258 lines
8.3 KiB
Java
258 lines
8.3 KiB
Java
import java.util.ArrayList;
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import java.util.HashMap;
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import java.util.List;
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import java.util.Map;
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import java.util.Objects;
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import java.util.function.Function;
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import java.util.stream.Collectors;
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public final class CatmullClarkSurfaceSubdivision {
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public static void main(String[] args) {
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List<Face> faces = List.of( new Face(List.of( new Point(-1.0, 1.0, 1.0),
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new Point(-1.0, -1.0, 1.0),
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new Point( 1.0, -1.0, 1.0),
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new Point( 1.0, 1.0, 1.0) )),
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new Face(List.of( new Point( 1.0, 1.0, 1.0),
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new Point( 1.0, -1.0, 1.0),
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new Point( 1.0, -1.0, -1.0),
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new Point( 1.0, 1.0, -1.0) )),
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new Face(List.of( new Point( 1.0, 1.0, -1.0),
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new Point( 1.0, -1.0, -1.0),
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new Point(-1.0, -1.0, -1.0),
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new Point(-1.0, 1.0, -1.0) )),
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new Face(List.of( new Point(-1.0, 1.0, -1.0),
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new Point(-1.0, 1.0, 1.0),
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new Point( 1.0, 1.0, 1.0),
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new Point( 1.0, 1.0, -1.0) )),
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new Face(List.of( new Point(-1.0, 1.0, -1.0),
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new Point(-1.0, -1.0, -1.0),
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new Point(-1.0, -1.0, 1.0),
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new Point(-1.0, 1.0, 1.0) )),
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new Face(List.of( new Point(-1.0, -1.0, -1.0),
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new Point(-1.0, -1.0, 1.0),
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new Point( 1.0, -1.0, 1.0),
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new Point( 1.0, -1.0, -1.0) )) );
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displaySurface(faces);
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final int iterations = 1;
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for ( int i = 0; i < iterations; i++ ) {
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faces = catmullClarkSurfaceSubdivision(faces);
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}
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displaySurface(faces);
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}
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// The Catmull-Clarke surface subdivision algorithm.
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private static List<Face> catmullClarkSurfaceSubdivision(List<Face> faces) {
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// Determine, for each edge, whether or not it is an edge of a hole, and set its edge point accordingly.
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List<Edge> edges = faces.stream().map( face -> face.edges.stream() ).flatMap(Function.identity()).toList();
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for ( Edge edge : edges ) {
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List<Point> facePointsForEdge =
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faces.stream().filter( face -> face.contains(edge) ).map( face -> face.facePoint ).toList();
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if ( facePointsForEdge.size() == 2 ) {
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edge.holeEdge = false;
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edge.edgePoint = centroid(List.of( edge.midEdge, centroid(facePointsForEdge) ));
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} else {
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edge.holeEdge = true;
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edge.edgePoint = edge.midEdge;
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}
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}
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Map<Point, Point> nextVertices = nextVertices(edges, faces);
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List<Face> nextFaces = new ArrayList<Face>();
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for ( Face face : faces ) { // The face may contain any number of points
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if ( face.vertices.size() >= 3 ) { // A face with 2 or fewer points does not contribute to the surface
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Point facePoint = face.facePoint;
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for ( int i = 0; i < face.vertices.size(); i++ ) {
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nextFaces.addLast( new Face(List.of(
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nextVertices.get(face.vertices.get(i)),
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face.edges.get(i).edgePoint,
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facePoint,
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face.edges.get(Math.floorMod(i - 1, face.vertices.size())).edgePoint )) );
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}
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}
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}
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return nextFaces;
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}
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// Return a map containing, for each vertex,
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// the new vertex created by the current iteration of the Catmull-Clark surface subdivision algorithm.
