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verlet

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;(function(e,t,n){function i(n,s){if(!t[n]){if(!e[n]){var o=typeof require=="function"&&require;if(!s&&o)return o(n,!0);if(r)return r(n,!0);throw new Error("Cannot find module '"+n+"'")}var u=t[n]={exports:{}};e[n][0].call(u.exports,function(t){var r=e[n][1][t];return i(r?r:t)},u,u.exports)}return t[n].exports}var r=typeof require=="function"&&require;for(var s=0;s<n.length;s++)i(n[s]);return i})({1:[function(require,module,exports){ //this exports all the verlet methods globally, so that the demos work. var VerletJS = require('./verlet') var constraint = require('./constraint') require('./objects') //patches VerletJS.prototype (bad) window.Vec2 = require('./vec2') window.VerletJS = VerletJS window.Particle = VerletJS.Particle window.DistanceConstraint = constraint.DistanceConstraint window.PinConstraint = constraint.PinConstraint window.AngleConstraint = constraint.AngleConstraint },{"./verlet":2,"./constraint":3,"./objects":4,"./vec2":5}],3:[function(require,module,exports){ /* Copyright 2013 Sub Protocol and other contributors http://subprotocol.com/ Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */ // DistanceConstraint -- constrains to initial distance // PinConstraint -- constrains to static/fixed point // AngleConstraint -- constrains 3 particles to an angle exports.DistanceConstraint = DistanceConstraint exports.PinConstraint = PinConstraint exports.AngleConstraint = AngleConstraint function DistanceConstraint(a, b, stiffness, distance /*optional*/) { this.a = a; this.b = b; this.distance = typeof distance != "undefined" ? distance : a.pos.sub(b.pos).length(); this.stiffness = stiffness; } DistanceConstraint.prototype.relax = function(stepCoef) { var normal = this.a.pos.sub(this.b.pos); var m = normal.length2(); normal.mutableScale(((this.distance*this.distance - m)/m)*this.stiffness*stepCoef); this.a.pos.mutableAdd(normal); this.b.pos.mutableSub(normal); } DistanceConstraint.prototype.draw = function(ctx) { ctx.beginPath(); ctx.moveTo(this.a.pos.x, this.a.pos.y); ctx.lineTo(this.b.pos.x, this.b.pos.y); ctx.strokeStyle = "#d8dde2"; ctx.stroke(); } function PinConstraint(a, pos) { this.a = a; this.pos = (new Vec2()).mutableSet(pos); } PinConstraint.prototype.relax = function(stepCoef) { this.a.pos.mutableSet(this.pos); } PinConstraint.prototype.draw = function(ctx) { ctx.beginPath(); ctx.arc(this.pos.x, this.pos.y, 6, 0, 2*Math.PI); ctx.fillStyle = "rgba(0,153,255,0.1)"; ctx.fill(); } function AngleConstraint(a, b, c, stiffness) { this.a = a; this.b = b; this.c = c; this.angle = this.b.pos.angle2(this.a.pos, this.c.pos); this.stiffness = stiffness; } AngleConstraint.prototype.relax = function(stepCoef) { var angle = this.b.pos.angle2(this.a.pos, this.c.pos); var diff = angle - this.angle; if (diff <= -Math.PI) diff += 2*Math.PI; else if (diff >= Math.PI) diff -= 2*Math.PI; diff *= stepCoef*this.stiffness; this.a.pos = this.a.pos.rotate(this.b.pos, diff); this.c.pos = this.c.pos.rotate(this.b.pos, -diff); this.b.pos = this.b.pos.rotate(this.a.pos, diff); this.b.pos = this.b.pos.rotate(this.c.pos, -diff); } AngleConstraint.prototype.draw = function(ctx) { ctx.beginPath(); ctx.moveTo(this.a.pos.x, this.a.pos.y); ctx.lineTo(this.b.pos.x, this.b.pos.y); ctx.lineTo(this.c.pos.x, this.c.pos.y); var tmp = ctx.lineWidth; ctx.lineWidth = 5; ctx.strokeStyle = "rgba(255,255,0,0.2)"; ctx.stroke(); ctx.lineWidth = tmp; } },{}],5:[function(require,module,exports){ /* Copyright 2013 Sub Protocol and other contributors http://subprotocol.com/ Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */ // A simple 2-dimensional vector implementation module.exports = Vec2 function Vec2(x, y) { this.x = x || 0; this.y = y || 0; } Vec2.prototype.add = function(v) { return new Vec2(this.x + v.x, this.y + v.y); } Vec2.prototype.sub = function(v) { return new Vec2(this.x - v.x, this.y - v.y); } Vec2.prototype.mul = function(v) { return new Vec2(this.x * v.x, this.y * v.y); } Vec2.prototype.div = function(v) { return new Vec2(this.x / v.x, this.y / v.y); } Vec2.prototype.scale = function(coef) { return new Vec2(this.x*coef, this.y*coef); } Vec2.prototype.mutableSet = function(v) { this.x = v.x; this.y = v.y; return