Index: ps/trunk/binaries/data/mods/public/maps/random/rmgen/math.js =================================================================== --- ps/trunk/binaries/data/mods/public/maps/random/rmgen/math.js (revision 22027) +++ ps/trunk/binaries/data/mods/public/maps/random/rmgen/math.js (revision 22028) @@ -1,175 +1,177 @@ const g_TileVertices = deepfreeze([ new Vector2D(0, 0), new Vector2D(0, 1), new Vector2D(1, 0), new Vector2D(1, 1) ]); const g_AdjacentCoordinates = deepfreeze([ new Vector2D(1, 0), new Vector2D(1, 1), new Vector2D(0, 1), new Vector2D(-1, 1), new Vector2D(-1, 0), new Vector2D(-1, -1), new Vector2D(0, -1), new Vector2D(1, -1) ]); function diskArea(radius) { return Math.PI * Math.square(radius); } /** * Returns the angle of the vector between point 1 and point 2. * The angle is counterclockwise from the positive x axis. */ function getAngle(x1, z1, x2, z2) { return Math.atan2(z2 - z1, x2 - x1); } /** * Get pointCount points equidistantly located on a circle. * @param {Vector2D} center */ function distributePointsOnCircle(pointCount, startAngle, radius, center) { return distributePointsOnCircularSegment(pointCount, 2 * Math.PI * (pointCount - 1) / pointCount, startAngle, radius, center); } /** * Get pointCount points equidistantly located on a circular segment, including both endpoints. */ function distributePointsOnCircularSegment(pointCount, maxAngle, startAngle, radius, center) { let points = []; let angle = []; pointCount = Math.round(pointCount); for (let i = 0; i < pointCount; ++i) { angle[i] = startAngle + maxAngle * i / Math.max(1, pointCount - 1); points[i] = Vector2D.add(center, new Vector2D(radius, 0).rotate(-angle[i])); } return [points, angle]; } /** * Returns the shortest distance from a point to a line. * The sign of the return value determines the direction! * * @param {Vector2D} - lineStart, lineEnd, point */ function distanceOfPointFromLine(lineStart, lineEnd, point) { // Since the cross product is the area of the parallelogram with the vectors for sides and // one of the two vectors having length one, that area equals the distance between the points. return Vector2D.sub(lineStart, lineEnd).normalize().cross(Vector2D.sub(point, lineEnd)); } /** * Returns whether the two lines of the given width going through the given Vector2D intersect. */ function testLineIntersection(start1, end1, start2, end2, width) { let start1end1 = Vector2D.sub(start1, end1); let start2end2 = Vector2D.sub(start2, end2); let start1start2 = Vector2D.sub(start1, start2); return ( Math.abs(distanceOfPointFromLine(start1, end1, start2)) < width || Math.abs(distanceOfPointFromLine(start1, end1, end2)) < width || Math.abs(distanceOfPointFromLine(start2, end2, start1)) < width || Math.abs(distanceOfPointFromLine(start2, end2, end1)) < width || start1end1.cross(start1start2) * start1end1.cross(Vector2D.sub(start1, end2)) <= 0 && start2end2.cross(start1start2) * start2end2.cross(Vector2D.sub(start2, end1)) >= 0); } /** * Returns the topleft and bottomright coordinate of the given two points. */ function getBoundingBox(points) { let min = points[0].clone(); let max = points[0].clone(); for (let point of points) { min.set(Math.min(min.x, point.x), Math.min(min.y, point.y)); max.set(Math.max(max.x, point.x), Math.max(max.y, point.y)); } return { "min": min, "max": max }; } function getPointsInBoundingBox(boundingBox) { let points = []; for (let x = boundingBox.min.x; x <= boundingBox.max.x; ++x) for (let y = boundingBox.min.y; y <= boundingBox.max.y; ++y) points.push(new Vector2D(x, y)); return points; } /** - * Sorts the given (x, y) points so that the distance between neighboring points becomes minimal (similar to the traveling salesman problem). + * Get the order of the given points to get the shortest closed path (similar to the traveling salesman problem). + * @param {Vectro2D[]} points - Points the path should go through + * @returns {number[]} Ordered indices, same length as points */ function sortPointsShortestCycle(points) { let order = []; let distances = []; if (points.length <= 3) { for (let i = 0; i < points.length; ++i) order.push(i); return order; } // Just add the first 3 points let pointsToAdd = points.map(p => p.clone()); for (let i = 0; i < 3; ++i) { order.push(i); - pointsToAdd.shift(i); + pointsToAdd.shift(); if (i) - distances.push(Math.euclidDistance2D(points[order[i]].x, points[order[i]].y, points[order[i - 1]].x, points[order[i - 1]].y)); + distances.push(points[order[i]].distanceTo(points[order[i - 1]])); } distances.push(points[order[0]].distanceTo(points[order[order.length - 1]])); // Add remaining points so the path lengthens the least let numPointsToAdd = pointsToAdd.length; for (let i = 0; i < numPointsToAdd; ++i) { let indexToAddTo; let minEnlengthen = Infinity; let minDist1 = 0; let minDist2 = 0; for (let k = 0; k < order.length; ++k) { let dist1 = pointsToAdd[0].distanceTo(points[order[k]]); let dist2 = pointsToAdd[0].distanceTo(points[order[(k + 1) % order.length]]); let enlengthen = dist1 + dist2 - distances[k]; if (enlengthen < minEnlengthen) { indexToAddTo = k; minEnlengthen = enlengthen; minDist1 = dist1; minDist2 = dist2; } } order.splice(indexToAddTo + 1, 0, i + 3); distances.splice(indexToAddTo, 1, minDist1, minDist2); pointsToAdd.shift(); } return order; }