新增verlet物理引擎（实验性）

source/src/Physics/Verlet/Composites/Ball.ts

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+///<reference path="./Composite.ts" />
+module es {
+    export class Ball extends Composite {
+        constructor(position: Vector2, radius: number = 10) {
+            super();
+            this.addParticle(new Particle(position)).radius = radius;
+        }
+    }
+}

source/src/Physics/Verlet/Composites/Box.ts

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+///<reference path="./Composite.ts" />
+module es {
+    export class VerletBox extends es.Composite {
+        constructor(center: es.Vector2, width: number, height: number, borderStiffness: number = 0.2, diagonalStiffness: number = 0.5) {
+            super();
+
+            const tl = this.addParticle(new Particle(center.add(new Vector2(-width / 2, -height / 2))));
+            const tr = this.addParticle(new Particle(center.add(new Vector2(width / 2, -height / 2))));
+            const br = this.addParticle(new Particle(center.add(new Vector2(width / 2, height / 2))));
+            const bl = this.addParticle(new Particle(center.add(new Vector2(-width / 2, height / 2))));
+
+            this.addConstraint(new DistanceConstraint(tl, tr, borderStiffness));
+            this.addConstraint(new DistanceConstraint(tr, br, borderStiffness));
+            this.addConstraint(new DistanceConstraint(br, bl, borderStiffness));
+            this.addConstraint(new DistanceConstraint(bl, tl, borderStiffness));
+
+            this.addConstraint(new DistanceConstraint(tl, br, diagonalStiffness))
+                .setCollidesWithColliders(false);
+            this.addConstraint(new DistanceConstraint(bl, tr, diagonalStiffness))
+                .setCollidesWithColliders(false);
+        }
+    }
+}

source/src/Physics/Verlet/Composites/Composite.ts

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+module es {
+    export class Composite {
+        public friction: Vector2 = new Vector2(0.98, 1);
+        public drawParticles: boolean = true;
+        public drawConstraints: boolean = true;
+        public collidesWithLayers: number = Physics.allLayers;
+        public particles: Particle[] = [];
+        _constraints: Constraint[] = [];
+
+        public addParticle(particle: Particle): Particle {
+            this.particles.push(particle);
+            return particle;
+        }
+
+        public removeParticle(particle: Particle) {
+            const index = this.particles.indexOf(particle);
+            this.particles.splice(index, 1);
+        }
+
+        public removeAll() {
+            this.particles.length = 0;
+            this._constraints.length = 0;
+        }
+
+        public addConstraint<T extends Constraint>(constraint: T): T {
+            this._constraints.push(constraint);
+            constraint.composite = this;
+            return constraint;
+        }
+
+        public removeConstraint(constraint: Constraint) {
+            const index = this._constraints.indexOf(constraint);
+            this._constraints.splice(index, 1);
+        }
+
+        public applyForce(force: Vector2) {
+            for (let j = 0; j < this.particles.length; j ++)
+                this.particles[j].applyForce(force);
+        }
+
+        public solveConstraints() {
+            for (let i = this._constraints.length - 1; i >= 0; i --)
+                this._constraints[i].solve();
+        }
+
+        public updateParticles(deltaTimeSquared: number, gravity: Vector2) {
+            for (let j = 0; j < this.particles.length; j ++) {
+                const p = this.particles[j];
+                if (p.isPinned) {
+                    p.position = p.pinnedPosition;
+                    continue;
+                }
+
+                p.applyForce(gravity.scale(p.mass));
+
+                const vel = p.position.sub(p.lastPosition).multiply(this.friction);
+                const nextPos = p.position.add(vel).add(p.acceleration.scale(0.5 * deltaTimeSquared));
+
+                p.lastPosition = p.position;
+                p.position = nextPos;
+                p.acceleration.x = p.acceleration.y = 0;
+            }
+        }
+
+        public handleConstraintCollisions() {
+            for (let i = this._constraints.length - 1; i >= 0; i --) {
+                if (this._constraints[i].collidesWithColliders)
+                    this._constraints[i].handleCollisions(this.collidesWithLayers);
+            }
+        }
+
+        public debugRender(batcher: IBatcher) {
+            if (this.drawConstraints) {
+                for (let i = 0; i < this._constraints.length; i ++)
+                    this._constraints[i].debugRender(batcher);
+            }
+
+            if (this.drawParticles) {
+                for (let i = 0; i < this.particles.length; i ++) {
+                    if (this.particles[i].radius == 0) 
+                        batcher.drawPixel(this.particles[i].position, new Color(220, 52, 94), 4);
+                    else
+                        batcher.drawCircleLow(this.particles[i].position, this.particles[i].radius, new Color(220, 52, 94), 1, 4);
+                }
+            }
+        }
+    }
+}

source/src/Physics/Verlet/Composites/LineSegments.ts

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+module es {
+    export class LineSegments extends Composite {
+        constructor(vertices: Vector2[], stiffness: number) {
+            super();
+
+            for (let i = 0; i < vertices.length; i ++) {
+                const p = new Particle(vertices[i]);
+                this.addParticle(p);
+
+                if (i > 0)
+                    this.addConstraint(new DistanceConstraint(this.particles[i], this.particles[i - 1], stiffness));
+            }
+        }
+
+        public pinParticleAtIndex(index: number): LineSegments {
+            this.particles[index].pin();
+            return this;
+        }
+    }
+}