flatten-js

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<article> <pre class="prettyprint source linenums"><code>"use strict"; let IntervalTree = require('flatten-interval-tree'); module.exports = function(Flatten) { let {Polygon, Point, Segment, Arc, Circle, Line, Ray, Vector} = Flatten; let {vector} = Flatten; Flatten.Distance = class Distance { /** * Calculate distance and shortest segment between points * @param pt1 * @param pt2 * @returns {Number | Segment} - distance and shortest segment */ static point2point(pt1, pt2) { return pt1.distanceTo(pt2); } /** * Calculate distance and shortest segment between point and line * @param pt * @param line * @returns {Number | Segment} - distance and shortest segment */ static point2line(pt, line) { let closest_point = pt.projectionOn(line); let vec = vector(pt, closest_point); return [vec.length, new Segment(pt, closest_point)]; } /** * Calculate distance and shortest segment between point and circle * @param pt * @param circle * @returns {Number | Segment} - distance and shortest segment */ static point2circle(pt, circle) { let [dist2center, shortest_dist] = pt.distanceTo(circle.center); if (Flatten.Utils.EQ_0(dist2center)) { return [circle.r, new Segment(pt, circle.toArc().start)]; } else { let dist = Math.abs(dist2center - circle.r); let v = vector(circle.pc, pt).normalize().multiply(circle.r); let closest_point = circle.pc.translate(v); return [dist, new Segment(pt, closest_point)]; } } /** * Calculate distance and shortest segment between point and segment * @param pt * @param segment * @returns {Number | Segment} - distance and shortest segment */ static point2segment(pt, segment) { /* Degenerated case of zero-length segment */ if (segment.start.equalTo(segment.end)) { return Distance.point2point(pt, segment.start); } let v_seg = new Flatten.Vector(segment.start, segment.end); let v_ps2pt = new Flatten.Vector(segment.start, pt); let v_pe2pt = new Flatten.Vector(segment.end, pt); let start_sp = v_seg.dot(v_ps2pt); /* dot product v_seg * v_ps2pt */ let end_sp = -v_seg.dot(v_pe2pt); /* minus dot product v_seg * v_pe2pt */ let dist; let closest_point; if (Flatten.Utils.GE(start_sp, 0) && Flatten.Utils.GE(end_sp, 0)) { /* point inside segment scope */ let v_unit = segment.tangentInStart(); // new Flatten.Vector(v_seg.x / this.length, v_seg.y / this.length); /* unit vector ||v_unit|| = 1 */ dist = Math.abs(v_unit.cross(v_ps2pt)); /* dist = abs(v_unit x v_ps2pt) */ closest_point = segment.start.translate(v_unit.multiply(v_unit.dot(v_ps2pt))); return [dist, new Segment(pt, closest_point)]; } else if (start_sp < 0) { /* point is out of scope closer to ps */ return pt.distanceTo(segment.start); } else { /* point is out of scope closer to pe */ return pt.distanceTo(segment.end); } }; /** * Calculate distance and shortest segment between point and arc * @param pt * @param arc * @returns {Number | Segment} - distance and shortest segment */ static point2arc(pt, arc) { let circle = new Flatten.Circle(arc.pc, arc.r); let dist_and_segment = []; let dist, shortest_segment; [dist, shortest_segment] = Distance.point2circle(pt, circle); if (shortest_segment.end.on(arc)) { dist_and_segment.push(Distance.point2circle(pt, circle)); } dist_and_segment.push( Distance.point2point(pt, arc.start) ); dist_and_segment.push( Distance.point2point(pt, arc.end) ); Distance.sort(dist_and_segment); return dist_and_segment[0]; } /** * Calculate distance and shortest segment between segment and line * @param seg * @param line * @returns {Number | Segment} */ static segment2line(seg, line) { let ip = seg.intersect(line); if (ip.length > 0) { return [0, new Segment(ip[0],ip[0])]; // distance = 0, closest point is the first point } let dist_and_segment = []; dist_and_segment.push(Distance.point2line(seg.start, line)); dist_and_segment.push(Distance.point2line(seg.end, line)); Distance.sort( dist_and_segment ); return dist_and_segment[0]; } /** * Calculate distance and shortest segment between two segments * @param seg1 * @param seg2 * @returns {Number | Segment} - distance and shortest segment */ static segment2segment(seg1, seg2) { let ip = Segment.intersectSegment2Segment(seg1, seg2); if (ip.length > 0) { return [0, new Segment(ip[0],ip[0])]; // distance = 0, closest point is the first point } // Seg1 and seg2 not intersected let dist_and_segment = []; dist_and_segment.push(Distance.point2segment(seg2.start, seg1)); dist_and_segment.push(Distance.point2segment(seg2.end, seg1)); dist_and_segment.push(Distance.point2segment(seg1.start, seg2)); dist_and_segment.push(Distance.point2segment(seg1.end, seg2)); Distance.sort( dist_and_segment ); return dist_and_segment[0]; } /** * Calculate distance and shortest segment between segment and circle * @param seg * @param circle * @returns {Number | Segment} - distance and shortest segment */ static segment2circle(seg, circle) { /* Case 1 Segment and circle intersected. Return the first point and zero distance */ let ip = seg.intersect(circle); if (ip.length > 0) { return [0, new Segment(ip[0], ip[0])]; } // No intersection between segment and circle /* Case 2. Distance to projection of center point to line bigger than radius * And projection point belong to segment * Then measure again distance from projection to circle and return it */ let line = new Flatten.Line(seg.ps, seg.pe); let [dist, shortest_segment] = Distance.point2line(circle.center, line); if (Flatten.Utils.GE(dist, circle.r) && shortest_segment.end.on(seg)) { return Distance.point2circle(shortest_segment.end, circle); } /* Case 3. Otherwise closest point is one of the end points of the segment */ else { let [dist_from_start, shortest_segment_from_start] = Distance.point2circle(seg.start, circle); let [dist_from_end, shortest_segment_from_end] = Distance.point2circle(seg.end, circle); return Flatten.Utils.LT(dist_from_start, dist_from_end) ? [dist_from_start, shortest_segment_from_start] : [dist_from_end, shortest_segment_from_end]; } } /** * Calculate distance and shortest segment between segment and arc * @param seg * @param arc * @returns {Number | Segment} - distance and shortest segment */ static segment2arc(seg, arc) { /* Case 1 Segment and arc intersected. Return the first point and zero distance */ let ip = seg.intersect(arc); if (ip.length > 0) { return [0, new Segment(ip[0], ip[0])]; } // No intersection between segment and arc let line = new Flatten.Line(seg.ps, seg.pe); let circle = new Flatten.Circle(arc.pc, arc.r); /* Case 2. Distance to projection of center point to line bigger than radius AND * projection point belongs to segment AND * distance from projection point to circle belongs to arc => * return this distance from projection to circle */ let [dist_from_center, shortest_segment_from_center] = Distance.point2line(circle.center, line); if (Flatten.Utils.GE(dist_from_center, circle.r) && shortest_segment_from_center.end.on(seg)) { let [dist_from_projection, shortest_segment_from_projection] = Distance.point2circle(shortest_segment_from_center.end, circle); if (shortest_segment_from_projection.end.on(arc)) { return [dist_from_projection, shortest_segment_from_projection]; } } /* Case 3. Otherwise closest point is one of the end points of the segment */ let dist_and_segment = []; dist_and_segment.push(Distance.point2arc(seg.start, arc)); dist_and_segment.push(Distance.point2arc(seg.end, arc)); let dist_tmp, segment_tmp; [dist_tmp, segment_tmp] = Distance.point2segment(arc.start, seg); dist_and_segment.push([dist_tmp, segment_tmp.reverse()]); [dist_tmp, segment_tmp] = Distance.point2segment(arc.end, seg); dist_and_segment.push([dist_tmp, segment_tmp.reverse()]); Distance.sort(dist_and_segment); return