using System; using Unity.UIWidgets.foundation; namespace Unity.UIWidgets.physics { public class SpringDescription { public SpringDescription( double mass, double stiffness, double damping ) { this.mass = mass; this.stiffness = stiffness; this.damping = damping; } public static SpringDescription withDampingRatio( double mass, double stiffness, double ratio = 1.0 ) { var damping = ratio * 2.0 * Math.Sqrt(mass * stiffness); return new SpringDescription(mass, stiffness, damping); } public readonly double mass; public readonly double stiffness; public readonly double damping; public override string ToString() { return $"{this.GetType()}(mass {this.mass:F1}, stiffness: {this.stiffness:F1}, damping: {this.damping:F1})"; } } public enum SpringType { criticallyDamped, underDamped, overDamped, } public class SpringSimulation : Simulation { public SpringSimulation( SpringDescription spring, double start, double end, double velocity, Tolerance tolerance = null ) : base(tolerance: tolerance) { this._endPosition = end; this._solution = _SpringSolution.create(spring, start - end, velocity); } protected readonly double _endPosition; readonly _SpringSolution _solution; public SpringType type { get { return this._solution.type; } } public override double x(double time) { return this._endPosition + this._solution.x(time); } public override double dx(double time) { return this._solution.dx(time); } public override bool isDone(double time) { return PhysicsUtils.nearZero(this._solution.x(time), this.tolerance.distance) && PhysicsUtils.nearZero(this._solution.dx(time), this.tolerance.velocity); } public override string ToString() { return $"{this.GetType()}(end: {this._endPosition}, {this.type}"; } } public class ScrollSpringSimulation : SpringSimulation { public ScrollSpringSimulation( SpringDescription spring, double start, double end, double velocity, Tolerance tolerance = null ) : base(spring, start, end, velocity, tolerance: tolerance) { } public override double x(double time) { return this.isDone(time) ? this._endPosition : base.x(time); } } abstract class _SpringSolution { internal static _SpringSolution create( SpringDescription spring, double initialPosition, double initialVelocity ) { D.assert(spring != null); double cmk = spring.damping * spring.damping - 4 * spring.mass * spring.stiffness; if (cmk == 0.0) { return _CriticalSolution.create(spring, initialPosition, initialVelocity); } if (cmk > 0.0) { return _OverdampedSolution.create(spring, initialPosition, initialVelocity); } return _UnderdampedSolution.create(spring, initialPosition, initialVelocity); } public abstract double x(double time); public abstract double dx(double time); public abstract SpringType type { get; } } class _CriticalSolution : _SpringSolution { internal new static _CriticalSolution create( SpringDescription spring, double distance, double velocity ) { double r = -spring.damping / (2.0 * spring.mass); double c1 = distance; double c2 = velocity / (r * distance); return new _CriticalSolution(r, c1, c2); } _CriticalSolution( double r, double c1, double c2 ) { this._r = r; this._c1 = c1; this._c2 = c2; } readonly double _r, _c1, _c2; public override double x(double time) { return (this._c1 + this._c2 * time) * Math.Pow(Math.E, this._r * time); } public override double dx(double time) { double power = Math.Pow(Math.E, this._r * time); return this._r * (this._c1 + this._c2 * time) * power + this._c2 * power; } public override SpringType type { get { return SpringType.criticallyDamped; } } } class _OverdampedSolution : _SpringSolution { internal new static _OverdampedSolution create( SpringDescription spring, double distance, double velocity ) { double cmk = spring.damping * spring.damping - 4 * spring.mass * spring.stiffness; double r1 = (-spring.damping - Math.Sqrt(cmk)) / (2.0 * spring.mass); double r2 = (-spring.damping + Math.Sqrt(cmk)) / (2.0 * spring.mass); double c2 = (velocity - r1 * distance) / (r2 - r1); double c1 = distance - c2; return new _OverdampedSolution(r1, r2, c1, c2); } _OverdampedSolution( double r1, double r2, double c1, double c2 ) { this._r1 = r1; this._r2 = r2; this._c1 = c1; this._c2 = c2; } readonly double _r1, _r2, _c1, _c2; public override double x(double time) { return this._c1 * Math.Pow(Math.E, this._r1 * time) + this._c2 * Math.Pow(Math.E, this._r2 * time); } public override double dx(double time) { return this._c1 * this._r1 * Math.Pow(Math.E, this._r1 * time) + this._c2 * this._r2 * Math.Pow(Math.E, this._r2 * time); } public override SpringType type { get { return SpringType.overDamped; } } } class _UnderdampedSolution : _SpringSolution { internal new static _UnderdampedSolution create( SpringDescription spring, double distance, double velocity ) { double w = Math.Sqrt(4.0 * spring.mass * spring.stiffness - spring.damping * spring.damping) / (2.0 * spring.mass); double r = -(spring.damping / 2.0 * spring.mass); double c1 = distance; double c2 = (velocity - r * distance) / w; return new _UnderdampedSolution(w, r, c1, c2); } _UnderdampedSolution( double w, double r, double c1, double c2 ) { this._w = w; this._r = r; this._c1 = c1; this._c2 = c2; } readonly double _w, _r, _c1, _c2; public override double x(double time) { return Math.Pow(Math.E, this._r * time) * (this._c1 * Math.Cos(this._w * time) + this._c2 * Math.Sin(this._w * time)); } public override double dx(double time) { double power = Math.Pow(Math.E, this._r * time); double cosine = Math.Cos(this._w * time); double sine = Math.Sin(this._w * time); return power * (this._c2 * this._w * cosine - this._c1 * this._w * sine) + this._r * power * (this._c2 * sine + this._c1 * cosine); } public override SpringType type { get { return SpringType.underDamped; } } } }