refactor: roads - Urquhart graph approach

src/config/generation.ts

@@ -61,6 +61,6 @@ export const FOREST_BIOMES = [
 
 export const ROUTES = {
   MAIN_ROAD: 1,
-  SMALL_ROAD: 2,
+  TRAIL: 2,
   SEA_ROUTE: 3
 };

src/layers/renderers/drawRoutes.ts

@@ -6,7 +6,7 @@ export function drawRoutes() {
   routes.selectAll("path").remove();
 
   const {cells, burgs} = pack;
-  const lineGen = d3.line().curve(d3.curveBasis);
+  const lineGen = d3.line().curve(d3.curveCatmullRom.alpha(0.1));
 
   const getBurgCoords = (burgId: number): TPoint => {
     if (!burgId) throw new Error("burgId must be positive");
@@ -24,8 +24,8 @@ export function drawRoutes() {
 
   const routePaths: Dict<string[]> = {};
 
-  for (const {i, type, cells: routeCells} of pack.routes) {
-    const points = getPathPoints(routeCells);
+  for (const {i, type, cells} of pack.routes) {
+    const points = getPathPoints(cells);
     const path = round(lineGen(points)!, 1);
 
     if (!routePaths[type]) routePaths[type] = [];

src/scripts/generation/generation.ts

@@ -64,8 +64,8 @@ async function generate(options?: IGenerationOptions) {
     // temp rendering for debug
     // renderLayer("cells");
     renderLayer("features");
-    renderLayer("heightmap");
-    renderLayer("rivers");
+    // renderLayer("heightmap");
+    // renderLayer("rivers");
     // renderLayer("biomes");
     renderLayer("burgs");
     renderLayer("routes");

src/scripts/generation/pack/generateRoutes.ts

@@ -1,14 +1,16 @@
+import Delaunator from "delaunator";
 import FlatQueue from "flatqueue";
 
 import {TIME} from "config/logging";
 import {ROUTES} from "config/generation";
-
-const isBurg = (burg: TNoBurg | IBurg): burg is IBurg => burg.i > 0;
+import {dist2} from "utils/functionUtils";
+import {drawLine} from "utils/debugUtils";
 
 export function generateRoutes(burgs: TBurgs, cells: Pick<IPack["cells"], "c" | "h" | "biome" | "state" | "burg">) {
   const cellRoutes = new Uint8Array(cells.h.length);
+  const validBurgs = burgs.filter(burg => burg.i && !(burg as IBurg).removed) as IBurg[];
   const mainRoads = generateMainRoads();
-  // const townRoutes = getTrails();
+  const trails = generateTrails();
   // const oceanRoutes = getSearoutes();
 
   const routes = combineRoutes();
@@ -18,50 +20,85 @@ export function generateRoutes(burgs: TBurgs, cells: Pick<IPack["cells"], "c" |
 
   function generateMainRoads() {
     TIME && console.time("generateMainRoads");
-    const mainRoads: {feature: number; from: number; to: number; end: number; cells: number[]}[] = [];
-
-    const capitalsByFeature = burgs.reduce((acc, burg) => {
-      if (!isBurg(burg)) return acc;
-      const {capital, removed, feature} = burg;
-      if (!capital || removed) return acc;
+    const mainRoads: {feature: number; cells: number[]}[] = [];
 
+    const capitalsByFeature = validBurgs.reduce((acc, burg) => {
+      const {capital, feature} = burg;
+      if (!capital) return acc;
       if (!acc[feature]) acc[feature] = [];
       acc[feature].push(burg);
       return acc;
     }, {} as {[feature: string]: IBurg[]});
 
     for (const [key, featureCapitals] of Object.entries(capitalsByFeature)) {
-      for (let i = 0; i < featureCapitals.length; i++) {
-        const {cell: from} = featureCapitals[i];
+      const points: TPoints = featureCapitals.map(burg => [burg.x, burg.y]);
+      const urquhartEdges = calculateUrquhartEdges(points);
+      urquhartEdges.forEach(([fromId, toId]) => {
+        drawLine(points[fromId], points[toId], {stroke: "red", strokeWidth: 0.05});
 
-        for (let j = i + 1; j < featureCapitals.length; j++) {
-          const {cell: to} = featureCapitals[j];
+        const start = featureCapitals[fromId].cell;
+        const exit = featureCapitals[toId].cell;
 