this; } Vec2.prototype.mutableAdd = function(v) { this.x += v.x; this.y += v.y; return this; } Vec2.prototype.mutableSub = function(v) { this.x -= v.x; this.y -= v.y; return this; } Vec2.prototype.mutableMul = function(v) { this.x *= v.x; this.y *= v.y; return this; } Vec2.prototype.mutableDiv = function(v) { this.x /= v.x; this.y /= v.y; return this; } Vec2.prototype.mutableScale = function(coef) { this.x *= coef; this.y *= coef; return this; } Vec2.prototype.equals = function(v) { return this.x == v.x && this.y == v.y; } Vec2.prototype.epsilonEquals = function(v, epsilon) { return Math.abs(this.x - v.x) <= epsilon && Math.abs(this.y - v.y) <= epsilon; } Vec2.prototype.length = function(v) { return Math.sqrt(this.x*this.x + this.y*this.y); } Vec2.prototype.length2 = function(v) { return this.x*this.x + this.y*this.y; } Vec2.prototype.dist = function(v) { return Math.sqrt(this.dist2(v)); } Vec2.prototype.dist2 = function(v) { var x = v.x - this.x; var y = v.y - this.y; return x*x + y*y; } Vec2.prototype.normal = function() { var m = Math.sqrt(this.x*this.x + this.y*this.y); return new Vec2(this.x/m, this.y/m); } Vec2.prototype.dot = function(v) { return this.x*v.x + this.y*v.y; } Vec2.prototype.angle = function(v) { return Math.atan2(this.x*v.y-this.y*v.x,this.x*v.x+this.y*v.y); } Vec2.prototype.angle2 = function(vLeft, vRight) { return vLeft.sub(this).angle(vRight.sub(this)); } Vec2.prototype.rotate = function(origin, theta) { var x = this.x - origin.x; var y = this.y - origin.y; return new Vec2(x*Math.cos(theta) - y*Math.sin(theta) + origin.x, x*Math.sin(theta) + y*Math.cos(theta) + origin.y); } Vec2.prototype.toString = function() { return "(" + this.x + ", " + this.y + ")"; } function test_Vec2() { var assert = function(label, expression) { console.log("Vec2(" + label + "): " + (expression == true ? "PASS" : "FAIL")); if (expression != true) throw "assertion failed"; }; assert("equality", (new Vec2(5,3).equals(new Vec2(5,3)))); assert("epsilon equality", (new Vec2(1,2).epsilonEquals(new Vec2(1.01,2.02), 0.03))); assert("epsilon non-equality", !(new Vec2(1,2).epsilonEquals(new Vec2(1.01,2.02), 0.01))); assert("addition", (new Vec2(1,1)).add(new Vec2(2, 3)).equals(new Vec2(3, 4))); assert("subtraction", (new Vec2(4,3)).sub(new Vec2(2, 1)).equals(new Vec2(2, 2))); assert("multiply", (new Vec2(2,4)).mul(new Vec2(2, 1)).equals(new Vec2(4, 4))); assert("divide", (new Vec2(4,2)).div(new Vec2(2, 2)).equals(new Vec2(2, 1))); assert("scale", (new Vec2(4,3)).scale(2).equals(new Vec2(8, 6))); assert("mutable set", (new Vec2(1,1)).mutableSet(new Vec2(2, 3)).equals(new Vec2(2, 3))); assert("mutable addition", (new Vec2(1,1)).mutableAdd(new Vec2(2, 3)).equals(new Vec2(3, 4))); assert("mutable subtraction", (new Vec2(4,3)).mutableSub(new Vec2(2, 1)).equals(new Vec2(2, 2))); assert("mutable multiply", (new Vec2(2,4)).mutableMul(new Vec2(2, 1)).equals(new Vec2(4, 4))); assert("mutable divide", (new Vec2(4,2)).mutableDiv(new Vec2(2, 2)).equals(new Vec2(2, 1))); assert("mutable scale", (new Vec2(4,3)).mutableScale(2).equals(new Vec2(8, 6))); assert("length", Math.abs((new Vec2(4,4)).length() - 5.65685) <= 0.00001); assert("length2", (new Vec2(2,4)).length2() == 20); assert("dist", Math.abs((new Vec2(2,4)).dist(new Vec2(3,5)) - 1.4142135) <= 0.000001); assert("dist2", (new Vec2(2,4)).dist2(new Vec2(3,5)) == 2); var normal = (new Vec2(2,4)).normal() assert("normal", Math.abs(normal.length() - 1.0) <= 0.00001 && normal.epsilonEquals(new Vec2(0.4472, 0.89443), 0.0001)); assert("dot", (new Vec2(2,3)).dot(new Vec2(4,1)) == 11); assert("angle", (new Vec2(0,-1)).angle(new Vec2(1,0))*(180/Math.PI) == 90); assert("angle2", (new Vec2(1,1)).angle2(new Vec2(1,0), new Vec2(2,1))*(180/Math.PI) == 90); assert("rotate", (new Vec2(2,0)).rotate(new Vec2(1,0), Math.PI/2).equals(new Vec2(1,1))); assert("toString", (new Vec2(2,4)) == "(2, 4)"); } },{}],4:[function(require,module,exports){ /* Copyright 2013 Sub Protocol and other contributors http://subprotocol.com/ Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */ // generic verlet entities var VerletJS = require('./verlet') var Particle = VerletJS.Particle var constraints = require('./constraint') var DistanceConstraint = constraints.DistanceConstraint VerletJS.prototype.point = function(pos) { var