Get the point(s) at which a line segment intersects a circle.

getSegmentCircleIntersections.ts

function getSegmentCircleIntersections(
  cx: number,
  cy: number,
  r: number,
  x0: number,
  y0: number,
  x1: number,
  y1: number
) {
  var b: number,
    c: number,
    d: number,
    u1: number,
    u2: number,
    ret: number[][],
    retP1: number[],
    retP2: number[],
    v1 = [x1 - x0, y1 - y0],
    v2 = [x0 - cx, y0 - cy];

  b = v1[0] * v2[0] + v1[1] * v2[1];
  c = 2 * (v1[0] * v1[0] + v1[1] * v1[1]);
  b *= -2;
  d = Math.sqrt(b * b - 2 * c * (v2[0] * v2[0] + v2[1] * v2[1] - r * r));
  if (isNaN(d)) {
    // no intercept
    return [];
  }
  u1 = (b - d) / c; // these represent the unit distance of point one and two on the line
  u2 = (b + d) / c;
  retP1 = []; // return points
  retP2 = [];
  ret = []; // return array

  if (u1 <= 1 && u1 >= 0) {
    // add point if on the line segment
    retP1[0] = x0 + v1[0] * u1;
    retP1[1] = y0 + v1[1] * u1;
    ret[0] = retP1;
  }

  if (u2 <= 1 && u2 >= 0) {
    // second add point if on the line segment
    retP2[0] = x0 + v1[0] * u2;
    retP2[1] = y0 + v1[1] * u2;
    ret[ret.length] = retP2;
  }

  return ret;
}