"use strict"; Object.defineProperty(exports, "__esModule", { value: true }); exports.getCenter = exports.circleCircleIntersection = exports.circleOverlap = exports.distance = exports.circleArea = exports.containedInCircles = exports.intersectionArea = void 0; var SMALL = 1e-10; /** Returns the intersection area of a bunch of circles (where each circle is an object having an x,y and radius property) */ function intersectionArea(circles, stats) { // get all the intersection points of the circles var intersectionPoints = getIntersectionPoints(circles); // filter out points that aren't included in all the circles var innerPoints = intersectionPoints.filter(function (p) { return containedInCircles(p, circles); }); var arcArea = 0, polygonArea = 0, i; var arcs = []; // if we have intersection points that are within all the circles, // then figure out the area contained by them if (innerPoints.length > 1) { // sort the points by angle from the center of the polygon, which lets // us just iterate over points to get the edges var center = getCenter(innerPoints); for (i = 0; i < innerPoints.length; ++i) { var p = innerPoints[i]; p.angle = Math.atan2(p.x - center.x, p.y - center.y); } innerPoints.sort(function (a, b) { return b.angle - a.angle; }); // iterate over all points, get arc between the points // and update the areas var p2 = innerPoints[innerPoints.length - 1]; for (i = 0; i < innerPoints.length; ++i) { var p1 = innerPoints[i]; // polygon area updates easily ... polygonArea += (p2.x + p1.x) * (p1.y - p2.y); // updating the arc area is a little more involved var midPoint = { x: (p1.x + p2.x) / 2, y: (p1.y + p2.y) / 2 }; var arc = null; for (var j = 0; j < p1.parentIndex.length; ++j) { if (p2.parentIndex.indexOf(p1.parentIndex[j]) > -1) { // figure out the angle halfway between the two points // on the current circle var circle = circles[p1.parentIndex[j]], a1 = Math.atan2(p1.x - circle.x, p1.y - circle.y), a2 = Math.atan2(p2.x - circle.x, p2.y - circle.y); var angleDiff = a2 - a1; if (angleDiff < 0) { angleDiff += 2 * Math.PI; } // and use that angle to figure out the width of the // arc var a = a2 - angleDiff / 2; var width = distance(midPoint, { x: circle.x + circle.radius * Math.sin(a), y: circle.y + circle.radius * Math.cos(a), }); // clamp the width to the largest is can actually be // (sometimes slightly overflows because of FP errors) if (width > circle.radius * 2) { width = circle.radius * 2; } // pick the circle whose arc has the smallest width if (arc === null || arc.width > width) { arc = { circle: circle, width: width, p1: p1, p2: p2 }; } } } if (arc !== null) { arcs.push(arc); arcArea += circleArea(arc.circle.radius, arc.width); p2 = p1; } } } else { // no intersection points, is either disjoint - or is completely // overlapped. figure out which by examining the smallest circle var smallest = circles[0]; for (i = 1; i < circles.length; ++i) { if (circles[i].radius < smallest.radius) { smallest = circles[i]; } } // make sure the smallest circle is completely contained in all // the other circles var disjoint = false; for (i = 0; i < circles.length; ++i) { if (distance(circles[i], smallest) > Math.abs(smallest.radius - circles[i].radius)) { disjoint = true; break; } } if (disjoint) { arcArea = polygonArea = 0; } else { arcArea = smallest.radius * smallest.radius * Math.PI; arcs.push({ circle: smallest, p1: { x: smallest.x, y: smallest.y + smallest.radius }, p2: { x: smallest.x - SMALL, y: smallest.y + smallest.radius }, width: smallest.radius * 2, }); } } polygonArea /= 2; if (stats) { stats.area = arcArea + polygonArea; stats.arcArea = arcArea; stats.polygonArea = polygonArea; stats.arcs = arcs; stats.innerPoints = innerPoints; stats.intersectionPoints = intersectionPoints; } return arcArea + polygonArea; } exports.intersectionArea = intersectionArea; /** returns whether a point is contained by all of a list of circles */ function containedInCircles(point, circles) { for (var i = 0; i < circles.length; ++i) { if (distance(point, circles[i]) > circles[i].radius + SMALL) { return false; } } return true; } exports.containedInCircles = containedInCircles; /** Gets all intersection points between a bunch of circles */ function getIntersectionPoints(circles) { var ret = []; for (var i = 0; i < circles.length; ++i) { for (var j = i + 1; j < circles.length; ++j) { var intersect = circleCircleIntersection(circles[i], circles[j]); for (var k = 0; k < intersect.length; ++k) { var p = intersect[k]; p.parentIndex = [i, j]; ret.push(p); } } } return ret; } /** Circular segment area calculation. See http://mathworld.wolfram.com/CircularSegment.html */ function circleArea(r, width) { return r * r * Math.acos(1 - width / r) - (r - width) * Math.sqrt(width * (2 * r - width)); } exports.circleArea = circleArea; /** euclidean distance between two points */ function distance(p1, p2) { return Math.sqrt((p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y)); } exports.distance = distance; /** Returns the overlap area of two circles of radius r1 and r2 - that have their centers separated by distance d. Simpler faster circle intersection for only two circles */ function circleOverlap(r1, r2, d) { // no overlap if (d >= r1 + r2) { return 0; } // completely overlapped if (d <= Math.abs(r1 - r2)) { return Math.PI * Math.min(r1, r2) * Math.min(r1, r2); } var w1 = r1 - (d * d - r2 * r2 + r1 * r1) / (2 * d), w2 = r2 - (d * d - r1 * r1 + r2 * r2) / (2 * d); return circleArea(r1, w1) + circleArea(r2, w2); } exports.circleOverlap = circleOverlap; /** Given two circles (containing a x/y/radius attributes), returns the intersecting points if possible. note: doesn't handle cases where there are infinitely many intersection points (circles are equivalent):, or only one intersection point*/ function circleCircleIntersection(p1, p2) { var d = distance(p1, p2), r1 = p1.radius, r2 = p2.radius; // if to far away, or self contained - can't be done if (d >= r1 + r2 || d <= Math.abs(r1 - r2)) { return []; } var a = (r1 * r1 - r2 * r2 + d * d) / (2 * d), h = Math.sqrt(r1 * r1 - a * a), x0 = p1.x + (a * (p2.x - p1.x)) / d, y0 = p1.y + (a * (p2.y - p1.y)) / d, rx = -(p2.y - p1.y) * (h / d), ry = -(p2.x - p1.x) * (h / d); return [ { x: x0 + rx, y: y0 - ry }, { x: x0 - rx, y: y0 + ry }, ]; } exports.circleCircleIntersection = circleCircleIntersection; /** Returns the center of a bunch of points */ function getCenter(points) { var center = { x: 0, y: 0 }; for (var i = 0; i < points.length; ++i) { center.x += points[i].x; center.y += points[i].y; } center.x /= points.length; center.y /= points.length; return center; } exports.getCenter = getCenter; //# sourceMappingURL=circleintersection.js.map