composite = new this.Composite(); composite.particles.push(new Particle(pos)); this.composites.push(composite); return composite; } VerletJS.prototype.lineSegments = function(vertices, stiffness) { var i; var composite = new this.Composite(); for (i in vertices) { composite.particles.push(new Particle(vertices[i])); if (i > 0) composite.constraints.push(new DistanceConstraint(composite.particles[i], composite.particles[i-1], stiffness)); } this.composites.push(composite); return composite; } VerletJS.prototype.cloth = function(origin, width, height, segments, pinMod, stiffness) { var composite = new this.Composite(); var xStride = width/segments; var yStride = height/segments; var x,y; for (y=0;y<segments;++y) { for (x=0;x<segments;++x) { var px = origin.x + x*xStride - width/2 + xStride/2; var py = origin.y + y*yStride - height/2 + yStride/2; composite.particles.push(new Particle(new Vec2(px, py))); if (x > 0) composite.constraints.push(new DistanceConstraint(composite.particles[y*segments+x], composite.particles[y*segments+x-1], stiffness)); if (y > 0) composite.constraints.push(new DistanceConstraint(composite.particles[y*segments+x], composite.particles[(y-1)*segments+x], stiffness)); } } for (x=0;x<segments;++x) { if (x%pinMod == 0) composite.pin(x); } this.composites.push(composite); return composite; } VerletJS.prototype.tire = function(origin, radius, segments, spokeStiffness, treadStiffness) { var stride = (2*Math.PI)/segments; var i; var composite = new this.Composite(); // particles for (i=0;i<segments;++i) { var theta = i*stride; composite.particles.push(new Particle(new Vec2(origin.x + Math.cos(theta)*radius, origin.y + Math.sin(theta)*radius))); } var center = new Particle(origin); composite.particles.push(center); // constraints for (i=0;i<segments;++i) { composite.constraints.push(new DistanceConstraint(composite.particles[i], composite.particles[(i+1)%segments], treadStiffness)); composite.constraints.push(new DistanceConstraint(composite.particles[i], center, spokeStiffness)) composite.constraints.push(new DistanceConstraint(composite.particles[i], composite.particles[(i+5)%segments], treadStiffness)); } this.composites.push(composite); return composite; } },{"./verlet":2,"./constraint":3}],2:[function(require,module,exports){ /* Copyright 2013 Sub Protocol and other contributors http://subprotocol.com/ Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */ window.requestAnimFrame = window.requestAnimationFrame || window.webkitRequestAnimationFrame || window.mozRequestAnimationFrame || window.oRequestAnimationFrame || window.msRequestAnimationFrame || function(callback) { window.setTimeout(callback, 1000 / 60); }; var Vec2 = require('./vec2') exports = module.exports = VerletJS exports.Particle = Particle exports.Composite = Composite function Particle(pos) { this.pos = (new Vec2()).mutableSet(pos); this.lastPos = (new Vec2()).mutableSet(pos); } Particle.prototype.draw = function(ctx) { ctx.beginPath(); ctx.arc(this.pos.x, this.pos.y, 2, 0, 2*Math.PI); ctx.fillStyle = "#2dad8f"; ctx.fill(); } function VerletJS(width, height, canvas) { this.width = width; this.height = height; this.canvas = canvas; this.ctx = canvas.getContext("2d"); this.mouse = new Vec2(0,0); this.mouseDown = false; this.draggedEntity = null; this.selectionRadius = 20; this.highlightColor = "#4f545c"; this.bounds = function (particle) { if (particle.pos.y > this.height-1) particle.pos.y = this.height-1; if (particle.pos.x < 0) particle.pos.x = 0; if (particle.pos.x > this.width-1) particle.pos.x = this.width-1; } var _this = this; // prevent context menu this.canvas.oncontextmenu = function(e) { e.preventDefault(); }; this.canvas.onmousedown = function(e) { _this.mouseDown = true; var nearest = _this.nearestEntity(); if (nearest) { _this.draggedEntity = nearest; } }; this.canvas.onmouseup = function(e) { _this.mouseDown = false; _this.draggedEntity = null; }; this.canvas.onmousemove = function(e) { var rect = _this.canvas.getBoundingClientRect(); _this.mouse.x = e.clientX - rect.left; _this.mouse.y = e.clientY - rect.top; }; // simulation params this.gravity = new Vec2(0,0.2); this.friction = 0.99; this.groundFriction = 0.8; // holds composite entities this.composites = []; } VerletJS.prototype.Composite = Composite