Smooth Floating Action Button notch (#14851)

packages/flutter/lib/src/material/floating_action_button.dart

@@ -227,65 +227,95 @@ class _FloatingActionButtonState extends State<FloatingActionButton> {
   }
 
   Path _computeNotch(Rect host, Rect guest, Offset start, Offset end) {
-    assert(() {
-      if (end.dy != host.top)
-        throw new FlutterError(
-          'The floating action button\'s notch maker must only be used for a notch in the top edge of the host.\n'
-          'The notch\'s path end point: $end is not in the top edge of $host'
-        );
-      if (start.dy != host.top)
-        throw new FlutterError(
-          'The floating action button\'s notch maker must only be used for a notch in the top edge the host.\n'
-          'The notch\'s path start point: $start is not in the top edge of $host'
-        );
-      return true;
-    }());
-
-    assert(() {
-      if (!host.overlaps(guest))
-        throw new FlutterError('Notch host must intersect with its guest');
-      return true;
-    }());
-
     // The FAB's shape is a circle bounded by the guest rectangle.
     // So the FAB's radius is half the guest width.
     final double fabRadius = guest.width / 2.0;
-
     final double notchRadius = fabRadius + widget.notchMargin;
-    assert(() {
-      if (guest.center.dx - notchRadius < start.dx)
-        throw new FlutterError(
-          'The notch\'s path start point must be to the left of the notch.\n'
-          'Start point was $start, guest was $guest, notchMargin was ${widget.notchMargin}.'
-        );
-      if (guest.center.dx + notchRadius > end.dx)
-        throw new FlutterError(
-          'The notch\'s end point must be to the right of the guest.\n'
-          'End point was $start, notch was $guest, notchMargin was ${widget.notchMargin}.'
-        );
-      return true;
-    }());
-
-    // We find the intersection of the notch's circle with the top edge of the host
-    // using the Pythagorean theorem for the right triangle that connects the
-    // center of the notch and the intersection of the notch's circle and the host's
-    // top edge.
-    //
-    // The hypotenuse of this triangle equals the notch's radius, and one side
-    // (a) is the distance from the notch's center to the top edge.
+
+    assert(_notchAssertions(host, guest, start, end, fabRadius, notchRadius));
+
+    // If there's no overlap between the guest's margin boundary and the host,
+    // don't make a notch, just return a straight line from start to end.
+    if (!host.overlaps(guest.inflate(widget.notchMargin)))
+      return new Path()..lineTo(end.dx, end.dy);
+
+    // 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.
     //
-    // The other side (b) would be the distance on the horizontal axis between the
-    // notch's center and the intersection points with it's top edge.
-    final double a = host.top - guest.center.dy;
-    final double b = math.sqrt(notchRadius * notchRadius - a * a);
+    // 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 = new List<Offset>(6);
+
+    // p0, p1, and p2 are the control points for segment A.
+    p[0] = new Offset(a - s1, b);
+    p[1] = new Offset(a, b);
+    final double cmp = b < 0 ? -1.0 : 1.0;
+    p[2] = cmp * p2yA > cmp * p2yB ? new Offset(p2xA, p2yA) : new 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] = new Offset(-1.0 * p[2].dx, p[2].dy);
+    p[4] = new Offset(-1.0 * p[1].dx, p[1].dy);
+    p[5] = new 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 new Path()
-      ..lineTo(guest.center.dx - b, host.top)
+      ..lineTo(p[0].dx, p[0].dy)
+      ..quadraticBezierTo(p[1].dx, p[1].dy, p[2].dx, p[2].dy)
       ..arcToPoint(
-        new Offset(guest.center.dx + b, host.top),
+        p[3],
         radius: new Radius.circular(notchRadius),
         clockwise: false,
       )
+      ..quadraticBezierTo(p[4].dx, p[4].dy, p[5].dx, p[5].dy)
       ..lineTo(end.dx, end.dy);
   }
+
+  bool _notchAssertions(Rect host, Rect guest, Offset start, Offset end,
+    double fabRadius, double notchRadius) {
+    if (end.dy != host.top)
+      throw new FlutterError(
+        'The notch of the floating action button must end at the top edge of the host.\n'
+        'The notch\'s path end point: $end is not in the top edge of $host'
+      );
+
+    if (start.dy != host.top)
+      throw new FlutterError(
+        'The notch of the floating action button must start at the top edge of the host.\n'
+        'The notch\'s path start point: $start is not in the top edge of $host'
+      );
+
+    if (guest.center.dx - notchRadius < start.dx)
+      throw new FlutterError(
+        'The notch\'s path start point must be to the left of the floating action button.\n'
+        'Start point was $start, guest was $guest, notchMargin was ${widget.notchMargin}.'
+      );
+
+    if (guest.center.dx + notchRadius > end.dx)
+      throw new FlutterError(
+        'The notch\'s end point must be to the right of the floating action button.\n'
+        'End point was $start, notch was $guest, notchMargin was ${widget.notchMargin}.'
+      );
+
+    return true;
+  }
 }

