import earcut from 'earcut'; import { add, divide, distanceTo, normalize, subtract, normal, dot } from './src/sliceActions/helpers/vector2.js'; function lineIntersection(a1, a2, b1, b2) { // source: http://mathworld.wolfram.com/Line-LineIntersection.html const intersection = { x: ((a1.x * a2.y - a1.y * a2.x) * (b1.x - b2.x) - (a1.x - a2.x) * (b1.x * b2.y - b1.y * b2.x)) / ((a1.x - a2.x) * (b1.y - b2.y) - (a1.y - a2.y) * (b1.x - b2.x)), y: ((a1.x * a2.y - a1.y * a2.x) * (b1.y - b2.y) - (a1.y - a2.y) * (b1.x * b2.y - b1.y * b2.x)) / ((a1.x - a2.x) * (b1.y - b2.y) - (a1.y - a2.y) * (b1.x - b2.x)) }; const intersectionA = subtract(intersection, a1); const directionA = subtract(a2, a1); const normalA = normalize(directionA); const distanceA = dot(normalA, intersectionA); if (distanceA < 0 || distanceA > dot(normalA, directionA)) return false; const intersectionB = subtract(intersection, b1); const directionB = subtract(b2, b1); const normalB = normalize(directionB); const distanceB = dot(normalB, intersectionB); if (distanceB < 0 || distanceB > dot(normalB, directionB)) return false; return intersection; } function pointIsInsideConvex(point, convex, vertices) { for (let i = 0; i < convex.length; i ++) { const vertexA = vertices[convex[i]]; const vertexB = vertices[convex[(i + 1) % convex.length]]; const n = normalize(normal(subtract(vertexB, vertexA))); const p = subtract(point, vertexA); if (dot(p, n) < 0) return false; } return true; } function decompose(polygon) { const vertices = polygon.reduce((points, path) => { points.push(...path); return points; }, []); const flatVertices = vertices.reduce((points, { x, y }) => { points.push(x, y); return points; }, []); let offset = 0; const holes = polygon .map(path => offset += path.length) .slice(0, -1); const flatTrainglesIndexed = earcut(flatVertices, holes); const convexPolygons = []; for (let i = 0; i < flatTrainglesIndexed.length; i += 3) { const face = [ flatTrainglesIndexed[i], flatTrainglesIndexed[i + 1], flatTrainglesIndexed[i + 2] ]; const center = divide(face.reduce((total, point) => { if (!total) { return vertices[point]; } else { return add(total, vertices[point]); } }, null), face.length); convexPolygons.push({ center, face, connects: [] }); } for (let i = 0; i < convexPolygons.length; i ++) { for (let j = i + 1; j < convexPolygons.length; j ++) { const triangleIndexedA = convexPolygons[i]; const triangleIndexedB = convexPolygons[j]; const overlap = []; triangleIndexedA.face.map(index => { if (triangleIndexedB.face.includes(index)) overlap.push(index); }); if (overlap.length === 2) { const distance = distanceTo(convexPolygons[i].center, convexPolygons[j].center); triangleIndexedA.connects.push({ to: j, edge: overlap, distance }); triangleIndexedB.connects.push({ to: i, edge: overlap, distance }); } } } return { vertices, convexPolygons }; } function findClosestPath(convexPolygons, start, end, visited = [], path = []) { if (start === end) return []; visited = [...visited, start]; const { connects } = convexPolygons[start]; const finish = connects.find(({ to }) => to === end); if (finish) return [...path, finish]; const posibilities = []; for (const connect of connects) { if (visited.includes(connect.to)) continue; const posibility = findClosestPath(convexPolygons, connect.to, end, visited, [...path, connect]); if (posibility) posibilities.push(posibility); } if (posibilities.length === 0) { return null; } else if (posibilities.length === 1) { return posibilities[0]; } else if (posibilities.length > 1) { const distanceMap = new WeakMap(); for (const posibility of posibilities) { const distance = posibility.reduce((totalDistance, connect) => totalDistance + connect.distance, 0); distanceMap.set(posibility, distance); } return posibilities.sort((a, b) => distanceMap.get(a) - distanceMap.get(b))[0]; } } // const parse = string => parseFloat(string); // function findClosestPath(map, start, end) { // // dijkstra's algorithm // const costs = { [start]: 0 }; // const open = { [0]: [start] }; // const predecessors = {}; // // while (open) { // const keys = Object.keys(open).map(parse); // if (keys.length === 0) break; // keys.sort(); // // const [key] = keys; // const bucket = open[key]; // const node = bucket.shift(); // const currentCost = key; // const { connects } = map[node]; // // if (!bucket.length) delete open[key]; // // for (const { distance, to } of connects) { // const totalCost = distance + currentCost; // const vertexCost = costs[to]; // // if ((typeof vertexCost === 'undefined') || (vertexCost > totalCost)) { // costs[to] = totalCost; // // if (!open[totalCost]) open[totalCost] = []; // open[totalCost].push(to); // // predecessors[to] = node; // } // } // } // // if (typeof costs[end] === 'undefined') return null; // // const nodes = []; // let node = end; // while (typeof node !