function Composite() { this.particles = []; this.constraints = []; this.drawParticles = null; this.drawConstraints = null; } Composite.prototype.pin = function(index, pos) { pos = pos || this.particles[index].pos; var pc = new PinConstraint(this.particles[index], pos); this.constraints.push(pc); return pc; } VerletJS.prototype.frame = function(step) { var i, j, c; for (c in this.composites) { for (i in this.composites[c].particles) { var particles = this.composites[c].particles; // calculate velocity var velocity = particles[i].pos.sub(particles[i].lastPos).scale(this.friction); // ground friction if (particles[i].pos.y >= this.height-1 && velocity.length2() > 0.000001) { var m = velocity.length(); velocity.x /= m; velocity.y /= m; velocity.mutableScale(m*this.groundFriction); } // save last good state particles[i].lastPos.mutableSet(particles[i].pos); // gravity particles[i].pos.mutableAdd(this.gravity); // inertia particles[i].pos.mutableAdd(velocity); } } // handle dragging of entities if (this.draggedEntity) this.draggedEntity.pos.mutableSet(this.mouse); // relax var stepCoef = 1/step; for (c in this.composites) { var constraints = this.composites[c].constraints; for (i=0;i<step;++i) for (j in constraints) constraints[j].relax(stepCoef); } // bounds checking for (c in this.composites) { var particles = this.composites[c].particles; for (i in particles) this.bounds(particles[i]); } } VerletJS.prototype.draw = function() { var i, c; this.ctx.clearRect(0, 0, this.canvas.width, this.canvas.height); for (c in this.composites) { // draw constraints if (this.composites[c].drawConstraints) { this.composites[c].drawConstraints(this.ctx, this.composites[c]); } else { var constraints = this.composites[c].constraints; for (i in constraints) constraints[i].draw(this.ctx); } // draw particles if (this.composites[c].drawParticles) { this.composites[c].drawParticles(this.ctx, this.composites[c]); } else { var particles = this.composites[c].particles; for (i in particles) particles[i].draw(this.ctx); } } // highlight nearest / dragged entity var nearest = this.draggedEntity || this.nearestEntity(); if (nearest) { this.ctx.beginPath(); this.ctx.arc(nearest.pos.x, nearest.pos.y, 8, 0, 2*Math.PI); this.ctx.strokeStyle = this.highlightColor; this.ctx.stroke(); } } VerletJS.prototype.nearestEntity = function() { var c, i; var d2Nearest = 0; var entity = null; var constraintsNearest = null; // find nearest point for (c in this.composites) { var particles = this.composites[c].particles; for (i in particles) { var d2 = particles[i].pos.dist2(this.mouse); if (d2 <= this.selectionRadius*this.selectionRadius && (entity == null || d2 < d2Nearest)) { entity = particles[i]; constraintsNearest = this.composites[c].constraints; d2Nearest = d2; } } } // search for pinned constraints for this entity for (i in constraintsNearest) if (constraintsNearest[i] instanceof PinConstraint && constraintsNearest[i].a == entity) entity = constraintsNearest[i]; return entity; } },{"./vec2":5}]},{},[1]) //@ 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exports all the verlet methods globally, so that the demos work.\n\nvar VerletJS = require('./verlet')\nvar constraint = require('./constraint')\n\t\t\t\t\t\t\t\t require('./objects') //patches VerletJS.prototype (bad)\nwindow.Vec2 = require('./vec2')\nwindow.VerletJS = VerletJS\n\nwindow.Particle = VerletJS.Particle\n\nwindow.DistanceConstraint = constraint.DistanceConstraint\nwindow.PinConstraint      = constraint.PinConstraint\nwindow.AngleConstraint    = constraint.AngleConstraint\n\n\n","\n/*\nCopyright 2013 Sub Protocol and other contributors\nhttp://subprotocol.com/\n\nPermission is hereby granted, free of charge, to any person obtaining\na copy of this software and associated documentation files (the\n\"Software\"), to deal in the Software without restriction, including\nwithout limitation the rights to use, copy, modify, merge, publish,\ndistribute, sublicense, and/or sell copies of the Software, and to\npermit persons to whom the Software is furnished to do so, subject to\nthe following conditions:\n\nThe above copyright notice and this permission notice shall be\nincluded in all copies or substantial portions of the Software.