frontend/osu/js/curves/CircumscribedCircle.js

define([],
    function () {
        // Adapted from CircumscribedCircle.java @ github.com/itdelatrisu/opsu
        function CircumscribedCircle(hit) {

            var start = {
                x: hit.x,
                y: hit.y
            };
            var mid = {
                x: hit.keyframes[0].x,
                y: hit.keyframes[0].y
            };
            var end = {
                x: hit.keyframes[1].x,
                y: hit.keyframes[1].y
            };

            // find the circle center
            var mida = vecmid(start, mid);
            var midb = vecmid(end, mid);
            var nora = nor(vecsub(mid, start));
            var norb = nor(vecsub(mid, end));
            var circleCenter = intersect(mida, nora, midb, norb);
            if (!circleCenter) return [];

            // find the angles relative to the circle center
            var startAngPoint = vecsub(start, circleCenter);
            var midAngPoint = vecsub(mid, circleCenter);
            var endAngPoint = vecsub(end, circleCenter);

            var startAng = Math.atan2(startAngPoint.y, startAngPoint.x);
            var midAng = Math.atan2(midAngPoint.y, midAngPoint.x);
            var endAng = Math.atan2(endAngPoint.y, endAngPoint.x);

            const TWO_PI = Math.PI * 2;
            const HALF_PI = Math.PI / 2;

            // find the angles that pass through midAng
            if (!isIn(startAng, midAng, endAng)) {
                if (Math.abs(startAng + TWO_PI - endAng) < TWO_PI && isIn(startAng + (TWO_PI), midAng, endAng))
                    startAng += TWO_PI;
                else if (Math.abs(startAng - (endAng + TWO_PI)) < TWO_PI && isIn(startAng, midAng, endAng + (TWO_PI)))
                    endAng += TWO_PI;
                else if (Math.abs(startAng - TWO_PI - endAng) < TWO_PI && isIn(startAng - (TWO_PI), midAng, endAng))
                    startAng -= TWO_PI;
                else if (Math.abs(startAng - (endAng - TWO_PI)) < TWO_PI && isIn(startAng, midAng, endAng - (TWO_PI)))
                    endAng -= TWO_PI;
                else
                    throw "Cannot find angles between midAng.";
            }

            // find an angle with an arc length of pixelLength along this circle
            var radius = veclen(startAngPoint);
            var arcAng = Math.abs(startAng - endAng);
            let expectAng = hit.pixelLength / radius;
            if (arcAng > expectAng * 0.97) {
                // console.log("truncating arc to ", expectAng / arcAng);
                arcAng = expectAng; // truncate to given len
            } else {
                console.warn("[curve] P shorter than given", arcAng / expectAng);
            }

            // now use it for our new end angle
            endAng = (endAng > startAng) ? startAng + arcAng : startAng - arcAng;

            // calculate points
            var step = Math.floor(hit.pixelLength / CURVE_POINTS_SEPERATION);
            var curve = new Array(step + 1);

            pointAt = function (t) {
                if (t > 1) t = 1;
                var ang = lerp(startAng, endAng, t);
                return {
                    x: Math.cos(ang) * radius + circleCenter.x,
                    y: Math.sin(ang) * radius + circleCenter.y,
                    t: t,
                };
            };
            for (var i = 0; i < curve.length; i++) {
                curve[i] = pointAt(i / step);
            }

            // check total distance
            var l = 0;
            for (let i = 1; i < curve.length; ++i) {
                let dx = curve[i].x - curve[i - 1].x;
                let dy = curve[i].y - curve[i - 1].y;
                l += Math.hypot(dx, dy);
            }
            return {
                curve: curve,
                pointAt: pointAt,
                totalDistance: l
            };
        };
        return CircumscribedCircle;

        function lerp(a, b, t) {
            return a * (1 - t) + b * t;
        }

        function veclen(a) {
            return Math.sqrt(a.x * a.x + a.y * a.y);
        }

        function nor(a) {
            return {
                x: -a.y,
                y: a.x
            };
        }

        function vecsub(a, b) {
            return {
                x: a.x - b.x,
                y: a.y - b.y
            };
        }

        function vecmid(a, b) {
            return {
                x: (a.x + b.x) / 2,
                y: (a.y + b.y) / 2
            };
        }

        function isIn(a, b, c) {
            return (b > a && b < c) || (b < a && b > c);
        }

        function intersect(a, ta, b, tb) {
            // xy = a + ta * t = b + tb * u
            // t =(b + tb*u -a)/ta
            //t(x) == t(y)
            //(b.x + tb.x*u -a.x)/ta.x = (b.y + tb.y*u -a.y)/ta.y
            // b.x*ta.y + tb.x*u*ta.y -a.x*ta.y = b.y*ta.x + tb.y*u*ta.x -a.y*ta.x
            // tb.x*u*ta.y - tb.y*u*ta.x= b.y*ta.x  -a.y*ta.x -b.x*ta.y +a.x*ta.y
            //u *(tb.x*ta.y - tb.y*ta.x) = (b.y-a.y)ta.x +(a.x-b.x)ta.y
            //u = ((b.y-a.y)ta.x +(a.x-b.x)ta.y) / (tb.x*ta.y - tb.y*ta.x);

            var des = tb.x * ta.y - tb.y * ta.x;
            if (Math.abs(des) < 0.00001) {
                console.warn("[curve] encountering straight P slider");
                return undefined;
            }
            var u = ((b.y - a.y) * ta.x + (a.x - b.x) * ta.y) / des;
            return {
                x: b.x + tb.x * u,
                y: b.y + tb.y * u
            };
        }
    });