packages/flutter/test/material/floating_action_button_test.dart

@@ -2,6 +2,7 @@
 // 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 'dart:ui';
 
 import 'package:flutter/foundation.dart';
@@ -255,36 +256,15 @@ void main() {
       final Offset end = const Offset(220.0, 100.0);
 
       final Path actualNotch = computeNotch(host, guest, start, end);
-      final Path expectedNotch = new Path()
-        ..lineTo(190.0, 100.0)
-        ..arcToPoint(
-          const Offset(210.0, 100.0),
-          radius: const Radius.circular(10.0),
-          clockwise: false
-        )
-        ..lineTo(220.0, 100.0);
-
-      expect(
-        createNotchedRectangle(host, start.dx, end.dx, actualNotch),
-        coversSameAreaAs(
-          createNotchedRectangle(host, start.dx, end.dx, expectedNotch),
-          areaToCompare: host.inflate(10.0)
-        )
-      );
+      final Path notchedRectangle =
+        createNotchedRectangle(host, start.dx, end.dx, actualNotch);
 
-      expect(
-        createNotchedRectangle(host, start.dx, end.dx, actualNotch),
-        coversSameAreaAs(
-          createNotchedRectangle(host, start.dx, end.dx, expectedNotch),
-          areaToCompare: guest.inflate(10.0),
-          sampleSize: 50,
-        )
-      );
+      expect(pathDoesNotContainCircle(notchedRectangle, guest), isTrue);
     });
 
     testWidgets('notch with margin', (WidgetTester tester) async {
       final ComputeNotch computeNotch = await fetchComputeNotch(tester,
-        const FloatingActionButton(onPressed: null, notchMargin: 4.0)
+	const FloatingActionButton(onPressed: null, notchMargin: 4.0)
       );
       final Rect host = new Rect.fromLTRB(0.0, 100.0, 300.0, 300.0);
       final Rect guest = new Rect.fromLTRB(190.0, 90.0, 210.0, 110.0);
@@ -292,33 +272,58 @@ void main() {
       final Offset end = const Offset(220.0, 100.0);
 
