java-topology/tests/workbench/Manifold.java

package workbench;

import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.List;
import java.util.Set;

/**
 * Sym² manifold — pure geometry + heat diffusion.
 *
 * Given m seed points, maps every pair (u,v) to a 3D vertex:
 *   x,y = midpoint of p_u and p_v (centered)
 *   z   = distance between p_u and p_v * 8
 *
 * This is the symmetric product Sym²(curve). The seam (u==v diagonal)
 * re-embeds the original curve at z=0.
 *
 * No Swing dependencies — pure data structure.
 */
public class Manifold {

    public static final int M = 32;          // grid resolution
    public static final float DECAY = 0.96f; // heat decay per frame

    // flat float arrays: vertex i → positions[i*3 .. i*3+2]
    public float[] positions;        // current positions (displaced by heat + wobble)
    public float[] originalPositions;// rest positions (no displacement)
    public int[]   indices;          // triangle index list

    // seam: diagonal u==v re-embeds original curve at z=0
    public float[] seamPositions;    // M points, flat x,y,z

    // adjacency[i] = list of vertex indices adjacent to i
    public List<List<Integer>> adjacency;

    public float[] heat;             // heat per vertex

    public int vertexCount;
    public boolean built = false;

    // ── Sym² computation ──────────────────────────────────────────────────────

    /**
     * Pure math: compute M*M vertex positions from seed points.
     * Returns flat float array: [x0,y0,z0, x1,y1,z1, ...]
     */
    public static float[] computePositions(float[] seedX, float[] seedY, int n) {
        // sample M evenly-spaced seeds
        float[] sx = new float[M], sy = new float[M];
        for (int i = 0; i < M; i++) {
            int k = (int)(i * n / (double)M);
            sx[i] = seedX[k];
            sy[i] = seedY[k];
        }
        // center
        float cx = 0, cy = 0;
        for (int i = 0; i < M; i++) { cx += sx[i]; cy += sy[i]; }
        cx /= M; cy /= M;

        float[] pos = new float[M * M * 3];
        for (int u = 0; u < M; u++) {
            for (int v = 0; v < M; v++) {
                int base = (u * M + v) * 3;
                float midX = (sx[u] + sx[v]) / 2f - cx;
                float midY = (sy[u] + sy[v]) / 2f - cy;
                float dx   = sx[u] - sx[v];
                float dy   = sy[u] - sy[v];
                pos[base]     =  midX * 12f;
                pos[base + 1] = -midY * 12f;
                pos[base + 2] = (float)Math.sqrt(dx*dx + dy*dy) * 8f;
            }
        }
        return pos;
    }

    /**
     * Build manifold from seed points. Call when seeds change.
     * Resets heat to zero.
     */
    public void build(float[] seedX, float[] seedY, int n) {
        if (n < 5) return;

        vertexCount = M * M;
        positions         = computePositions(seedX, seedY, n);
        originalPositions = Arrays.copyOf(positions, positions.length);

        // triangle indices: quad (u,v) split into 2 triangles
        int quadCount = (M - 1) * (M - 1);
        indices = new int[quadCount * 6];
        int idx = 0;
        for (int u = 0; u < M - 1; u++) {
            for (int v = 0; v < M - 1; v++) {
                int a = u*M+v, b = (u+1)*M+v, c = u*M+(v+1), d = (u+1)*M+(v+1);
                indices[idx++] = a; indices[idx++] = b; indices[idx++] = c;
                indices[idx++] = b; indices[idx++] = d; indices[idx++] = c;
            }
        }

        // adjacency from triangle index list
        adjacency = new ArrayList<>(vertexCount);
        for (int i = 0; i < vertexCount; i++) adjacency.add(new ArrayList<>());
        for (int i = 0; i < indices.length; i += 3) {
            int a = indices[i], b = indices[i+1], c = indices[i+2];
            adjacency.get(a).add(b); adjacency.get(b).add(a);
            adjacency.get(b).add(c); adjacency.get(c).add(b);
            adjacency.get(a).add(c); adjacency.get(c).add(a);
        }
        // deduplicate
        for (int i = 0; i < vertexCount; i++) {
            Set<Integer> seen = new HashSet<>(adjacency.get(i));
            adjacency.set(i, new ArrayList<>(seen));
        }

        // seam: diagonal u==v
        seamPositions = new float[M * 3];
        for (int u = 0; u < M; u++) {
            int base = (u * M + u) * 3;
            seamPositions[u*3]     = positions[base];
            seamPositions[u*3 + 1] = positions[base + 1];
            seamPositions[u*3 + 2] = positions[base + 2];
        }

        heat = new float[vertexCount];
        built = true;
    }

    // ── Heat diffusion (graph Laplacian, one step) ────────────────────────────

    public void diffuseHeat() {
        if (!built) return;
        float[] next = new float[heat.length];
        for (int i = 0; i < heat.length; i++) {
            List<Integer> nb = adjacency.get(i);
            float sum = heat[i];
            for (int j : nb) sum += heat[j];
            next[i] = (sum / (nb.size() + 1)) * DECAY;
        }
        heat = next;
    }

    // ── Bounding box for viewport scaling ────────────────────────────────────

    public float[] bounds() {
        if (!built) return new float[]{-1,-1,-1,1,1,1};
        float minX = Float.MAX_VALUE, minY = Float.MAX_VALUE, minZ = Float.MAX_VALUE;
        float maxX = -Float.MAX_VALUE, maxY = -Float.MAX_VALUE, maxZ = -Float.MAX_VALUE;
        for (int i = 0; i < vertexCount; i++) {
            float x = originalPositions[i*3], y = originalPositions[i*3+1], z = originalPositions[i*3+2];
            if (x < minX) minX = x; if (x > maxX) maxX = x;
            if (y < minY) minY = y; if (y > maxY) maxY = y;
            if (z < minZ) minZ = z; if (z > maxZ) maxZ = z;
        }
        return new float[]{minX, minY, minZ, maxX, maxY, maxZ};
    }
}