// Möbius transformation that maps (0, 1, ∞) to (-1, 0, 1)
function transform_point(x, y) {
const d = (x + 1) * (x + 1) + y * y;
return [(x * x - 1 + y * y) / d, 2 * y / d];
}
// The image of a circle under the Möbius transformation
function transform_circle(x, y, r) {
return circle_through_points(
transform_point(x - r, y),
transform_point(x + r, y),
transform_point(x, y + r)
);
}
// The unique circle passing through three non-collinear points
function circle_through_points([ax, ay], [bx, by], [cx, cy]) {
const na = ax * ax + ay * ay;
const nb = bx * bx + by * by;
const nc = cx * cx + cy * cy;
const dy = 2 * (by - ay) * (bx - cx) - 2 * (ax - bx) * (cy - by);
const y = ((ax - bx) * (nb - nc) - (bx - cx) * (na - nb)) / dy;
const x = (na - nb + 2 * (by - ay) * y) / (2 * (ax - bx));
const r = Math.hypot(x - ax, y - ay);
return [x, y, r];
}
function crot(z, theta) {
return cmul(z, [Math.cos(theta), Math.sin(theta)]);
}
function cmul([wr, wi], [zr, zi]) {
return [wr * zr - wi * zi, wr * zi + wi * zr];
}
root = doyle(p, q)
doyle = require("https://bl.ocks.org/robinhouston/raw/6096562/8a03f4253b2908482f191e58627b6ededfe64250/doyle.js").catch(() => window.doyle)
//https://bl.ocks.org/robinhouston/raw/6096562/8a03f4253b2908482f191e58627b6ededfe64250/doyle.js
md`
[code](https://bl.ocks.org/robinhouston/raw/6096562/8a03f4253b2908482f191e58627b6ededfe64250/doyle.js)
`
d3 = require("d3@5")
import {slider, checkbox, color, select} from "@jashkenas/inputs"
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