this.minimumCircle = function() { var data; layout.data = function(_) { if (!arguments.length) return data; data = _; return layout; }; function layout() { return makeCircle(data); } function makeCircle(points) { // Knuth shuffle var shuffled = points.slice(0); for (var i = points.length - 1; i >= 0; i--) { var j = Math.floor(Math.random() * (i + 1)); j = Math.max(Math.min(j, i), 0); var temp = shuffled[i]; shuffled[i] = shuffled[j]; shuffled[j] = temp; } // Incrementally add points to circle var c = null; for (var i = 0; i < shuffled.length; i++) { var p = shuffled[i]; if (c == null || !isInCircle(c, p.x, p.y)) c = makeCircleOnePoint(shuffled.slice(0, i + 1), p); } return c; } function makeCircleOnePoint(points, p) { var c = {x: p.x, y: p.y, r: 0}; for (var i = 0; i < points.length; i++) { var q = points[i]; if (!isInCircle(c, q.x, q.y)) { if (c.r == 0) c = makeDiameter(p, q); else c = makeCircleTwoPoints(points.slice(0, i + 1), p, q); } } return c; } function makeCircleTwoPoints(points, p, q) { var temp = makeDiameter(p, q); var containsAll = true; for (var i = 0; i < points.length; i++) containsAll = containsAll && isInCircle(temp, points[i].x, points[i].y); if (containsAll) return temp; var left = null; var right = null; for (var i = 0; i < points.length; i++) { var r = points[i]; var cross = crossProduct(p.x, p.y, q.x, q.y, r.x, r.y); var c = makeCircumcircle(p, q, r); if (cross > 0 && (left == null || crossProduct(p.x, p.y, q.x, q.y, c.x, c.y) > crossProduct(p.x, p.y, q.x, q.y, left.x, left.y))) left = c; else if (cross < 0 && (right == null || crossProduct(p.x, p.y, q.x, q.y, c.x, c.y) < crossProduct(p.x, p.y, q.x, q.y, right.x, right.y))) right = c; } return right == null || left != null && left.r <= right.r ? left : right; } function makeCircumcircle(p0, p1, p2) { // Mathematical algorithm from Wikipedia: Circumscribed circle var ax = p0.x, ay = p0.y; var bx = p1.x, by = p1.y; var cx = p2.x, cy = p2.y; var d = (ax * (by - cy) + bx * (cy - ay) + cx * (ay - by)) * 2; var x = ((ax * ax + ay * ay) * (by - cy) + (bx * bx + by * by) * (cy - ay) + (cx * cx + cy * cy) * (ay - by)) / d; var y = ((ax * ax + ay * ay) * (cx - bx) + (bx * bx + by * by) * (ax - cx) + (cx * cx + cy * cy) * (bx - ax)) / d; return {x: x, y: y, r: distance(x, y, ax, ay)}; } function makeDiameter(p0, p1) { return { x: (p0.x + p1.x) / 2, y: (p0.y + p1.y) / 2, r: distance(p0.x, p0.y, p1.x, p1.y) / 2 }; } var EPSILON = 1e-12; function isInCircle(c, x, y) { return c != null && distance(x, y, c.x, c.y) < c.r + EPSILON; } // Returns twice the signed area of the triangle defined by (x0, y0), (x1, y1), (x2, y2) function crossProduct(x0, y0, x1, y1, x2, y2) { return (x1 - x0) * (y2 - y0) - (y1 - y0) * (x2 - x0); } function distance(x0, y0, x1, y1) { return Math.sqrt((x0 - x1) * (x0 - x1) + (y0 - y1) * (y0 - y1)); } return layout; }