Circle from three points.

circleFromThreePoints.ts

// This is a very fast implementation.
const det = (
  a: number,
  b: number,
  c: number,
  d: number,
  e: number,
  f: number,
  g: number,
  h: number,
  i: number
) => a * e * i + b * f * g + c * d * h - a * f * h - b * d * i - c * e * g

export function circleFromThreePoints(
  x0: number,
  y0: number,
  x1: number,
  y1: number,
  x2: number,
  y2: number
) {
  var a1 = det(x0, y0, 1, x1, y1, 1, x2, y2, 1)
  var a = det(x0, y0, 1, x1, y1, 1, x2, y2, 1)
  var b = x0 * x0 + y0 * y0
  var c = x1 * x1 + y1 * y1
  var d = x2 * x2 + y2 * y2
  var cx = -det(b, y0, 1, c, y1, 1, d, y2, 1)
  var cy = det(b, x0, 1, c, x1, 1, d, x2, 1)
  var cr = -det(b, x0, y0, c, x1, y1, d, x2, y2)
  return [
    -cx / (2 * a),
    -cy / (2 * a),
    Math.sqrt(cx * cx + cy * cy - 4 * a * cr) / (2 * Math.abs(a))
  ]
}

slowerImplementation.ts

// This implementation is about 50% slower, though maybe easier to understand.

export function circleFromThreePoints(
  x0: number,
  y0: number,
  x1: number,
  y1: number,
  x2: number,
  y2: number
) {

  // Slopes
  var a = (y1 - y0) / (x1 - x0)
  var b = (y2 - y1) / (x2 - x1)

  const cx = (a * b * (y0 - y2) + b * (x0 + x1) - a * (x1 + x2)) / (2 * (b - a))
  const cy = (-1 * (cx - (x0 + x1) / 2)) / a + (y0 + y1) / 2
  const radius = Math.hypot(cy - y0, cx - x0)

  return [cx, cy, radius]
}