max().orElse(10);
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return new Octree<Hittable>(center, dimension);
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}
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private static class State {
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HitResult result;
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Range range;
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}
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}
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