== 'undefined') { // nodes.push(node); // node = predecessors[node]; // } // nodes.reverse(); // // const path = []; // for (let i = 1; i < nodes.length; i ++) { // const from = nodes[i - 1]; // const to = nodes[i]; // // const connection = map[from].connects.find(connect => connect.to === to); // path.push(connection); // } // // return path; // } function containLineInPath(path, start, end, vertices) { const line = [start]; for (const { edge: [indexA, indexB] } of path) { const vertexA = vertices[indexA]; const vertexB = vertices[indexB]; const intersection = lineIntersection(start, end, vertexA, vertexB); if (!intersection) { const lastPoint = line[line.length - 1]; const distanceA = distanceTo(lastPoint, vertexA) + distanceTo(vertexA, end); const distanceB = distanceTo(lastPoint, vertexB) + distanceTo(vertexB, end); line.push(distanceA < distanceB ? vertexA : vertexB); } } line.push(end); return line; } const canvas = document.createElement('canvas'); document.body.appendChild(canvas); canvas.width = 610; canvas.height = 610; const context = canvas.getContext('2d'); context.lineJoin = 'bevel'; function circle(radius = 10, x = 0, y = 0, clockWise = true, segments = 40) { const shape = []; for (let rad = 0; rad < Math.PI * 2; rad += Math.PI * 2 / segments) { if (clockWise) { shape.push({ x: Math.cos(rad) * radius + x, y: Math.sin(rad) * radius + y }); } else { shape.push({ x: Math.cos(rad) * radius + x, y: -Math.sin(rad) * radius + y }); } } return shape; } const START = { x: 300, y: 300 }; const END = { x: 300, y: 20 }; // const CONCAVE_POLYGON = [[ // { x: 10, y: 10 }, // { x: 600, y: 10 }, // { x: 500, y: 200 }, // { x: 600, y: 600 }, // { x: 10, y: 600 } // ], [ // { x: 160, y: 120 }, // { x: 120, y: 400 }, // { x: 400, y: 400 } // ], circle(50, 300, 100, false)]; const CONCAVE_POLYGON = [circle(300, 305, 305, true, 100), circle(50, 300, 100, false)]; canvas.onmousedown = (event) => { START.x = event.offsetX; START.y = event.offsetY; compute(); }; canvas.onmousemove = (event) => { END.x = event.offsetX; END.y = event.offsetY; compute(); }; compute(); function compute() { const { convexPolygons, vertices } = decompose(CONCAVE_POLYGON); const startPolygon = convexPolygons.findIndex(({ face }) => pointIsInsideConvex(START, face, vertices)); const endPolygon = convexPolygons.findIndex(({ face }) => pointIsInsideConvex(END, face, vertices)); if (startPolygon === -1 || endPolygon === -1) return; const path = findClosestPath(convexPolygons, startPolygon, endPolygon); if (!path) return; const line = containLineInPath(path, START, END, vertices); // draw context.clearRect(0, 0, canvas.width, canvas.height); context.beginPath(); for (const shape of CONCAVE_POLYGON) { let first = true; for (const { x, y } of shape) { if (first) { context.moveTo(x, y); } else { context.lineTo(x, y); } first = false; } } context.closePath(); context.fillStyle = 'lightgray'; context.fill(); // context.fillStyle = 'black'; // context.strokeStyle = 'black'; // context.textAlign = 'center'; // context.textBaseline = 'middle'; // context.lineWidth = 1; // context.font = '14px arial'; // for (let i = 0; i < convexPolygons.length; i ++) { // const { face, center } = convexPolygons[i]; // // context.beginPath(); // for (const index of face) { // const vertex = vertices[index]; // context.lineTo(vertex.x, vertex.y); // } // context.closePath(); // context.stroke(); // // context.fillText(i, center.x, center.y); // } // if (path) { // context.beginPath(); // for (const { edge: [indexA, indexB] } of path) { // const pointA = vertices[indexA]; // const pointB = vertices[indexB]; // context.moveTo(pointA.x, pointA.y); // context.lineTo(pointB.x, pointB.y); // } // context.strokeStyle = 'blue'; // context.lineWidth = 3; // context.stroke(); // } if (line) { context.beginPath(); for (const point of line) { context.lineTo(point.x, point.y); } context.strokeStyle = 'green'; context.lineWidth = 2; context.stroke(); } context.beginPath(); context.arc(START.x, START.y, 3, 0, Math.PI * 2); context.fillStyle = 'blue'; context.fill(); context.beginPath(); context.arc(END.x, END.y, 3, 0, Math.PI * 2); context.fillStyle = 'red'; context.fill(); }