\n\nTHE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND,\nEXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF\nMERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND\nNONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE\nLIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION\nOF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION\nWITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.\n*/\n\n// DistanceConstraint -- constrains to initial distance\n// PinConstraint -- constrains to static/fixed point\n// AngleConstraint -- constrains 3 particles to an angle\n\nexports.DistanceConstraint = DistanceConstraint\nexports.PinConstraint = PinConstraint\nexports.AngleConstraint = AngleConstraint\n\nfunction DistanceConstraint(a, b, stiffness, distance /*optional*/) {\n\tthis.a = a;\n\tthis.b = b;\n\tthis.distance = typeof distance != \"undefined\" ? distance : a.pos.sub(b.pos).length();\n\tthis.stiffness = stiffness;\n}\n\nDistanceConstraint.prototype.relax = function(stepCoef) {\n\tvar normal = this.a.pos.sub(this.b.pos);\n\tvar m = normal.length2();\n\tnormal.mutableScale(((this.distance*this.distance - m)/m)*this.stiffness*stepCoef);\n\tthis.a.pos.mutableAdd(normal);\n\tthis.b.pos.mutableSub(normal);\n}\n\nDistanceConstraint.prototype.draw = function(ctx) {\n\tctx.beginPath();\n\tctx.moveTo(this.a.pos.x, this.a.pos.y);\n\tctx.lineTo(this.b.pos.x, this.b.pos.y);\n\tctx.strokeStyle = \"#d8dde2\";\n\tctx.stroke();\n}\n\n\n\nfunction PinConstraint(a, pos) {\n\tthis.a = a;\n\tthis.pos = (new Vec2()).mutableSet(pos);\n}\n\nPinConstraint.prototype.relax = function(stepCoef) {\n\tthis.a.pos.mutableSet(this.pos);\n}\n\nPinConstraint.prototype.draw = function(ctx) {\n\tctx.beginPath();\n\tctx.arc(this.pos.x, this.pos.y, 6, 0, 2*Math.PI);\n\tctx.fillStyle = \"rgba(0,153,255,0.1)\";\n\tctx.fill();\n}\n\n\nfunction AngleConstraint(a, b, c, stiffness) {\n\tthis.a = a;\n\tthis.b = b;\n\tthis.c = c;\n\tthis.angle = this.b.pos.angle2(this.a.pos, this.c.pos);\n\tthis.stiffness = stiffness;\n}\n\nAngleConstraint.prototype.relax = function(stepCoef) {\n\tvar angle = this.b.pos.angle2(this.a.pos, this.c.pos);\n\tvar diff = angle - this.angle;\n\t\n\tif (diff <= -Math.PI)\n\t\tdiff += 2*Math.PI;\n\telse if (diff >= Math.PI)\n\t\tdiff -= 2*Math.PI;\n\n\tdiff *= stepCoef*this.stiffness;\n\t\n\tthis.a.pos = this.a.pos.rotate(this.b.pos, diff);\n\tthis.c.pos = this.c.pos.rotate(this.b.pos, -diff);\n\tthis.b.pos = this.b.pos.rotate(this.a.pos, diff);\n\tthis.b.pos = this.b.pos.rotate(this.c.pos, -diff);\n}\n\nAngleConstraint.prototype.draw = function(ctx) {\n\tctx.beginPath();\n\tctx.moveTo(this.a.pos.x, this.a.pos.y);\n\tctx.lineTo(this.b.pos.x, this.b.pos.y);\n\tctx.lineTo(this.c.pos.x, this.c.pos.y);\n\tvar tmp = ctx.lineWidth;\n\tctx.lineWidth = 5;\n\tctx.strokeStyle = \"rgba(255,255,0,0.2)\";\n\tctx.stroke();\n\tctx.lineWidth = tmp;\n}\n","\n/*\nCopyright 2013 Sub Protocol and other contributors\nhttp://subprotocol.com/\n\nPermission is hereby granted, free of charge, to any person obtaining\na copy of this software and associated documentation files (the\n\"Software\"), to deal in the Software without restriction, including\nwithout limitation the rights to use, copy, modify, merge, publish,\ndistribute, sublicense, and/or sell copies of the Software, and to\npermit persons to whom the Software is furnished to do so, subject to\nthe following conditions:\n\nThe above copyright notice and this permission notice shall be\nincluded in all copies or substantial portions of the Software.\n\nTHE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND,\nEXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF\nMERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND\nNONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE\nLIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION\nOF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION\nWITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.