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private static Map<Point, Point> nextVertices(List<Edge> edges, List<Face> faces) {
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Map<Point, Point> nextVertices = new HashMap<Point, Point>();
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List<Point> vertices =
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faces.stream().map( face -> face.vertices.stream() ).flatMap(Function.identity()).distinct().toList();
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for ( Point vertex : vertices ) {
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List<Face> facesForVertex = faces.stream().filter( face -> face.contains(vertex) ).toList();
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List<Edge> edgesForVertex = edges.stream().filter( edge -> edge.contains(vertex) ).distinct().toList();
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if ( facesForVertex.size() != edgesForVertex.size() ) {
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List<Point> midEdgeOfHoleEdges = edgesForVertex.stream().filter( edge -> edge.holeEdge )
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.map( edge -> edge.midEdge ).collect(Collectors.toList());
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midEdgeOfHoleEdges.add(vertex);
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nextVertices.put(vertex, centroid(midEdgeOfHoleEdges));
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} else {
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final int faceCount = facesForVertex.size();
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final double multipleOne = (double) ( faceCount - 3 ) / faceCount;
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final double multipleTwo = 1.0 / faceCount;
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final double multipleThree = 2.0 / faceCount;
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Point nextVertexOne = vertex.multiply(multipleOne);
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List<Point> facePoints = facesForVertex.stream().map( face -> face.facePoint ).toList();
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Point nextVertexTwo = centroid(facePoints).multiply(multipleTwo);
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List<Point> midEdges = edgesForVertex.stream().map( edge -> edge.midEdge ).toList();
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Point nextVertexThree = centroid(midEdges).multiply(multipleThree);
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Point nextVertexFour = nextVertexOne.add(nextVertexTwo);
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nextVertices.put(vertex, nextVertexFour.add(nextVertexThree));
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}
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}
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return nextVertices;
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}
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// Return the centroid point of the given list of points.
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private static Point centroid(List<Point> points) {
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return points.stream().reduce(Point.ZERO, (left, right) -> left.add(right) ).divide(points.size());
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}
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// Display the current Catmull-Clark surface on the console.
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private static void displaySurface(List<Face> faces) {
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System.out.println("Surface {");
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faces.stream().forEach(System.out::println);
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System.out.println("}" + System.lineSeparator());
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}
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// A point of the current Catmull-Clark surface.
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private static final class Point implements Comparable<Point> {
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public Point(double aX, double aY, double aZ) {
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x = aX; y = aY; z = aZ;
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}
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@Override
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public int compareTo(Point other) {
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if ( x == other.x ) {
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if ( y == other.y ) {
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return Double.compare(z, other.z);
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}
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return Double.compare(y, other.y);
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}
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return Double.compare(x, other.x);
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}
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@Override
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public boolean equals(Object other) {
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return switch ( other ) {
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case Point point -> x == point.x && y == point.y && z == point.z;
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default -> false;
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};
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}
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@Override
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public int hashCode() {
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return Objects.hash(x, y, z);
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}
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public Point add(Point other) {
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return new Point(x + other.x, y + other.y, z + other.z);
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}
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public Point multiply(double factor) {
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return new Point(x * factor, y * factor, z * factor);
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}
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public Point divide(double factor) {
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return multiply(1.0 / factor);
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}
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public String toString() {
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return "(" + format(x) + ", " + format(y) + ", " + format(z) + ")";
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}
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public static Point ZERO = new Point(0.0, 0.0, 0.0);
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private String format(double value) {
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return ( value >= 0 ) ? String.format(" %.3f", value) : String.format("%.3f", value);
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}
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private final double x, y, z;
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}
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// An edge of the current Catmull-Clark surface.
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private static final class Edge {
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public Edge(Point aBegin, Point aEnd) {
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if ( aBegin.compareTo(aEnd) <= 0 ) {
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begin = aBegin; end = aEnd;
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} else {
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begin = aEnd; end = aBegin;
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}
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midEdge = centroid(List.of( begin, end ));
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}
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@Override
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public boolean equals(Object other) {
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return switch ( other ) {
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case Edge edge -> begin.equals(edge.begin) && end.equals(edge.end);
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default -> false;
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};
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}
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@Override
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public int hashCode() {
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return Objects.hash(begin, end);
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}
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public boolean contains(Point point) {
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return point.equals(begin) || point.equals(end);
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}
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public boolean holeEdge;
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public Point edgePoint;
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public final Point begin, end, midEdge;
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}
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// A face of the current Catmull-Clark surface.
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private static final class Face {
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public Face(List<Point> aVertices) {
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vertices = new ArrayList<Point>(aVertices);
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facePoint = centroid(vertices);
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edges = new ArrayList<Edge>();
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for ( int i = 0; i < vertices.size() - 1; i++ ) {
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edges.addLast( new Edge(vertices.get(i), vertices.get(i + 1)) );
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}
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edges.addLast( new Edge(vertices.getLast(), vertices.getFirst()) );;
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}
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public boolean contains(Point vertex) {
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return vertices.contains(vertex);
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}
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public boolean contains(Edge edge) {
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return contains(edge.begin) && contains(edge.end);
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}
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public String toString() {
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return "Face: " + vertices.stream().map( point -> point.toString() ).collect(Collectors.joining("; "));
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}
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public final List<Point> vertices;
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public final Point facePoint;
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public final List<Edge> edges;
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}
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}
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