binaries/data/mods/public/maps/random/rmgen/math.js

   1 const g_TileVertices = deepfreeze([
   2         new Vector2D(0, 0),
   3         new Vector2D(0, 1),
   4         new Vector2D(1, 0),
   5         new Vector2D(1, 1)
   6 ]);
   7
   8 const g_AdjacentCoordinates = deepfreeze([
   9         new Vector2D(1, 0),
  10         new Vector2D(1, 1),
  11         new Vector2D(0, 1),
  12         new Vector2D(-1, 1),
  13         new Vector2D(-1, 0),
  14         new Vector2D(-1, -1),
  15         new Vector2D(0, -1),
  16         new Vector2D(1, -1)
  17 ]);
  18
  19 function diskArea(radius)
  20 {
  21         return Math.PI * Math.square(radius);
  22 }
  23
  24 /**
  25  * Returns the angle of the vector between point 1 and point 2.
  26  * The angle is counterclockwise from the positive x axis.
  27  */
  28 function getAngle(x1, z1, x2, z2)
  29 {
  30         return Math.atan2(z2 - z1, x2 - x1);
  31 }
  32
  33 /**
  34  * Get pointCount points equidistantly located on a circle.
  35  * @param {Vector2D} center
  36  */
  37 function distributePointsOnCircle(pointCount, startAngle, radius, center)
  38 {
  39         return distributePointsOnCircularSegment(pointCount, Math. PI * 2, startAngle, radius, center);
  40 }
  41
  42 function distributePointsOnCircularSegment(pointCount, maxAngle, startAngle, radius, center)
  43 {
  44         let points = [];
  45         let angle = [];
  46
  47         for (let i = 0; i < pointCount; ++i)
  48         {
  49                 angle[i] = startAngle + maxAngle * i / pointCount;
  50                 points[i] = Vector2D.add(center, new Vector2D(radius, 0).rotate(-angle[i]));
  51         }
  52
  53         return [points, angle];
  54 }
  55
  56 /**
  57  * Returns the shortest distance from a point to a line.
  58  * The sign of the return value determines the direction!
  59  *
  60  * @param {Vector2D} - lineStart, lineEnd, point
  61  */
  62 function distanceOfPointFromLine(lineStart, lineEnd, point)
  63 {
  64         // Since the cross product is the area of the parallelogram with the vectors for sides and
  65         // one of the two vectors having length one, that area equals the distance between the points.
  66         return Vector2D.sub(lineStart, lineEnd).normalize().cross(Vector2D.sub(point, lineEnd));
  67 }
  68
  69 /**
  70  * Returns whether the two lines of the given width going through the given Vector2D intersect.
  71  */
  72 function testLineIntersection(start1, end1, start2, end2, width)
  73 {
  74         let start1end1 = Vector2D.sub(start1, end1);
  75         let start2end2 = Vector2D.sub(start2, end2);
  76         let start1start2 = Vector2D.sub(start1, start2);
  77
  78         return (
  79                 Math.abs(distanceOfPointFromLine(start1, end1, start2)) < width ||
  80                 Math.abs(distanceOfPointFromLine(start1, end1, end2)) < width ||
  81                 Math.abs(distanceOfPointFromLine(start2, end2, start1)) < width ||
  82                 Math.abs(distanceOfPointFromLine(start2, end2, end1)) < width ||
  83                 start1end1.cross(start1start2) * start1end1.cross(Vector2D.sub(start1, end2)) <= 0 &&
  84                 start2end2.cross(start1start2) * start2end2.cross(Vector2D.sub(start2, end1)) >= 0);
  85 }
  86
  87 /**
  88  * Returns the topleft and bottomright coordinate of the given two points.
  89  */
  90 function getBoundingBox(points)
  91 {
  92         let min = points[0].clone();
  93         let max = points[0].clone();
  94
  95         for (let point of points)
  96         {
  97                 min.set(Math.min(min.x, point.x), Math.min(min.y, point.y));
  98                 max.set(Math.max(max.x, point.x), Math.max(max.y, point.y));
  99         }
 100
 101         return {
 102                 "min": min,
 103                 "max": max
 104         };
 105 }
 106
 107 function getPointsInBoundingBox(boundingBox)
 108 {
 109         let points = [];
 110         for (let x = boundingBox.min.x; x <= boundingBox.max.x; ++x)
 111                 for (let y = boundingBox.min.y; y <= boundingBox.max.y; ++y)
 112                         points.push(new Vector2D(x, y));
 113         return points;
 114 }
 115
 116 /**
 117  * Sorts the given (x, y) points so that the distance between neighboring points becomes minimal (similar to the traveling salesman problem).
 118  */
 119 function sortPointsShortestCycle(points)
 120 {
 121         let order = [];
 122         let distances = [];
 123         if (points.length <= 3)
 124         {
 125                 for (let i = 0; i < points.length; ++i)
 126                         order.push(i);
 127
 128                 return order;
 129         }
 130
 131         // Just add the first 3 points
 132         let pointsToAdd = points.map(p => p.clone());
 133         for (let i = 0; i < 3; ++i)
 134         {
 135                 order.push(i);
 136                 pointsToAdd.shift(i);
 137                 if (i)
 138                         distances.push(Math.euclidDistance2D(points[order[i]].x, points[order[i]].y, points[order[i - 1]].x, points[order[i - 1]].y));
 139         }
 140
 141         distances.push(points[order[0]].distanceTo(points[order[order.length - 1]]));
 142
 143         // Add remaining points so the path lengthens the least
 144         let numPointsToAdd = pointsToAdd.length;
 145         for (let i = 0; i < numPointsToAdd; ++i)
 146         {
 147                 let indexToAddTo;
 148                 let minEnlengthen = Infinity;
 149                 let minDist1 = 0;
 150                 let minDist2 = 0;
 151                 for (let k = 0; k < order.length; ++k)
 152                 {
 153                         let dist1 = pointsToAdd[0].distanceTo(points[order[k]]);
 154                         let dist2 = pointsToAdd[0].distanceTo(points[order[(k + 1) % order.length]]);
 155
 156                         let enlengthen = dist1 + dist2 - distances[k];
 157                         if (enlengthen < minEnlengthen)
 158                         {
 159                                 indexToAddTo = k;
 160                                 minEnlengthen = enlengthen;
 161                                 minDist1 = dist1;
 162                                 minDist2 = dist2;
 163                         }
 164                 }
 165                 order.splice(indexToAddTo + 1, 0, i + 3);
 166                 distances.splice(indexToAddTo, 1, minDist1, minDist2);
 167                 pointsToAdd.shift();
 168         }
 169
 170         return order;
 171 }