@antv/g2/lib/data/utils/venn/circleintersection.js

the Grammar of Graphics in Javascript

"use strict";
Object.defineProperty(exports, "__esModule", { value: true });
exports.getCenter = exports.circleCircleIntersection = exports.circleOverlap = exports.distance = exports.circleArea = exports.containedInCircles = exports.intersectionArea = void 0;
const 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
    const intersectionPoints = getIntersectionPoints(circles);
    // Filter out points that aren't included in all the circles
    const innerPoints = intersectionPoints.filter(function (p) {
        return containedInCircles(p, circles);
    });
    let arcArea = 0, polygonArea = 0, i;
    const 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
        const center = getCenter(innerPoints);
        for (i = 0; i < innerPoints.length; ++i) {
            const 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
        let p2 = innerPoints[innerPoints.length - 1];
        for (i = 0; i < innerPoints.length; ++i) {
            const 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
            const midPoint = { x: (p1.x + p2.x) / 2, y: (p1.y + p2.y) / 2 };
            let arc = null;
            for (let 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
                    const 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);
                    let angleDiff = a2 - a1;
                    if (angleDiff < 0) {
                        angleDiff += 2 * Math.PI;
                    }
                    // and use that angle to figure out the width of the
                    // arc
                    const a = a2 - angleDiff / 2;
                    let 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
        let 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
        let 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 (let 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) {
    const ret = [];
    for (let i = 0; i < circles.length; ++i) {
        for (let j = i + 1; j < circles.length; ++j) {
            const intersect = circleCircleIntersection(circles[i], circles[j]);
            for (let k = 0; k < intersect.length; ++k) {
                const 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);
    }
    const 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) {
    const 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 [];
    }
    const 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) {
    const center = { x: 0, y: 0 };
    for (let 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;
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