\n*/\n\n// A simple 2-dimensional vector implementation\n\nmodule.exports = Vec2\n\nfunction Vec2(x, y) {\n\tthis.x = x || 0;\n\tthis.y = y || 0;\n}\n\nVec2.prototype.add = function(v) {\n\treturn new Vec2(this.x + v.x, this.y + v.y);\n}\n\nVec2.prototype.sub = function(v) {\n\treturn new Vec2(this.x - v.x, this.y - v.y);\n}\n\nVec2.prototype.mul = function(v) {\n\treturn new Vec2(this.x * v.x, this.y * v.y);\n}\n\nVec2.prototype.div = function(v) {\n\treturn new Vec2(this.x / v.x, this.y / v.y);\n}\n\nVec2.prototype.scale = function(coef) {\n\treturn new Vec2(this.x*coef, this.y*coef);\n}\n\nVec2.prototype.mutableSet = function(v) {\n\tthis.x = v.x;\n\tthis.y = v.y;\n\treturn this;\n}\n\nVec2.prototype.mutableAdd = function(v) {\n\tthis.x += v.x;\n\tthis.y += v.y;\n\treturn this;\n}\n\nVec2.prototype.mutableSub = function(v) {\n\tthis.x -= v.x;\n\tthis.y -= v.y;\n\treturn this;\n}\n\nVec2.prototype.mutableMul = function(v) {\n\tthis.x *= v.x;\n\tthis.y *= v.y;\n\treturn this;\n}\n\nVec2.prototype.mutableDiv = function(v) {\n\tthis.x /= v.x;\n\tthis.y /= v.y;\n\treturn this;\n}\n\nVec2.prototype.mutableScale = function(coef) {\n\tthis.x *= coef;\n\tthis.y *= coef;\n\treturn this;\n}\n\nVec2.prototype.equals = function(v) {\n\treturn this.x == v.x && this.y == v.y;\n}\n\nVec2.prototype.epsilonEquals = function(v, epsilon) {\n\treturn Math.abs(this.x - v.x) <= epsilon && Math.abs(this.y - v.y) <= epsilon;\n}\n\nVec2.prototype.length = function(v) {\n\treturn Math.sqrt(this.x*this.x + this.y*this.y);\n}\n\nVec2.prototype.length2 = function(v) {\n\treturn this.x*this.x + this.y*this.y;\n}\n\nVec2.prototype.dist = function(v) {\n\treturn Math.sqrt(this.dist2(v));\n}\n\nVec2.prototype.dist2 = function(v) {\n\tvar x = v.x - this.x;\n\tvar y = v.y - this.y;\n\treturn x*x + y*y;\n}\n\nVec2.prototype.normal = function() {\n\tvar m = Math.sqrt(this.x*this.x + this.y*this.y);\n\treturn new Vec2(this.x/m, this.y/m);\n}\n\nVec2.prototype.dot = function(v) {\n\treturn this.x*v.x + this.y*v.y;\n}\n\nVec2.prototype.angle = function(v) {\n\treturn Math.atan2(this.x*v.y-this.y*v.x,this.x*v.x+this.y*v.y);\n}\n\nVec2.prototype.angle2 = function(vLeft, vRight) {\n\treturn vLeft.sub(this).angle(vRight.sub(this));\n}\n\nVec2.prototype.rotate = function(origin, theta) {\n\tvar x = this.x - origin.x;\n\tvar y = this.y - origin.y;\n\treturn new Vec2(x*Math.cos(theta) - y*Math.sin(theta) + origin.x, x*Math.sin(theta) + y*Math.cos(theta) + origin.y);\n}\n\nVec2.prototype.toString = function() {\n\treturn \"(\" + this.x + \", \" + this.y + \")\";\n}\n\nfunction test_Vec2() {\n\tvar assert = function(label, expression) {\n\t\tconsole.log(\"Vec2(\" + label + \"): \" + (expression == true ? \"PASS\" : \"FAIL\"));\n\t\tif (expression != true)\n\t\t\tthrow \"assertion failed\";\n\t};\n\t\n\tassert(\"equality\", (new Vec2(5,3).equals(new Vec2(5,3))));\n\tassert(\"epsilon equality\", (new Vec2(1,2).epsilonEquals(new Vec2(1.01,2.02), 0.03)));\n\tassert(\"epsilon non-equality\", !(new Vec2(1,2).epsilonEquals(new Vec2(1.01,2.02), 0.01)));\n\tassert(\"addition\", (new Vec2(1,1)).add(new Vec2(2, 3)).equals(new Vec2(3, 4)));\n\tassert(\"subtraction\", (new Vec2(4,3)).sub(new Vec2(2, 1)).equals(new Vec2(2, 2)));\n\tassert(\"multiply\", (new Vec2(2,4)).mul(new Vec2(2, 1)).equals(new Vec2(4, 4)));\n\tassert(\"divide\", (new Vec2(4,2)).div(new Vec2(2, 2)).equals(new Vec2(2, 1)));\n\tassert(\"scale\", (new Vec2(4,3)).scale(2).equals(new Vec2(8, 6)));\n\tassert(\"mutable set\", (new Vec2(1,1)).mutableSet(new Vec2(2, 3)).equals(new Vec2(2, 3)));\n\tassert(\"mutable addition\", (new Vec2(1,1)).mutableAdd(new Vec2(2, 3)).equals(new Vec2(3, 4)));\n\tassert(\"mutable subtraction\", (new Vec2(4,3)).mutableSub(new Vec2(2, 1)).equals(new Vec2(2, 2)));\n\tassert(\"mutable multiply\", (new Vec2(2,4)).mutableMul(new Vec2(2, 1)).equals(new Vec2(4, 4)));\n\tassert(\"mutable divide\", (new Vec2(4,2)).mutableDiv(new Vec2(2, 2)).equals(new Vec2(2, 1)));\n\tassert(\"mutable scale\", (new Vec2(4,3)).mutableScale(2).equals(new Vec2(8, 6)));\n\tassert(\"length\", Math.abs((new Vec2(4,4)).length() - 5.65685) <= 0.00001);\n\tassert(\"length2\", (new Vec2(2,4)).length2() == 20);\n\tassert(\"dist\", Math.abs((new Vec2(2,4)).dist(new Vec2(3,5)) - 1.4142135) <= 0.000001);\n\tassert(\"dist2\", (new Vec2(2,4)).dist2(new Vec2(3,5)) == 2);\n\n\tvar normal = (new Vec2(2,4)).normal()\n\tassert(\"normal\", Math.abs(normal.length() - 1.0) <= 0.00001 && normal.epsilonEquals(new Vec2(0.4472, 0.89443), 0.0001));\n\tassert(\"dot\", (new Vec2(2,3)).dot(new Vec2(4,1)) == 11);\n\tassert(\"angle\", (new Vec2(0,-1)).angle(new Vec2(1,0))*(180/Math.PI) == 