dist_and_segment[0]; } /** * Calculate distance and shortest segment between two circles * @param circle1 * @param circle2 * @returns {Number | Segment} - distance and shortest segment */ static circle2circle(circle1, circle2) { let ip = circle1.intersect(circle2); if (ip.length > 0) { return [0, new Segment(ip[0], ip[0])]; } // Case 1. Concentric circles. Convert to arcs and take distance between two arc starts if (circle1.center.equalTo(circle2.center)) { let arc1 = circle1.toArc(); let arc2 = circle2.toArc(); return Distance.point2point(arc1.start, arc2.start); } else { // Case 2. Not concentric circles let line = new Line(circle1.center, circle2.center); let ip1 = line.intersect(circle1); let ip2 = line.intersect(circle2); let dist_and_segment = []; dist_and_segment.push(Distance.point2point(ip1[0], ip2[0])); dist_and_segment.push(Distance.point2point(ip1[0], ip2[1])); dist_and_segment.push(Distance.point2point(ip1[1], ip2[0])); dist_and_segment.push(Distance.point2point(ip1[1], ip2[1])); Distance.sort(dist_and_segment); return dist_and_segment[0]; } } /** * Calculate distance and shortest segment between two circles * @param circle * @param line * @returns {Number | Segment} - distance and shortest segment */ static circle2line(circle, line) { let ip = circle.intersect(line); if (ip.length > 0) { return [0, new Segment(ip[0], ip[0])]; } let [dist_from_center, shortest_segment_from_center] = Distance.point2line(circle.center, line); let [dist, shortest_segment] = Distance.point2circle(shortest_segment_from_center.end, circle); shortest_segment = shortest_segment.reverse(); return [dist, shortest_segment]; } /** * Calculate distance and shortest segment between arc and line * @param arc * @param line * @returns {Number | Segment} - distance and shortest segment */ static arc2line(arc, line) { /* Case 1 Line and arc intersected. Return the first point and zero distance */ let ip = line.intersect(arc); if (ip.length > 0) { return [0, new Segment(ip[0], ip[0])]; } let circle = new Flatten.Circle(arc.center, arc.r); /* Case 2. Distance to projection of center point to line bigger than radius AND * projection point belongs to segment AND * distance from projection point to circle belongs to arc => * return this distance from projection to circle */ let [dist_from_center, shortest_segment_from_center] = Distance.point2line(circle.center, line); if (Flatten.Utils.GE(dist_from_center, circle.r)) { let [dist_from_projection, shortest_segment_from_projection] = Distance.point2circle(shortest_segment_from_center.end, circle); if (shortest_segment_from_projection.end.on(arc)) { return [dist_from_projection, shortest_segment_from_projection]; } } else { let dist_and_segment = []; dist_and_segment.push( Distance.point2line(arc.start, line) ); dist_and_segment.push( Distance.point2line(arc.end, line) ); Distance.sort(dist_and_segment); return dist_and_segment[0]; } } /** * Calculate distance and shortest segment between arc and circle * @param arc * @param circle2 * @returns {Number | Segment} - distance and shortest segment */ static arc2circle(arc, circle2) { let ip = arc.intersect(circle2); if (ip.length > 0) { return [0, new Segment(ip[0], ip[0])]; } let circle1 = new Flatten.Circle(arc.center, arc.r); let [dist, shortest_segment] = Distance.circle2circle(circle1, circle2); if (shortest_segment.start.on(arc)) { return [dist, shortest_segment]; } else { let dist_and_segment = []; dist_and_segment.push(Distance.point2circle(arc.start, circle2)); dist_and_segment.push(Distance.point2circle(arc.end, circle2)); Distance.sort(dist_and_segment); return dist_and_segment[0]; } } /** * Calculate distance and shortest segment between