three subgraphs of Delaunay: Gabriel, Urquhart, and minimal spanning tree

for #928

Author: Fil

src/index.js

@@ -4,7 +4,7 @@ export {Arrow, arrow} from "./marks/arrow.js";
 export {BarX, BarY, barX, barY} from "./marks/bar.js";
 export {boxX, boxY} from "./marks/box.js";
 export {Cell, cell, cellX, cellY} from "./marks/cell.js";
-export {delaunayLink, delaunayMesh, hull, voronoi, voronoiMesh} from "./marks/delaunay.js";
+export {delaunayLink, delaunayMesh, hull, voronoi, voronoiMesh, gabrielMesh, urquhartMesh, mstMesh} from "./marks/delaunay.js";
 export {Dot, dot, dotX, dotY, circle, hexagon} from "./marks/dot.js";
 export {Frame, frame} from "./marks/frame.js";
 export {Hexgrid, hexgrid} from "./marks/hexgrid.js";

src/marks/delaunay.js

@@ -1,4 +1,4 @@
-import {create, group, path, select, Delaunay} from "d3";
+import {bisector, create, extent, group, path, select, Delaunay} from "d3";
 import {Curve} from "../curve.js";
 import {constant, maybeTuple, maybeZ} from "../options.js";
 import {Mark} from "../plot.js";
@@ -266,3 +266,120 @@ export function voronoi(data, options) {
 export function voronoiMesh(data, options) {
   return delaunayMark(VoronoiMesh, data, options);
 }
+
+class GabrielMesh extends AbstractDelaunayMark {
+  constructor(data, options) {
+    super(data, options, voronoiMeshDefaults);
+    this.fill = "none";
+  }
+  _accept(delaunay) {
+    const {points, triangles} = delaunay;
+    return (i) => {
+      const a = triangles[i];
+      const b = triangles[i % 3 === 2 ? i - 2 : i + 1];
+      return [a, b].includes(delaunay.find((points[2 * a] + points[2 * b]) / 2, (points[2 * a + 1] + points[2 * b + 1]) / 2, a));
+    };
+  }
+  _render(delaunay) {
+    const p = new path();
+    const {points, halfedges, triangles} = delaunay;
+    const accept = this._accept(delaunay);
+    for (let i = 0, n = triangles.length; i < n; ++i) {
+      const j = halfedges[i];
+      if (i < j) continue;
+      if (accept(i)) {
+        const a = triangles[i];
+        const b = triangles[i % 3 === 2 ? i - 2 : i + 1];
+        p.moveTo(points[2 * a], points[2 * a + 1]);
+        p.lineTo(points[2 * b], points[2 * b + 1]);
+      }
+    }
+    return "" + p;
+  }
+}
+
+class UrquhartMesh extends GabrielMesh {
+  constructor(data, options) {
+    super(data, options, voronoiMeshDefaults);
+    this.fill = "none";
+  }
+  _accept(delaunay, score = euclidean2) {
+    const {halfedges, points, triangles} = delaunay;
+    const n = triangles.length;
+    const removed = new Uint8Array(n);
+    for (let e = 0; e < n; e += 3) {
+      const p0 = triangles[e], p1 = triangles[e + 1], p2 = triangles[e + 2];
+      const p01 = score(points, p0, p1), p12 = score(points, p1, p2), p20 = score(points, p2, p0);
+      removed[p20 > p01 && p20 > p12 ? Math.max(e + 2, halfedges[e + 2])
+          : p12 > p01 && p12 > p20 ? Math.max(e + 1, halfedges[e + 1])
+          : Math.max(e, halfedges[e])] = 1;
+    }
+    return (i) => !removed[i];
+  }
+}
+
+function euclidean2(points, i, j) {
+  return (points[i * 2] - points[j * 2]) ** 2 + (points[i * 2 + 1] - points[j * 2 + 1]) ** 2;
+}
+
+class MSTMesh extends GabrielMesh {
+  constructor(data, options) {
+    super(data, options, voronoiMeshDefaults);
+    this.fill = "none";
+  }
+  _accept(delaunay, score = euclidean2) {
+    const {points, triangles} = delaunay;
+    const set = new Uint8Array(points.length / 2);
+    const tree = new Set();
+    const heap = [];
+    
+    const bisect = bisector(([v]) => -v).left;
+    function heap_insert(x, v) {
+      heap.splice(bisect(heap, -v), 0, [v, x]);
+    }
+    function heap_pop() {
+      return heap.length && heap.pop()[1];
+    }
+  
+    // Initialize the heap with the outgoing edges of vertex zero.
+    set[0] = 1;
+    for (const i of delaunay.neighbors(0)) {
+      heap_insert([0, i], score(points, 0, i));
+    }
+  
+    // For each remaining minimum edge in the heap…
+    let edge;
+    while (edge = heap_pop()) {
+      const [i, j] = edge;
+  
+      // If j is already connected, skip; otherwise add the new edge to point j.
+      if (set[j]) continue;
+      set[j] = 1;
+      tree.add(`${extent([i, j])}`);
+  
+      // Add each unconnected neighbor k of point j to the heap.
+      for (const k of delaunay.neighbors(j)) {
+        if (set[k]) continue;
+        heap_insert([j, k], score(points, j, k));
+      }
+    }
+  
+    return (i) => {
+      const a = triangles[i];
+      const b = triangles[i % 3 === 2 ? i - 2 : i + 1];
+      return tree.has(`${extent([a, b])}`);
+    };
+  }
+}
+
+export function gabrielMesh(data, options) {
+  return delaunayMark(GabrielMesh, data, options);
+}
+
+export function urquhartMesh(data, options) {
+  return delaunayMark(UrquhartMesh, data, options);
+}
+
+export function mstMesh(data, options) {
+  return delaunayMark(MSTMesh, data, options);
+}