90);\n\tassert(\"angle2\", (new Vec2(1,1)).angle2(new Vec2(1,0), new Vec2(2,1))*(180/Math.PI) == 90);\n\tassert(\"rotate\", (new Vec2(2,0)).rotate(new Vec2(1,0), Math.PI/2).equals(new Vec2(1,1)));\n\tassert(\"toString\", (new Vec2(2,4)) == \"(2, 4)\");\n}\n\n","\n/*\nCopyright 2013 Sub Protocol and other contributors\nhttp://subprotocol.com/\n\nPermission is hereby granted, free of charge, to any person obtaining\na copy of this software and associated documentation files (the\n\"Software\"), to deal in the Software without restriction, including\nwithout limitation the rights to use, copy, modify, merge, publish,\ndistribute, sublicense, and/or sell copies of the Software, and to\npermit persons to whom the Software is furnished to do so, subject to\nthe following conditions:\n\nThe above copyright notice and this permission notice shall be\nincluded in all copies or substantial portions of the Software.\n\nTHE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND,\nEXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF\nMERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND\nNONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE\nLIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION\nOF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION\nWITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.\n*/\n\n// generic verlet entities\n\nvar VerletJS = require('./verlet')\nvar Particle = VerletJS.Particle\nvar constraints = require('./constraint')\nvar DistanceConstraint = constraints.DistanceConstraint\n\nVerletJS.prototype.point = function(pos) {\n\tvar composite = new this.Composite();\n\tcomposite.particles.push(new Particle(pos));\n\tthis.composites.push(composite);\n\treturn composite;\n}\n\nVerletJS.prototype.lineSegments = function(vertices, stiffness) {\n\tvar i;\n\t\n\tvar composite = new this.Composite();\n\t\n\tfor (i in vertices) {\n\t\tcomposite.particles.push(new Particle(vertices[i]));\n\t\tif (i > 0)\n\t\t\tcomposite.constraints.push(new DistanceConstraint(composite.particles[i], composite.particles[i-1], stiffness));\n\t}\n\t\n\tthis.composites.push(composite);\n\treturn composite;\n}\n\nVerletJS.prototype.cloth = function(origin, width, height, segments, pinMod, stiffness) {\n\t\n\tvar composite = new this.Composite();\n\t\n\tvar xStride = width/segments;\n\tvar yStride = height/segments;\n\t\n\tvar x,y;\n\tfor (y=0;y<segments;++y) {\n\t\tfor (x=0;x<segments;++x) {\n\t\t\tvar px = origin.x + x*xStride - width/2 + xStride/2;\n\t\t\tvar py = origin.y + y*yStride - height/2 + yStride/2;\n\t\t\tcomposite.particles.push(new Particle(new Vec2(px, py)));\n\t\t\t\n\t\t\tif (x > 0)\n\t\t\t\tcomposite.constraints.push(new DistanceConstraint(composite.particles[y*segments+x], composite.particles[y*segments+x-1], stiffness));\n\t\t\t\n\t\t\tif (y > 0)\n\t\t\t\tcomposite.constraints.push(new DistanceConstraint(composite.particles[y*segments+x], composite.particles[(y-1)*segments+x], stiffness));\n\t\t}\n\t}\n\t\n\tfor (x=0;x<segments;++x) {\n\t\tif (x%pinMod == 0)\n\t\tcomposite.pin(x);\n\t}\n\t\n\tthis.composites.push(composite);\n\treturn composite;\n}\n\nVerletJS.prototype.tire = function(origin, radius, segments, spokeStiffness, treadStiffness) {\n\tvar stride = (2*Math.PI)/segments;\n\tvar i;\n\t\n\tvar composite = new this.Composite();\n\t\n\t// particles\n\tfor (i=0;i<segments;++i) {\n\t\tvar theta = i*stride;\n\t\tcomposite.particles.push(new Particle(new Vec2(origin.x + Math.cos(theta)*radius, origin.y + Math.sin(theta)*radius)));\n\t}\n\t\n\tvar center = new Particle(origin);\n\tcomposite.particles.push(center);\n\t\n\t// constraints\n\tfor (i=0;i<segments;++i) {\n\t\tcomposite.constraints.push(new DistanceConstraint(composite.particles[i], composite.particles[(i+1)%segments], treadStiffness));\n\t\tcomposite.constraints.push(new DistanceConstraint(composite.particles[i], center, spokeStiffness))\n\t\tcomposite.constraints.push(new DistanceConstraint(composite.particles[i], composite.particles[(i+5)%segments], treadStiffness));\n\t}\n\t\t\n\tthis.composites.push(composite);\n\treturn composite;\n}\n\n","\n/*\nCopyright 2013 Sub Protocol and other contributors\nhttp://subprotocol.com/\n\nPermission is hereby granted, free of charge, to any person obtaining\na copy of this software and associated documentation files (the\n\"Software\"), to deal in the Software without restriction, including\nwithout limitation the rights to use, copy, modify, merge, publish,\ndistribute, sublicense, and/or sell copies of the Software, and to\npermit persons to whom the Software is furnished to do so, subject to\nthe following conditions:\n\nThe above copyright notice and this permission notice shall be\nincluded in all copies or substantial portions of the Software.