-          const {end, pathCells} = findLandPath({start: from, exit: to});
-          if (end !== null && pathCells.length) {
-            pathCells.forEach(cellId => {
-              cellRoutes[cellId] = ROUTES.MAIN_ROAD;
-            });
-            mainRoads.push({feature: Number(key), from, to, end, cells: pathCells});
-          }
+        const segments = findLandPathSegments(cellRoutes, start, exit);
+        for (const segment of segments) {
+          segment.forEach(cellId => {
+            cellRoutes[cellId] = ROUTES.MAIN_ROAD;
+          });
+          mainRoads.push({feature: Number(key), cells: segment});
         }
-      }
+      });
     }
 
     TIME && console.timeEnd("generateMainRoads");
     return mainRoads;
   }
 
-  // find land path to a specific cell or to a closest road
-  function findLandPath({start, exit}: {start: number; exit: number}) {
-    const from: number[] = [];
-    const end = findPath();
-    if (end === null) return {end, pathCells: []};
+  function generateTrails() {
+    TIME && console.time("generateTrails");
 
-    const pathCells = restorePath(start, end, from);
-    return {end, pathCells};
+    const trails: {feature: number; cells: number[]}[] = [];
+
+    const burgsByFeature = validBurgs.reduce((acc, burg) => {
+      const {feature} = burg;
+      if (!acc[feature]) acc[feature] = [];
+      acc[feature].push(burg);
+      return acc;
+    }, {} as {[feature: string]: IBurg[]});
+
+    for (const [key, featureBurgs] of Object.entries(burgsByFeature)) {
+      const points: TPoints = featureBurgs.map(burg => [burg.x, burg.y]);
+      const urquhartEdges = calculateUrquhartEdges(points);
+      urquhartEdges.forEach(([fromId, toId]) => {
+        drawLine(points[fromId], points[toId], {strokeWidth: 0.05});
+
+        const start = featureBurgs[fromId].cell;
+        const exit = featureBurgs[toId].cell;
+
+        const segments = findLandPathSegments(cellRoutes, start, exit);
+        for (const segment of segments) {
+          segment.forEach(cellId => {
+            cellRoutes[cellId] = ROUTES.TRAIL;
+          });
+          trails.push({feature: Number(key), cells: segment});
+        }
+      });
+    }
+
+    TIME && console.timeEnd("generateTrails");
+    return trails;
+  }
+
+  // find land route segments from cell to cell
+  function findLandPathSegments(cellRoutes: Uint8Array, start: number, exit: number): number[][] {
+    const from = findPath();
+    if (!from) return [];
+
+    const pathCells = restorePath(start, exit, from);
+    const segments = getRouteSegments(pathCells, cellRoutes);
+    return segments;
 
     function findPath() {
+      const from: number[] = [];
       const cost: number[] = [];
       const queue = new FlatQueue<number>();
       queue.push(start, 0);
@@ -70,38 +107,40 @@ export function generateRoutes(burgs: TBurgs, cells: Pick<IPack["cells"], "c" |
         const priority = queue.peekValue()!;
         const next = queue.pop()!;
 
-        if (cellRoutes[next]) return next;
-
         for (const neibCellId of cells.c[next]) {
           if (cells.h[neibCellId] < 20) continue; // ignore water cells
-          const stateChangeCost = cells.state && cells.state[neibCellId] !== cells.state[next] ? 400 : 0; // trails tend to lay within the same state
+          const stateChangeCost = cells.state && cells.state[neibCellId] !== cells.state[next] ? 400 : 0; // prefer to lay within the same state
           const habitability = biomesData.habitability[cells.biome[neibCellId]];
           if (!habitability) continue; // avoid inhabitable cells (eg. lava, glacier)
           const habitedCost = habitability ? Math.max(100 - habitability, 0) : 400; // routes tend to lay within populated areas
           const heightChangeCost = Math.abs(cells.h[neibCellId] - cells.h[next]) * 10; // routes tend to avoid elevation changes
           const heightCost = cells.h[neibCellId] > 80 ? cells.h[neibCellId] : 0; // routes tend to avoid mountainous areas
           const cellCoast = 10 + stateChangeCost + habitedCost + heightChangeCost + heightCost;
-          const totalCost = priority + (cellRoutes[neibCellId] || cells.burg[neibCellId] ? cellCoast / 3 : cellCoast);
+          const totalCost = priority + (cellRoutes[neibCellId] || cells.burg[neibCellId] ? cellCoast / 2 : cellCoast);
 
           if (from[neibCellId] || totalCost >= cost[neibCellId]) continue;
           from[neibCellId] = next;
 
