2f:T471,## Requirements: - Lanes should be rectangles along road (or triangles / trapezoid if width changes?) - (***new***) Lanes should not enter the overall crossing area - Corner geometry should be compact - Corner geometry should not introduce angles steeper than corner angle - Corner polygon should not be self-intersecting - Lane should not overlap other lanes in crossing area - Adjacent lanes should stay adjacent through corner - Adjacent lanes should not overlap or leave a gap - Corner polygon should not be narrower than the narrower track - Geometry should change *continuous* with parameters (no jumps at certain points), including addition of ways/lanes ## Assumptions: - Streets do not intersect at an angle below cutoff (45° or 30°) - Streets at an angle > 180-45° are a *continuation* (not sure if this is relevant) - Lanes have different priorities (by default and per intersection / street) - Per-lane assumptions (e.g. parking does not continue through bends) - street line is aligned with the center of the overall road width (see questions) ## Questions: - map middle of overall road, or anchor e.g. on car lanes?30:Tbed,map3 = html``31:T16e7,corner_geometry4 = { let l1Pos1 = offsets[0] let l1Pos2 = offsets[0] + widths[0]; let l2Pos1 = offsets[1] let l2Pos2 = offsets[1] + widths[1]; let leftBend = cornerAngle <= 0; let rightBend = !leftBend; // check if l1 begins to the left of l2 - the special case where the lines are overlapping is dealt later on. let l1PosOuter = (l1Pos1 < l2Pos1) ? l1Pos1 : l1Pos2; let l1PosInner = (l1Pos1 < l2Pos1) ? l1Pos2 : l1Pos1; let l2PosOuter = (l1Pos1 < l2Pos1) ? l2Pos2 : l2Pos1; let l2PosInner = (l1Pos1 < l2Pos1) ? l2Pos1 : l2Pos2; let bendTowards = (leftBend != (l1Pos1 < l2Pos1)); let linesFullyOverlap = ((l1Pos1 < l2Pos1 && l1Pos2 > l2Pos2) || (l2Pos1 < l1Pos1 && l2Pos2 > l1Pos2)); let minWidth = Math.min(widths[0], widths[1]); let maxWidth = Math.max(widths[0], widths[1]); let angleTowards2 = (l1Pos1 < l2Pos1) != (cornerAngle < 0) let outerStartL1 = add(points[0], mult(normals[0],l1PosOuter)); let innerStartL1 = add(points[0], mult(normals[0],l1PosInner)); let outerEndL1 = add(points[1], mult(normals[0], l1PosOuter), mult(units[0], -margin2)); let innerEndL1 = add(points[1], mult(normals[0], l1PosInner), mult(units[0], -margin2)); let innerStartL2 = add(points[1], mult(normals[1], l2PosInner), mult(units[1], margin2)); let outerStartL2 = add(points[1], mult(normals[1], l2PosOuter), mult(units[1], margin2)); let innerEndL2 = add(points[2], mult(normals[1], l2PosInner)); let outerEndL2 = add(points[2], mult(normals[1], l2PosOuter)); let laneIntersectionPoints = [ intersect(outerEndL1, units[0], innerStartL2, units[1]), intersect(innerEndL1, units[0], innerStartL2, units[1]), intersect(innerEndL1, units[0], outerStartL2, units[1]), intersect(outerEndL1, units[0], outerStartL2, units[1]), ]; let geometry = { // modeled as polygons extensionPoly1: null, extensionPoly2: null, bendPoly1: null, // if lane gets only narrower, use only this (?) bendPoly2: null, crossingPoly: null, // modeled as lines extensionLine1: null, extensionLine2: null, bendPoint1: null, // if lane gets only narrower, use only this (?) bendPoint2: null, crossingLine: null, // legacy polygon: null }; // store 2 boundary lines separately let poly = [ [ outerEndL1, innerStartL2, ], [ outerStartL2, innerEndL1, ] ]; let outerIntersectionDistOnL1 = intersect_dist(outerStartL1, units[0], innerStartL2, units[1]); let innerIntersectionDistOnL1 = intersect_dist(innerStartL1, units[0], outerStartL2, units[1]); let outerIntersectionDistOnL2 = intersect_dist(outerStartL2, units[1], innerStartL1, units[0]); let innerIntersectionDistOnL2 = intersect_dist(innerStartL2, units[1], innerStartL1, units[0]); debugger; let outerCornerL1 = (leftBend || outerIntersectionDistOnL1 < lengths[0]-margin2) ? outerEndL1 : laneIntersectionPoints[0]; let tangentsL2 = tangentPoints(outerStartL2, minWidth, outerCornerL1); // choose tangent point closest to inner end point of lane let tDistances = tangentsL2.map(t => dist(t, innerEndL2)); let tangentPointL2 = (tDistances[1] > tDistances[0]) ? tangentsL2[0] : tangentsL2[1]; let crossingUnit = unit(sub(tangentPointL2, outerCornerL1)); let crossingNormal = normal(crossingUnit); let tangentsL1 = tangentPoints(outerCornerL1, minWidth, outerStartL2); // choose tangent point closest to inner start point of lane let startPoint = add(points[0], mult(normals[0], l1PosInner)); tDistances = tangentsL1.map(t => dist(t, innerStartL1)); let tangentPointL1 = (tDistances[1] > tDistances[0]) ? tangentsL1[0] : tangentsL1[1]; // intersect with outer lane to get point on edge of lane let bendInnerL2 = intersectLinesByPoints(outerEndL1, tangentPointL2, innerStartL2, innerEndL2); let bendOuterL2 = intersect(outerStartL2,units[1],bendInnerL2,normals[1]); let bendOuterL2Crossing = intersect(outerStartL2, crossingUnit, bendInnerL2, crossingNormal); if (!bendTowards || outerIntersectionDistOnL1 < lengths[0] - margin2) { //leftBend || poly[0][1] = bendInnerL2; // bend points fully within L2 geom? if (dist(outerEndL2, bendOuterL2) < lengths[1] - margin2) { geometry.bendPoly2 = [bendInnerL2, bendOuterL2, outerStartL2, bendOuterL2Crossing]; } else { geometry.bendPoly2 = [bendInnerL2, innerStartL2, outerStartL2, bendOuterL2Crossing]; } } let bendInnerL1 = intersectLinesByPoints(outerStartL2, tangentPointL1, innerStartL1, innerEndL1); let bendOuterL1 = intersect(outerEndL1, units[0], bendInnerL1, normals[0]); let bendOuterL1Crossing = intersect(outerEndL1, crossingUnit, bendInnerL1, crossingNormal); if (!bendTowards || outerIntersectionDistOnL1 < lengths[0]-margin2) { // && (!leftBend || innerIntersectionDistOnL2 > 0) poly[1][1] = bendInnerL1; // bend points fully within L1 geom if (dist(outerStartL1, bendOuterL1) < lengths[0] - margin2) { geometry.bendPoly1 = [bendInnerL1, bendOuterL1, outerEndL1, bendOuterL1Crossing]; } else { geometry.bendPoly1 = [bendInnerL1, innerEndL1, outerEndL1, bendOuterL1Crossing]; } } // check if intersection is after l1 and before l2 -> add intersection point if (outerIntersectionDistOnL1 > lengths[0]-margin2 && outerIntersectionDistOnL2 < margin2) { // add corner vertex to polygon poly[0].splice(1, 0, add(outerStartL1, mult(units[0], outerIntersectionDistOnL1))); } // again for other side of lines if (innerIntersectionDistOnL1 > lengths[0]-margin2 && outerIntersectionDistOnL2 < margin2) { // add corner vertex to polygon poly[1].splice(1, 0, add(innerStartL1, mult(units[0], innerIntersectionDistOnL1))); } // legacy //geometry.bendPoly1 = poly; geometry.polygon = poly; return geometry; }32:Ta39,map = html``33:T1247,corner_polygon3 = { let l1Pos1 = offsets[0] let l1Pos2 = offsets[0] + widths[0]; let l2Pos1 = offsets[1] let l2Pos2 = offsets[1] + widths[1]; let leftBend = cornerAngle <= 0; // check if l1 begins to the left of l2 - the special case where the lines are overlapping is dealt later on. let l1PosOuter = (l1Pos1 < l2Pos1) ? l1Pos1 : l1Pos2; let l1PosInner = (l1Pos1 < l2Pos1) ? l1Pos2 : l1Pos1; let l2PosOuter = (l1Pos1 < l2Pos1) ? l2Pos2 : l2Pos1; let l2PosInner = (l1Pos1 < l2Pos1) ? l2Pos1 : l2Pos2; let linesFullyOverlap = ((l1Pos1 < l2Pos1 && l1Pos2 > l2Pos2) || (l2Pos1 < l1Pos1 && l2Pos2 > l1Pos2)); let minWidth = Math.min(widths[0], widths[1]); let maxWidth = Math.max(widths[0], widths[1]); let angleTowards2 = (l1Pos1 < l2Pos1) != (cornerAngle < 0) let innerStartL1 = points[0]; let outerStartL1 = add(points[0], mult(normals[0],offsets[0])); let outerEndL1 = add(points[1], mult(normals[0], l1PosOuter), mult(units[0], -margin2)); let innerEndL1 = add(points[1], mult(normals[0], l1PosInner), mult(units[0], -margin2)); let innerStartL2 = add(points[1], mult(normals[1], l2PosInner), mult(units[1], margin2)); let innerEndL2 = add(innerStartL2, mult(units[1], lengths[1])); let outerStartL2 = add(points[1], mult(normals[1], l2PosOuter), mult(units[1], margin2)); let laneIntersectionPoints = [ intersect(outerEndL1, units[0], innerStartL2, units[1]), intersect(innerEndL1, units[0], innerStartL2, units[1]), intersect(innerEndL1, units[0], outerStartL2, units[1]), intersect(outerEndL1, units[0], outerStartL2, units[1]), ]; // store 2 boundary lines separately let poly = [ [ outerEndL1, // outer end l1 innerStartL2, // inner start l2 ], [ outerStartL2, // outer start l2 innerEndL1, // inner end l1 ] ]; let l2EndPointInner = add(points[1], mult(normals[1], l2PosInner), mult(units[1], lengths[1])); let outerIntersectionDistOnL1 = intersect_dist(outerStartL1, units[0], innerStartL2, units[1]); let innerIntersectionDistOnL1 = intersect_dist(outerStartL1, units[0], outerStartL2, units[1]); let outerIntersectionDistOnL2 = intersect_dist(innerStartL2, units[1], outerStartL1, units[0]); let innerIntersectionDistOnL2 = intersect_dist(innerStartL2, units[1], innerStartL1, units[0]); debugger; let outerCornerL1 = (leftBend || outerIntersectionDistOnL1 < lengths[0]-margin2) ? outerEndL1 : laneIntersectionPoints[0]; let tangentsOuter = tangentPoints(outerStartL2, minWidth, outerCornerL1); // choose tangent point closest to inner end point of lane let tDistances = tangentsOuter.map(t => dist(t, innerEndL2)); let tangentPointOuter = (tDistances[1] > tDistances[0]) ? tangentsOuter[0] : tangentsOuter[1]; // intersect with outer lane to get point on edge of lane let crossingIntersectionL2 = intersectLinesByPoints(outerEndL1, tangentPointOuter, innerStartL2, innerEndL2); if (leftBend || outerIntersectionDistOnL1 < lengths[0] - margin2) { poly[0][1] = crossingIntersectionL2; } let tangentsInner = tangentPoints(outerCornerL1, minWidth, outerStartL2); // choose tangent point closest to inner start point of lane let startPoint = add(points[0], mult(normals[0], l1PosInner)); tDistances = tangentsInner.map(t => dist(t, innerStartL1)); let tangentPointInner = (tDistances[1] > tDistances[0]) ? tangentsInner[0] : tangentsInner[1]; let crossingIntersectionL1 = intersectLinesByPoints(outerStartL2, tangentPointInner, innerStartL1, innerEndL1); let crossingIntersectionDistanceL1 = intersect_dist(innerStartL1, units[0], outerStartL2, sub(tangentPointInner, outerStartL2)); // check for "overbend" to the left if (crossingIntersectionDistanceL1 < lengths[0]-margin2 && (!leftBend || innerIntersectionDistOnL2 > 0)) { poly[1][1] = crossingIntersectionL1; } // check if intersection is after l1 and before l2 -> add intersection point //let innerStartL2 = add(points[1], mult(normals[1],offsets[1])); if (outerIntersectionDistOnL1 > lengths[0]-margin2 && outerIntersectionDistOnL2 < margin2) { // add corner vertex to polygon poly[0].splice(1, 0, add(outerStartL1, mult(units[0], outerIntersectionDistOnL1))); } // again for other side of lines let s1 = add(points[0], mult(normals[0], offsets[0]+widths[0])); let s2 = add(points[1], mult(normals[1], offsets[1]+widths[1])); let d1 = intersect_dist(s1, units[0], s2, units[1]); let d2 = intersect_dist(s2, units[1], s1, units[0]); if (d1 > lengths[0]-margin2 && d2 < margin2) { // add corner vertex to polygon poly[1].splice(1, 0, add(s1, mult(units[0], d1))); } return poly; }34:Ta09,map2 = html``35:T567,corner_polygon2 = { // store 2 boundary lines separately let poly = [ [ add(points[1], mult(normals[0], offsets[0]), mult(units[0], -margin2)), // left end l1 add(points[1], mult(normals[1], offsets[1]), mult(units[1], margin2)), // left start l2 ], [ add(points[1], mult(normals[1], offsets[1]+widths[1]), mult(units[1], margin2)),// right end l1 add(points[1], mult(normals[0], offsets[0]+widths[0]), mult(units[0], -margin2)), /// right start l2 ] ]; // check if intersection is after l1 and before l2 -> add intersection point let s1 = add(points[0], mult(normals[0],offsets[0])); let s2 = add(points[1], mult(normals[1],offsets[1])); let d1 = intersect_dist(s1, units[0], s2, units[1]); let d2 = intersect_dist(s2, units[1], s1, units[0]); debugger; if (d1 > lengths[0]-margin2 && d2 < margin2) { // add corner vertex to polygon poly[0].splice(1, 0, add(s1, mult(units[0], d1))); } // again for other side of lines s1 = add(points[0], mult(normals[0], offsets[0]+widths[0])); s2 = add(points[1], mult(normals[1], offsets[1]+widths[1])); d1 = intersect_dist(s1, units[0], s2, units[1]); d2 = intersect_dist(s2, units[1], s1, units[0]); if (d1 > lengths[0]-margin2 && d2 < margin2) { // add corner vertex to polygon poly[1].splice(1, 0, add(s1, mult(units[0], d1))); } return poly; }36:T98e,map1 = html``37:[] 2d:{"title":"Line Corner Test","cells":[{"id":0,"value":"# Line Corner Test","pinned":true,"hidden":false,"mode":"md"},{"id":9,"value":"points = [\n [100,350], [400,250], [400+300*Math.cos((cornerAngle-20)/180*Math.PI), 250+300*Math.sin((cornerAngle-20)/180*Math.PI)] \n]","pinned":true,"hidden":false,"mode":"ojs"},{"id":36,"value":"offsets = [ pos1-width1/2, pos2-width2/2 ]","pinned":false,"hidden":false,"mode":"ojs"},{"id":39,"value":"widths = [width1, width2]","pinned":false,"hidden":false,"mode":"ojs"},{"id":157,"value":"angle = deg_angles[1]-deg_angles[0]","pinned":false,"hidden":false,"mode":"ojs"},{"id":75,"value":"lines = [\n [points[0], points[1]],\n [points[1], points[2]]\n]","pinned":false,"hidden":false,"mode":"ojs"},{"id":53,"value":"lengths = lines.map(l => len(sub(l[1], l[0])))","pinned":true,"hidden":false,"mode":"ojs"},{"id":73,"value":"units = lines.map((l, i) => [(l[1][0]-l[0][0])/lengths[i], (l[1][1]-l[0][1])/lengths[i]])","pinned":true,"hidden":false,"mode":"ojs"},{"id":82,"value":"normals = units.map(([x,y]) => [-y, x])","pinned":true,"hidden":false,"mode":"ojs"},{"id":29,"value":"angles = lines.map(l => Math.atan2(l[1][1]-l[0][1], l[1][0]-l[0][0]))","pinned":true,"hidden":false,"mode":"ojs"},{"id":32,"value":"deg_angles = angles.map(a => a / Math.PI * 180)","pinned":false,"hidden":false,"mode":"ojs"},{"id":412,"value":"$2f","pinned":false,"hidden":false,"mode":"md"},{"id":259,"value":"viewof pos1 = Inputs.range([-100, 100], {value: 50, step: 1, label: \"Pos 1\", width: 500})","pinned":false,"hidden":false,"mode":"ojs"},{"id":264,"value":"viewof width1 = Inputs.range([1, 100], {value: 40, step: 1, label: \"Width 1\", width: 500})","pinned":false,"hidden":false,"mode":"ojs"},{"id":255,"value":"viewof pos2 = Inputs.range([-100, 100], {value: 50, step: 1, label: \"Pos 2\", width: 500})","pinned":false,"hidden":false,"mode":"ojs"},{"id":269,"value":"viewof width2 = Inputs.range([1, 100], {value: 20, step: 1, label: \"Width 2\", width: 500})","pinned":false,"hidden":false,"mode":"ojs"},{"id":202,"value":"viewof cornerAngle = Inputs.range([-120, 120], {value: 30, step: 1, label: \"Corner Angle\", width: 500})","pinned":false,"hidden":false,"mode":"ojs"},{"id":499,"value":"## Variant 4: Distinct polygons for various parts of the crossing","pinned":false,"hidden":false,"mode":"md"},{"id":508,"value":"$30","pinned":false,"hidden":false,"mode":"ojs"},{"id":655,"value":"$31","pinned":true,"hidden":false,"mode":"ojs"},{"id":644,"value":"## Variant 3: Keep minimum width of lane by drawing tangent at distance to corner point","pinned":false,"hidden":false,"mode":"md"},{"id":650,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":502,"value":"$33","pinned":true,"hidden":false,"mode":"ojs"},{"id":404,"value":"## Variant 2: Symmetrical distance from corner line","pinned":false,"hidden":false,"mode":"md"},{"id":283,"value":"$34","pinned":false,"hidden":false,"mode":"ojs"},{"id":372,"value":"margin2 = Math.max(\n Math.min(offsets[0], offsets[0]+width1, offsets[1], offsets[1]+width2) * Math.tan((angles[1]-angles[0])/2),\n Math.max(offsets[0], offsets[0]+width1, offsets[1], offsets[1]+width2) * Math.tan((angles[1]-angles[0])/2)\n)","pinned":true,"hidden":false,"mode":"ojs"},{"id":367,"value":"$35","pinned":true,"hidden":false,"mode":"ojs"},{"id":408,"value":"## Variant 1: Minimum distance","pinned":false,"hidden":false,"mode":"md"},{"id":5,"value":"$36","pinned":false,"hidden":false,"mode":"ojs"},{"id":86,"value":"intersections = [\n intersect(add(points[0], mult(normals[0],offsets[0])), units[0], add(points[1], mult(normals[1],offsets[1])), units[1]),\n intersect(add(points[0], mult(normals[0],offsets[0]+widths[0])), units[0], add(points[1], mult(normals[1],offsets[1])), units[1]),\n intersect(add(points[0], mult(normals[0],offsets[0])), units[0], add(points[1], mult(normals[1],offsets[1]+widths[1])), units[1]),\n intersect(add(points[0], mult(normals[0],offsets[0]+widths[0])), units[0], add(points[1], mult(normals[1],offsets[1]+widths[1])), units[1]),\n]","pinned":true,"hidden":false,"mode":"ojs"},{"id":189,"value":"margin = {\n let f = Math.tan((angles[1]-angles[0])/2);\n return [\n Math.max(f * (offsets[0] + widths[0]), f * offsets[0]),\n Math.max(f * (offsets[1] + widths[1]), f * offsets[1])\n ]\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":234,"value":"corner_polygon = [\n add(points[1], mult(normals[0], offsets[0]+widths[0]), mult(units[0], -margin[0])), // right end l1\n add(points[1], mult(normals[1], offsets[1]+widths[1]), mult(units[1], margin[1])), // right start l2\n add(points[1], mult(normals[1], offsets[1]), mult(units[1], margin[1])), /// left start l2\n add(points[1], mult(normals[0], offsets[0]), mult(units[0], -margin[0])),// left end l1\n]","pinned":true,"hidden":false,"mode":"ojs"},{"id":436,"value":"# Appendix: Vector algebra","pinned":false,"hidden":false,"mode":"md"},{"id":91,"value":"// Add vectors\nfunction add(...args) {\n return args.reduce((val, cur) => val.map((v,i) => v+cur[i]), [0,0])\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":485,"value":"function sub(a, b) {\n return a.map((x, i) => x-b[i]); \n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":95,"value":"// Multiply vector with scalar\nfunction mult(vec, scalar) {\n return vec.map(x => x*scalar);\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":476,"value":"function len(vec) {\n return Math.sqrt(vec.reduce((cur, val) => cur + val*val, 0));\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":685,"value":"function unit(vec) {\n return mult(vec, 1/len(vec));\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":688,"value":"function normal(vec) {\n return [vec[1], -vec[0]];\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":519,"value":"function dist(p1, p2) {\n return len(sub(p2,p1));\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":72,"value":"// Intersect two lines, given by starting point and direction vector\nfunction intersect(a, da, b, db) {\n let m = intersect_dist(a, da, b, db);\n return [a[0]+m*da[0], a[1]+m*da[1]];\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":581,"value":"// intersect two lines, given by two points on each line\nfunction intersectLinesByPoints(l1p1, l1p2, l2p1, l2p2) {\n return intersect(l1p1, sub(l1p2, l1p1), l2p1, sub(l2p2, l2p1));\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":397,"value":"// returns the distance of intersection of two lines, measured from the first point\nfunction intersect_dist(a, va, b, vb) {\n // check for parallel lines\n if (va[0]*vb[1] == va[1]*vb[0]) return Infinity;\n // check for div 0 (vb[0]==0) -> swap x,y (gives same result)\n if (vb[0] == 0) {\n a=[a[1],a[0]];\n b=[b[1],b[0]];\n va=[va[1],va[0]];\n vb=[vb[1],vb[0]];\n }\n let m = (b[1] + (a[0]-b[0])*vb[1]/vb[0]-a[1]) / (va[1] - va[0]*vb[1]/vb[0]);\n return m;\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":505,"value":"function tangentPoints(p1, r1, p2) {\n // tangent points on circle defined by p1, r1 from p2\n let len = Math.sqrt((p2[0] - p1[0])**2 + (p2[1] - p1[1])**2);\n let th = Math.acos(r1 / len); // theta\n let d = Math.atan2(p2[1] - p1[1], p2[0] - p1[0]); // angle of p2 from p1\n let d1 = d + th; // direction angle of tangent points from p1\n let d2 = d - th; \n\n return [\n [p1[0] + r1 * Math.cos(d1), p1[1] + r1 * Math.sin(d1)],\n [p1[0] + r1 * Math.cos(d2), p1[1] + r1 * Math.sin(d2)]\n ];\n}","pinned":true,"hidden":false,"mode":"ojs"}],"files":"$W37","stdlib":"1","titling":"auto"}