[Gallery] Fix directory structure (#312)

gallery/lib/demos/reference/transformations_demo_inertial_motion.dart

@@ -0,0 +1,72 @@
+// Copyright 2019 The Flutter team. 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';
+import 'package:flutter/material.dart';
+import 'package:vector_math/vector_math.dart' show Vector2;
+
+// Provides calculations for an object moving with inertia and friction using
+// the equation of motion from physics.
+// https://en.wikipedia.org/wiki/Equations_of_motion#Constant_translational_acceleration_in_a_straight_line
+// TODO(justinmc): Can this be replaced with friction_simulation.dart?
+@immutable
+class InertialMotion {
+  const InertialMotion(this._initialVelocity, this._initialPosition);
+
+  static const double _kFrictionalAcceleration = 0.01; // How quickly to stop
+  final Velocity _initialVelocity;
+  final Offset _initialPosition;
+
+  // The position when the motion stops.
+  Offset get finalPosition {
+    return _getPositionAt(Duration(milliseconds: duration.toInt()));
+  }
+
+  // The total time that the animation takes start to stop in milliseconds.
+  double get duration {
+    return (_initialVelocity.pixelsPerSecond.dx / 1000 / _acceleration.x).abs();
+  }
+
+  // The acceleration opposing the initial velocity in x and y components.
+  Vector2 get _acceleration {
+    // TODO(justinmc): Find actual velocity instead of summing?
+    final velocityTotal = _initialVelocity.pixelsPerSecond.dx.abs() +
+        _initialVelocity.pixelsPerSecond.dy.abs();
+    final vRatioX = _initialVelocity.pixelsPerSecond.dx / velocityTotal;
+    final vRatioY = _initialVelocity.pixelsPerSecond.dy / velocityTotal;
+    return Vector2(
+      _kFrictionalAcceleration * vRatioX,
+      _kFrictionalAcceleration * vRatioY,
+    );
+  }
+
+  // The position at a given time.
+  Offset _getPositionAt(Duration time) {
+    final xf = _getPosition(
+      r0: _initialPosition.dx,
+      v0: _initialVelocity.pixelsPerSecond.dx / 1000,
+      t: time.inMilliseconds,
+      a: _acceleration.x,
+    );
+    final yf = _getPosition(
+      r0: _initialPosition.dy,
+      v0: _initialVelocity.pixelsPerSecond.dy / 1000,
+      t: time.inMilliseconds,
+      a: _acceleration.y,
+    );
+    return Offset(xf, yf);
+  }
+
+  // Solve the equation of motion to find the position at a given point in time
+  // in one dimension.
+  double _getPosition({double r0, double v0, int t, double a}) {
+    // Stop movement when it would otherwise reverse direction.
+    final stopTime = (v0 / a).abs();
+    if (t > stopTime) {
+      t = stopTime.toInt();
+    }
+
+    return r0 + v0 * t + 0.5 * a * pow(t, 2);
+  }
+}