-          if (neibCellId === exit) return exit;
+          if (neibCellId === exit) return from;
 
           cost[neibCellId] = totalCost;
           queue.push(neibCellId, totalCost);
         }
       }
 
-      return null;
+      return null; // path is not found
     }
   }
 
   function combineRoutes() {
     const routes: TRoutes = [];
 
-    for (const {feature, from, to, end, cells} of mainRoads) {
-      routes.push({i: routes.length, type: "road", feature, from, to, end, cells});
+    for (const {feature, cells} of mainRoads) {
+      routes.push({i: routes.length, type: "road", feature, cells});
+    }
+
+    for (const {feature, cells} of trails) {
+      routes.push({i: routes.length, type: "trail", feature, cells});
     }
 
     return routes;
@@ -115,10 +154,84 @@ function restorePath(start: number, end: number, from: number[]) {
   let prev = end;
 
   while (current !== start) {
-    prev = from[current];
     cells.push(current);
+    prev = from[current];
     current = prev;
   }
 
+  cells.push(current);
+
   return cells;
 }
+
+function getRouteSegments(pathCells: number[], cellRoutes: Uint8Array) {
+  const hasRoute = (cellId: number) => cellRoutes[cellId] !== 0;
+  const noRoute = (cellId: number) => cellRoutes[cellId] === 0;
+
+  const segments: number[][] = [];
+  let segment: number[] = [];
+
+  // UC: complitely new route
+  if (pathCells.every(noRoute)) return [pathCells];
+
+  // UC: all cells already have route
+  if (pathCells.every(hasRoute)) return [];
+
+  // UC: only first and/or last cell have route
+  if (pathCells.slice(1, -1).every(noRoute)) return [pathCells];
+
+  // UC: discontinuous route
+  for (let i = 0; i < pathCells.length; i++) {
+    const cellId = pathCells[i];
+    const nextCellId = pathCells[i + 1];
+
+    const hasRoute = cellRoutes[cellId] !== 0;
+    const nextHasRoute = cellRoutes[nextCellId] !== 0;
+
+    const noConnection = !hasRoute || !nextHasRoute;
+    if (noConnection) segment.push(cellId);
+  }
+
+  return segments;
+}
+
+// Urquhart graph is obtained by removing the longest edge from each triangle in the Delaunay triangulation
+// this gives us an aproximation of a desired road network, i.e. connections between burgs
+// code from https://observablehq.com/@mbostock/urquhart-graph
+function calculateUrquhartEdges(points: TPoints) {
+  const score = (p0: number, p1: number) => dist2(points[p0], points[p1]);
+
+  const {halfedges, triangles} = Delaunator.from(points);
+  const n = triangles.length;
+
+  const removed = new Uint8Array(n);
+  const edges = [];
+
+  for (let e = 0; e < n; e += 3) {
+    const p0 = triangles[e],
+      p1 = triangles[e + 1],
+      p2 = triangles[e + 2];
+
+    const p01 = score(p0, p1),
+      p12 = score(p1, p2),
+      p20 = score(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;
+  }
+
+  for (let e = 0; e < n; ++e) {
+    if (e > halfedges[e] && !removed[e]) {
+      const t0 = triangles[e];
+      const t1 = triangles[e % 3 === 2 ? e - 2 : e + 1];
+      edges.push([t0, t1]);
+    }
+  }
+
+  return edges;
+}

src/types/pack/routes.d.ts

@@ -2,9 +2,6 @@ interface IRoute {
   i: number;
   type: "road" | "trail" | "sea";
   feature: number;
-  from: number;
-  to: number;
-  end: number;
   cells: number[];
 }
 

src/utils/debugUtils.ts

@@ -17,6 +17,17 @@ export function drawPolygon(
     .attr("stroke-width", strokeWidth);
 }
 
+export function drawLine([x1, y1]: TPoint, [x2, y2]: TPoint, {stroke = "#444", strokeWidth = 0.2} = {}) {
+  debug
+    .append("line")
+    .attr("x1", x1)
+    .attr("y1", y1)
+    .attr("x2", x2)
+    .attr("y2", y2)
+    .attr("stroke", stroke)
+    .attr("stroke-width", strokeWidth);
+}
+
 export function drawArrow([x1, y1]: TPoint, [x2, y2]: TPoint, {width = 1, color = "#444"} = {}): void {
   const angle = Math.atan2(y2 - y1, x2 - x1);
   const normal = angle + Math.PI / 2;