getOuterPath method

  1. @override
Path getOuterPath (Rect host, Rect guest)
override

Creates a Path that describes a rectangle with a smooth circular notch.

host is the bounding box for the returned shape. Conceptually this is the rectangle to which the notch will be applied.

guest is the bounding box of a circle that the notch accomodates. All points in the circle bounded by guest will be outside of the returned path.

The notch is curve that smoothly connects the host's top edge and the guest circle.

Implementation 

// TODO(amirh): add an example diagram here.
@override
Path getOuterPath(Rect host, Rect guest) {
  if (!host.overlaps(guest))
    return Path()..addRect(host);

  // The guest's shape is a circle bounded by the guest rectangle.
  // So the guest's radius is half the guest width.
  final double notchRadius = guest.width / 2.0;

  // We build a path for the notch from 3 segments:
  // Segment A - a Bezier curve from the host's top edge to segment B.
  // Segment B - an arc with radius notchRadius.
  // Segment C - a Bezier curver from segment B back to the host's top edge.
  //
  // A detailed explanation and the derivation of the formulas below is
  // available at: https://goo.gl/Ufzrqn

  const double s1 = 15.0;
  const double s2 = 1.0;

  final double r = notchRadius;
  final double a = -1.0 * r - s2;
  final double b = host.top - guest.center.dy;

  final double n2 = math.sqrt(b * b * r * r * (a * a + b * b - r * r));
  final double p2xA = ((a * r * r) - n2) / (a * a + b * b);
  final double p2xB = ((a * r * r) + n2) / (a * a + b * b);
  final double p2yA = math.sqrt(r * r - p2xA * p2xA);
  final double p2yB = math.sqrt(r * r - p2xB * p2xB);

  final List<Offset> p = List<Offset>(6);

  // p0, p1, and p2 are the control points for segment A.
  p[0] = Offset(a - s1, b);
  p[1] = Offset(a, b);
  final double cmp = b < 0 ? -1.0 : 1.0;
  p[2] = cmp * p2yA > cmp * p2yB ? Offset(p2xA, p2yA) : Offset(p2xB, p2yB);

  // p3, p4, and p5 are the control points for segment B, which is a mirror
  // of segment A around the y axis.
  p[3] = Offset(-1.0 * p[2].dx, p[2].dy);
  p[4] = Offset(-1.0 * p[1].dx, p[1].dy);
  p[5] = Offset(-1.0 * p[0].dx, p[0].dy);

  // translate all points back to the absolute coordinate system.
  for (int i = 0; i < p.length; i += 1)
    p[i] += guest.center;

  return Path()
    ..moveTo(host.left, host.top)
    ..lineTo(p[0].dx, p[0].dy)
    ..quadraticBezierTo(p[1].dx, p[1].dy, p[2].dx, p[2].dy)
    ..arcToPoint(
      p[3],
      radius: Radius.circular(notchRadius),
      clockwise: false,
    )
    ..quadraticBezierTo(p[4].dx, p[4].dy, p[5].dx, p[5].dy)
    ..lineTo(host.right, host.top)
    ..lineTo(host.right, host.bottom)
    ..lineTo(host.left, host.bottom)
    ..close();
}