\n\nTHE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND,\nEXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF\nMERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND\nNONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE\nLIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION\nOF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION\nWITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.\n*/\n\nwindow.requestAnimFrame = window.requestAnimationFrame\n|| window.webkitRequestAnimationFrame\n|| window.mozRequestAnimationFrame\n|| window.oRequestAnimationFrame\n|| window.msRequestAnimationFrame\n|| function(callback) {\n\twindow.setTimeout(callback, 1000 / 60);\n};\n\nvar Vec2 = require('./vec2')\n\nexports = module.exports = VerletJS\nexports.Particle = Particle\nexports.Composite = Composite\n\nfunction Particle(pos) {\n\tthis.pos = (new Vec2()).mutableSet(pos);\n\tthis.lastPos = (new Vec2()).mutableSet(pos);\n}\n\nParticle.prototype.draw = function(ctx) {\n\tctx.beginPath();\n\tctx.arc(this.pos.x, this.pos.y, 2, 0, 2*Math.PI);\n\tctx.fillStyle = \"#2dad8f\";\n\tctx.fill();\n}\n\nfunction VerletJS(width, height, canvas) {\n\tthis.width = width;\n\tthis.height = height;\n\tthis.canvas = canvas;\n\tthis.ctx = canvas.getContext(\"2d\");\n\tthis.mouse = new Vec2(0,0);\n\tthis.mouseDown = false;\n\tthis.draggedEntity = null;\n\tthis.selectionRadius = 20;\n\tthis.highlightColor = \"#4f545c\";\n\t\n\tthis.bounds = function (particle) {\n\t\tif (particle.pos.y > this.height-1)\n\t\t\tparticle.pos.y = this.height-1;\n\t\t\n\t\tif (particle.pos.x < 0)\n\t\t\tparticle.pos.x = 0;\n\n\t\tif (particle.pos.x > this.width-1)\n\t\t\tparticle.pos.x = this.width-1;\n\t}\n\t\n\tvar _this = this;\n\t\n\t// prevent context menu\n\tthis.canvas.oncontextmenu = function(e) {\n\t\te.preventDefault();\n\t};\n\t\n\tthis.canvas.onmousedown = function(e) {\n\t\t_this.mouseDown = true;\n\t\tvar nearest = _this.nearestEntity();\n\t\tif (nearest) {\n\t\t\t_this.draggedEntity = nearest;\n\t\t}\n\t};\n\t\n\tthis.canvas.onmouseup = function(e) {\n\t\t_this.mouseDown = false;\n\t\t_this.draggedEntity = null;\n\t};\n\t\n\tthis.canvas.onmousemove = function(e) {\n\t\tvar rect = _this.canvas.getBoundingClientRect();\n\t\t_this.mouse.x = e.clientX - rect.left;\n\t\t_this.mouse.y = e.clientY - rect.top;\n\t};  \n\t\n\t// simulation params\n\tthis.gravity = new Vec2(0,0.2);\n\tthis.friction = 0.99;\n\tthis.groundFriction = 0.8;\n\t\n\t// holds composite entities\n\tthis.composites = [];\n}\n\nVerletJS.prototype.Composite = Composite\n\nfunction Composite() {\n\tthis.particles = [];\n\tthis.constraints = [];\n\t\n\tthis.drawParticles = null;\n\tthis.drawConstraints = null;\n}\n\nComposite.prototype.pin = function(index, pos) {\n\tpos = pos || this.particles[index].pos;\n\tvar pc = new PinConstraint(this.particles[index], pos);\n\tthis.constraints.push(pc);\n\treturn pc;\n}\n\nVerletJS.prototype.frame = function(step) {\n\tvar i, j, c;\n\n\tfor (c in this.composites) {\n\t\tfor (i in this.composites[c].particles) {\n\t\t\tvar particles = this.composites[c].particles;\n\t\t\t\n\t\t\t// calculate velocity\n\t\t\tvar velocity = particles[i].pos.sub(particles[i].lastPos).scale(this.friction);\n\t\t\n\t\t\t// ground friction\n\t\t\tif (particles[i].pos.y >= this.height-1 && velocity.length2() > 0.000001) {\n\t\t\t\tvar m = velocity.length();\n\t\t\t\tvelocity.x /= m;\n\t\t\t\tvelocity.y /= m;\n\t\t\t\tvelocity.mutableScale(m*this.groundFriction);\n\t\t\t}\n\t\t\n\t\t\t// save last good state\n\t\t\tparticles[i].lastPos.mutableSet(particles[i].pos);\n\t\t\n\t\t\t// gravity\n\t\t\tparticles[i].pos.mutableAdd(this.gravity);\n\t\t\n\t\t\t// inertia  \n\t\t\tparticles[i].pos.mutableAdd(velocity);\n\t\t}\n\t}\n\t\n\t// handle dragging of entities\n\tif (this.draggedEntity)\n\t\tthis