       final Path actualNotch = computeNotch(host, guest, start, end);
-      final Path expectedNotch = new Path()
-        ..lineTo(186.0, 100.0)
-        ..arcToPoint(
-          const Offset(214.0, 100.0),
-          radius: const Radius.circular(14.0),
-          clockwise: false
-        )
-        ..lineTo(220.0, 100.0);
-
-      expect(
-        createNotchedRectangle(host, start.dx, end.dx, actualNotch),
-        coversSameAreaAs(
-          createNotchedRectangle(host, start.dx, end.dx, expectedNotch),
-          areaToCompare: host.inflate(10.0)
-        )
+      final Path notchedRectangle =
+        createNotchedRectangle(host, start.dx, end.dx, actualNotch);
+      expect(pathDoesNotContainCircle(notchedRectangle, guest.inflate(4.0)), isTrue);
+    });
+
+    testWidgets('notch circle center above BAB', (WidgetTester tester) async {
+      final ComputeNotch computeNotch = await fetchComputeNotch(tester,
+	const FloatingActionButton(onPressed: null, notchMargin: 4.0)
       );
+      final Rect host = new Rect.fromLTRB(0.0, 100.0, 300.0, 300.0);
+      final Rect guest = new Rect.fromLTRB(190.0, 85.0, 210.0, 105.0);
+      final Offset start = const Offset(180.0, 100.0);
+      final Offset end = const Offset(220.0, 100.0);
 
-      expect(
-        createNotchedRectangle(host, start.dx, end.dx, actualNotch),
-        coversSameAreaAs(
-          createNotchedRectangle(host, start.dx, end.dx, expectedNotch),
-          areaToCompare: guest.inflate(10.0),
-          sampleSize: 50,
-        )
+      final Path actualNotch = computeNotch(host, guest, start, end);
+      final Path notchedRectangle =
+        createNotchedRectangle(host, start.dx, end.dx, actualNotch);
+      expect(pathDoesNotContainCircle(notchedRectangle, guest.inflate(4.0)), isTrue);
+    });
+
+    testWidgets('notch circle center below BAB', (WidgetTester tester) async {
+      final ComputeNotch computeNotch = await fetchComputeNotch(tester,
+	const FloatingActionButton(onPressed: null, notchMargin: 4.0)
       );
+      final Rect host = new Rect.fromLTRB(0.0, 100.0, 300.0, 300.0);
+      final Rect guest = new Rect.fromLTRB(190.0, 95.0, 210.0, 115.0);
+      final Offset start = const Offset(180.0, 100.0);
+      final Offset end = const Offset(220.0, 100.0);
+
+      final Path actualNotch = computeNotch(host, guest, start, end);
+      final Path notchedRectangle =
+        createNotchedRectangle(host, start.dx, end.dx, actualNotch);
+      expect(pathDoesNotContainCircle(notchedRectangle, guest.inflate(4.0)), isTrue);
     });
+
+    testWidgets('no notch when there is no overlap', (WidgetTester tester) async {
+      final ComputeNotch computeNotch = await fetchComputeNotch(tester,
+	const FloatingActionButton(onPressed: null, notchMargin: 4.0)
+      );
+      final Rect host = new Rect.fromLTRB(0.0, 100.0, 300.0, 300.0);
+      final Rect guest = new Rect.fromLTRB(190.0, 40.0, 210.0, 60.0);
+      final Offset start = const Offset(180.0, 100.0);
+      final Offset end = const Offset(220.0, 100.0);
+
+      final Path actualNotch = computeNotch(host, guest, start, end);
+      final Path notchedRectangle =
+        createNotchedRectangle(host, start.dx, end.dx, actualNotch);
+      expect(pathDoesNotContainCircle(notchedRectangle, guest.inflate(4.0)), isTrue);
+    });
+
   });
+
 }
 
 Path createNotchedRectangle(Rect container, double startX, double endX, Path notch) {
@@ -393,3 +398,18 @@ class GeometryCachePainter extends CustomPainter {
     return true;
   }
 }
+
+bool pathDoesNotContainCircle(Path path, Rect circleBounds) {
+  assert(circleBounds.width == circleBounds.height);
+  final double radius = circleBounds.width / 2.0;
+
+  for (double theta = 0.0; theta <= 2.0 * math.PI; theta += math.PI / 20.0) {
+    for (double i = 0.0; i < 1; i += 0.01) {
+      final double x = i * radius * math.cos(theta);
+      final double y = i * radius * math.sin(theta);
+      if (path.contains(new Offset(x,y) + circleBounds.center))
+        return false;
+    }
+  }
+  return true;
+}