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// Copyright 2014 The Flutter Authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.
import 'dart:math' as math;
import 'basic_types.dart';
import 'borders.dart';
/// A shape with a notch in its outline.
/// Typically used as the outline of a 'host' widget to make a notch that
/// accommodates a 'guest' widget. e.g the [BottomAppBar] may have a notch to
/// accommodate the [FloatingActionButton].
/// See also:
/// * [ShapeBorder], which defines a shaped border without a dynamic notch.
/// * [AutomaticNotchedShape], an adapter from [ShapeBorder] to [NotchedShape].
abstract class NotchedShape {
/// Abstract const constructor. This constructor enables subclasses to provide
/// const constructors so that they can be used in const expressions.
const NotchedShape();
/// Creates a [Path] that describes the outline of the shape.
/// The `host` is the bounding rectangle of the shape.
/// The `guest` is the bounding rectangle of the shape for which a notch will
/// be made. It is null when there is no guest.
Path getOuterPath(Rect host, Rect guest);
/// A rectangle with a smooth circular notch.
/// See also:
/// * [CircleBorder], a [ShapeBorder] that describes a circle.
class CircularNotchedRectangle extends NotchedShape {
/// Creates a [CircularNotchedRectangle].
/// The same object can be used to create multiple shapes.
const CircularNotchedRectangle();
/// 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 accommodates. 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.
// TODO(amirh): add an example diagram here.
Path getOuterPath(Rect host, Rect guest) {
if (guest == null || !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 curve from segment B back to the host's top edge.
// A detailed explanation and the derivation of the formulas below is
// available at:
const double s1 = 15.0;
const double s2 = 1.0;
final double r = notchRadius;
final double a = -1.0 * r - s2;
final double b = -;
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] +=;
return Path()
..lineTo(p[0].dx, p[0].dy)
..quadraticBezierTo(p[1].dx, p[1].dy, p[2].dx, p[2].dy)
radius: Radius.circular(notchRadius),
clockwise: false,
..quadraticBezierTo(p[4].dx, p[4].dy, p[5].dx, p[5].dy)
..lineTo(host.right, host.bottom)
..lineTo(host.left, host.bottom)
/// A [NotchedShape] created from [ShapeBorder]s.
/// Two shapes can be provided. The [host] is the shape of the widget that
/// uses the [NotchedShape] (typically a [BottomAppBar]). The [guest] is
/// subtracted from the [host] to create the notch (typically to make room
/// for a [FloatingActionButton]).
class AutomaticNotchedShape extends NotchedShape {
/// Creates a [NotchedShape] that is defined by two [ShapeBorder]s.
/// The [host] must not be null.
/// The [guest] may be null, in which case no notch is created even
/// if a guest rectangle is provided to [getOuterPath].
const AutomaticNotchedShape(, [ this.guest ]);
/// The shape of the widget that uses the [NotchedShape] (typically a
/// [BottomAppBar]).
/// This shape cannot depend on the [TextDirection], as no text direction
/// is available to [NotchedShape]s.
final ShapeBorder host;
/// The shape to subtract from the [host] to make the notch.
/// This shape cannot depend on the [TextDirection], as no text direction
/// is available to [NotchedShape]s.
/// If this is null, [getOuterPath] ignores the guest rectangle.
final ShapeBorder guest;
Path getOuterPath(Rect hostRect, Rect guestRect) { // ignore: avoid_renaming_method_parameters, the
// parameters are renamed over the baseclass because they would clash
// with properties of this object, and the use of all four of them in
// the code below is really confusing if they have the same names.
final Path hostPath = host.getOuterPath(hostRect);
if (guest != null && guestRect != null) {
final Path guestPath = guest.getOuterPath(guestRect);
return Path.combine(PathOperation.difference, hostPath, guestPath);
return hostPath;