Find the control points for a quadratic bezier curve segment from point a to point c passing through point b.

getQuadraticControlPoint.ts

/**
 * Find the control points for a quadratic segment from point a to point c passing through point b.
 * @param a The segments's first point
 * @param b The point to curve through
 * @param c The segment's end point
 */
export function getQuadraticControlPoints(
  a: { x: number; y: number },
  b: { x: number; y: number },
  c: { x: number; y: number }
) {
  return {
    a,
    c1: {    
      x: b.x + (b.x - (a.x + c.x) * 0.5),
      y: b.y + (b.y - (a.y + c.y) * 0.5)
    },
    c
  };
}

Demo at https://codesandbox.io/s/find-handle-for-quadradic-curve-c20q5f