test/output/penguinCulmenGabriel.svg

@@ -130,6 +130,9 @@ export {default as penguinCulmenArray} from "./penguin-culmen-array.js";
 export {default as penguinCulmenDelaunay} from "./penguin-culmen-delaunay.js";
 export {default as penguinCulmenDelaunayMesh} from "./penguin-culmen-delaunay-mesh.js";
 export {default as penguinCulmenDelaunaySpecies} from "./penguin-culmen-delaunay-species.js";
+export {default as penguinCulmenGabriel} from "./penguin-culmen-gabriel.js";
+export {default as penguinCulmenMST} from "./penguin-culmen-mst.js";
+export {default as penguinCulmenUrquhart} from "./penguin-culmen-urquhart.js";
 export {default as penguinCulmenVoronoi} from "./penguin-culmen-voronoi.js";
 export {default as penguinVoronoi1D} from "./penguin-voronoi-1d.js";
 export {default as penguinDodge} from "./penguin-dodge.js";

test/output/penguinCulmenMST.svg

@@ -0,0 +1,13 @@
+import * as Plot from "@observablehq/plot";
+import * as d3 from "d3";
+
+export default async function() {
+  const data = await (await d3.csv("data/penguins.csv", d3.autoType));
+  return Plot.plot({
+    marks: [
+      Plot.delaunayMesh(data, {x: "culmen_depth_mm", y: "culmen_length_mm", stroke: "species", z: "species"}),
+      Plot.gabrielMesh(data, {x: "culmen_depth_mm", y: "culmen_length_mm", stroke: "species", z: "species", strokeOpacity: 1}),
+      Plot.dot(data, {x: "culmen_depth_mm", y: "culmen_length_mm", fill:"species", z: "species"})
+    ]
+  });
+}

test/output/penguinCulmenUrquhart.svg

@@ -0,0 +1,13 @@
+import * as Plot from "@observablehq/plot";
+import * as d3 from "d3";
+
+export default async function() {
+  const data = await (await d3.csv("data/penguins.csv", d3.autoType));
+  return Plot.plot({
+    marks: [
+      Plot.delaunayMesh(data, {x: "culmen_depth_mm", y: "culmen_length_mm", stroke: "species", z: "species"}),
+      Plot.mstMesh(data, {x: "culmen_depth_mm", y: "culmen_length_mm", stroke:"species", z: "species", strokeOpacity: 1}),
+      Plot.dot(data, {x: "culmen_depth_mm", y: "culmen_length_mm", fill:"species", z: "species"})
+    ]
+  });
+}

test/plots/index.js

@@ -0,0 +1,13 @@
+import * as Plot from "@observablehq/plot";
+import * as d3 from "d3";
+
+export default async function() {
+  const data = await (await d3.csv("data/penguins.csv", d3.autoType));
+  return Plot.plot({
+    marks: [
+      Plot.delaunayMesh(data, {x: "culmen_depth_mm", y: "culmen_length_mm", stroke: "species", z: "species"}),
+      Plot.urquhartMesh(data, {x: "culmen_depth_mm", y: "culmen_length_mm", stroke:"species", z: "species", strokeOpacity: 1}),
+      Plot.dot(data, {x: "culmen_depth_mm", y: "culmen_length_mm", fill:"species", z: "species"})
+    ]
+  });
+}