two arcs * @param arc1 * @param arc2 * @returns {Number | Segment} - distance and shortest segment */ static arc2arc(arc1, arc2) { let ip = arc1.intersect(arc2); if (ip.length > 0) { return [0, new Segment(ip[0], ip[0])]; } let circle1 = new Flatten.Circle(arc1.center, arc1.r); let circle2 = new Flatten.Circle(arc2.center, arc2.r); let [dist, shortest_segment] = Distance.circle2circle(circle1, circle2); if (shortest_segment.start.on(arc1) && shortest_segment.end.on(arc2)) { return [dist, shortest_segment]; } else { let dist_and_segment = []; let dist_tmp, segment_tmp; [dist_tmp, segment_tmp] = Distance.point2arc(arc1.start, arc2); if (segment_tmp.end.on(arc2)) { dist_and_segment.push([dist_tmp, segment_tmp]); } [dist_tmp, segment_tmp] = Distance.point2arc(arc1.end, arc2); if (segment_tmp.end.on(arc2)) { dist_and_segment.push([dist_tmp, segment_tmp]); } [dist_tmp, segment_tmp] = Distance.point2arc(arc2.start, arc1); if (segment_tmp.end.on(arc1)) { dist_and_segment.push([dist_tmp, segment_tmp.reverse()]); } [dist_tmp, segment_tmp] = Distance.point2arc(arc2.end, arc1); if (segment_tmp.end.on(arc1)) { dist_and_segment.push([dist_tmp, segment_tmp.reverse()]); } [dist_tmp, segment_tmp] = Distance.point2point(arc1.start, arc2.start); dist_and_segment.push([dist_tmp, segment_tmp]); [dist_tmp, segment_tmp] = Distance.point2point(arc1.start, arc2.end); dist_and_segment.push([dist_tmp, segment_tmp]); [dist_tmp, segment_tmp] = Distance.point2point(arc1.end, arc2.start); dist_and_segment.push([dist_tmp, segment_tmp]); [dist_tmp, segment_tmp] = Distance.point2point(arc1.end, arc2.end); dist_and_segment.push([dist_tmp, segment_tmp]); Distance.sort(dist_and_segment); return dist_and_segment[0]; } } /** * Calculate distance and shortest segment between point and polygon * @param point * @param polygon * @returns {Number | Segment} - distance and shortest segment */ static point2polygon(point, polygon) { let min_dist_and_segment = [Number.POSITIVE_INFINITY, new Segment()]; for (let edge of polygon.edges) { let [dist, shortest_segment] = (edge.shape instanceof Segment) ? Distance.point2segment(point, edge.shape) : Distance.point2arc(point, edge.shape); if (Flatten.Utils.LT(dist, min_dist_and_segment[0])) { min_dist_and_segment = [dist, shortest_segment]; } } return min_dist_and_segment; } static shape2polygon(shape, polygon) { let min_dist_and_segment = [Number.POSITIVE_INFINITY, new Segment()]; for (let edge of polygon.edges) { let [dist, shortest_segment] = shape.distanceTo(edge.shape); if (Flatten.Utils.LT(dist, min_dist_and_segment[0])) { min_dist_and_segment = [dist, shortest_segment]; } } return min_dist_and_segment; } /* static arc2polygon(arc, polygon) { let ip = arc.intersect(polygon); if (ip.length > 0) { return [0, new Segment(ip[0], ip[0])]; } let min_dist_and_segment = [Number.POSITIVE_INFINITY, new Segment()]; for (let edge of polygon.edges) { let [dist, shortest_segment] = arc.distanceTo(edge.shape); if (Flatten.Utils.LT(dist, min_dist_and_segment[0])) { min_dist_and_segment = [dist, shortest_segment]; } } return min_dist_and_segment; } static line2polygon(line, polygon) { let ip = line.intersect(polygon); if (ip.length > 0) { return [0, new Segment(ip[0], ip[0])]; } let min_dist_and_segment = [Number.POSITIVE_INFINITY, new Segment()]; for (let edge of polygon.edges) { let [dist, shortest_segment] = line.distanceTo(edge.shape); if (Flatten.Utils.LT(dist, min_dist_and_segment[0])) { min_dist_and_segment = [dist, shortest_segment]; } } return min_dist_and_segment; } static circle2polygon(circle, polygon) { let ip = circle.intersect(polygon); if (ip.length > 0) { return [0, new Segment(ip[0], ip[0])]; } let min_dist_and_segment = [Number.POSITIVE_INFINITY, new Segment()]; for (let edge of polygon.edges) { let [dist, shortest_segment] = circle.distanceTo(edge.shape); if (Flatten.Utils.LT(dist, min_dist_and_segment[0])) { min_dist_and_segment = [dist, shortest_segment]; } } return min_dist_and_segment; } */ /** * Calculate distance and shortest segment between two polygons * @param polygon1 * @param polygon2 * @returns {Number | Segment} - distance and shortest segment */ static polygon2polygon(polygon1, polygon2) { let min_dist_and_segment = [Number.POSITIVE_INFINITY, new Flatten.Segment()]; for (let edge1 of polygon1.edges) { for (let edge2 of polygon2.edges) { let [dist, shortest_segment] = edge1.shape.distanceTo(edge2.shape); if (Flatten.Utils.LT(dist, min_dist_and_segment[0])) { min_dist_and_segment = [dist, shortest_segment]; } } } return min_dist_and_segment; } /** * Returns [mindist, maxdist] array of squared minimal and maximal distance between boxes * Minimal distance by x is * (box2.xmin - box1.xmax), if box1 is left to box2 * (box1.xmin - box2.xmax), if box2 is left to box1 * 0, if box1 and box2 are intersected by x * Minimal distance by y is defined in the same way * * Maximal distance is estimated as a sum of squared dimensions of the merged box * * @param box1 * @param box2 * @returns {Number | Number} - minimal and maximal distance */ static box2box_minmax(box1, box2) { let mindist_x = Math.max( Math.max(box1.xmin - box2.xmax, 0), Math.max(box2.xmin - box1.xmax, 0) ); let mindist_y = Math.max( Math.max(box1.ymin - box2.ymax, 0), Math.max(box2.ymin - box1.ymax, 0) ); let mindist = mindist_x*mindist_x + mindist_y*mindist_y; let box = box1.merge(box2); let dx = box.xmax - box.xmin; let dy = box.ymax - box.ymin; let maxdist = dx*dx + dy*dy; return [mindist, maxdist]; } static minmax_tree_process_level(shape, level, min_stop, tree) { // Calculate minmax distance to each shape in current level // Insert result into the interval tree for further processing // update min_stop with maxdist, it will be the new stop distance let mindist, maxdist; for (let node of level) { // [mindist, maxdist] = Distance.box2box_minmax(shape.box, node.max); // if (Flatten.Utils.GT(mindist, min_stop)) // continue; // Estimate min-max dist to the shape stored in the node.item, using node.item.key which is shape's box [mindist, maxdist] = Distance.box2box_minmax(shape.box, node.item.key); if (node.item.value instanceof Flatten.Edge) { tree.insert([mindist, maxdist], node.item.value.shape); } else { tree.insert([mindist, maxdist], node.item.value); } if (Flatten.Utils.LT(maxdist, min_stop)) { min_stop = maxdist; // this will be the new distance estimation } } if (level.length === 0) return min_stop; // Calculate new level from left and right children of the current let new_level_left = level.map(node => node.left.isNil() ? undefined : node.left ).filter(node => node !== undefined); let new_level_right = level.map(node => node.right.isNil() ? undefined : node.right).filter(node => node !== undefined); // Merge left and right subtrees and leave only relevant subtrees let new_level = [...new_level_left, ...new_level_right].filter( node => { // Node subtree quick reject, node.max is a subtree box let [mindist, maxdist] = Distance.box2box_minmax(shape.box, node.max); return (Flatten.Utils.LE(mindist, min_stop)); }); min_stop = Distance.minmax_tree_process_level(shape, new_level, min_stop, tree); return min_stop; } /** * Calculates sorted tree of [mindist, maxdist] intervals between query shape * and shapes of the planar set. * @param shape * @param set */ static minmax_tree(shape, set, min_stop) { let tree = new IntervalTree(); let level = [set.index.root]; let squared_min_stop = min_stop < Number.POSITIVE_INFINITY ? min_stop*min_stop : Number.POSITIVE_INFINITY; squared_min_stop = Distance.minmax_tree_process_level(shape, level, squared_min_stop, tree); return tree; }