From c7024336d1ea81338ed802f6377d75ab0811fcc7 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergiusz=20Baza=C5=84ski?= <q3k@q3k.org>
Date: Mon, 25 Feb 2013 18:26:09 +0100
Subject: [PATCH] Use bezier curves to draw cables.

---
 main.js | 121 +++++++++++++++++++++++++++++++++++++-------------------
 1 file changed, 80 insertions(+), 41 deletions(-)

diff --git a/main.js b/main.js
index 2ad0334..097f45a 100644
--- a/main.js
+++ b/main.js
@@ -15,6 +15,7 @@ var Verlet = function(Width, Height)
     this.AddConstraint = function(Constraint)
     {
         this.Constraints.push(Constraint);
+        return Constraint;
     }
 
     this.Update = function(TimeDelta)
@@ -139,28 +140,75 @@ var Constraint = function(Mass1, Mass2)
     }
 }
 
+var Cable = function(Verlet, X1, Y1, X2, Y2, Steps)
+{
+    Steps = Steps || 10;
+    var StepX = (X2 - X1) / Steps;
+    var StepY = (Y2 - Y1) / Steps;
+
+    this.Masses = [];
+    var LastMass = v.AddMass(new Mass(X1, Y1, 0.5));
+    this.Masses.push(LastMass);
+    LastMass.Active = false;
+
+    for (var i = 1; i <= Steps; i++)
+    {
+        var NewMass = v.AddMass(new Mass(X1 + StepX * i, Y1 + StepY * i, 1));
+        this.Masses.push(NewMass);
+        v.AddConstraint(new Constraint(LastMass, NewMass));
+        LastMass = NewMass;
+    }
+
+    this.BinomialCache = {}
+    this.FastBinomial = function(n, k)
+    {
+        var key = n + ".." + k;
+        if (key in this.BinomialCache)
+            return this.BinomialCache[key];
+
+        function Factorial(num)
+        {
+            var rval=1;
+            for (var i = 2; i <= num; i++)
+                rval = rval * i;
+            return rval;
+        }  
+        return (Factorial(n) / (Factorial(k) * Factorial(n - k)));
+    }
+    this.Bezier = function(t)
+    {
+        var Points = this.Masses.length - 1;
+        var ValueX = 0;
+        var ValueY = 0;
+        for (var i = 0; i <= Points; i++)
+        {
+            var Coef = this.FastBinomial(Points, i) * Math.pow(1 -t, Points - i) * Math.pow(t, i);
+            ValueX += Coef * this.Masses[i].X;
+            ValueY += Coef * this.Masses[i].Y;
+        }
+
+        return {X: ValueX, Y: ValueY};
+    }
+
+    this.Render = function(context)
+    {
+        context.strokeStyle = '#FFFFFF';
+        context.beginPath();
+        var First = this.Bezier(0);
+        context.moveTo(First.X, First.Y);
+        for (var T = 1; T < 100; T++)
+        {
+            var t = T / 100;
+            var Next = this.Bezier(t);
+            context.lineTo(Next.X, Next.Y);
+        }
+        context.stroke();
+    }
+}
+
 var v = new Verlet(800, 600);
-var m1 = v.AddMass(new Mass( 5, 5, 1));
-var m2 = v.AddMass(new Mass(20, 5, 1));
-var m3 = v.AddMass(new Mass(35, 5, 1));
-var m4 = v.AddMass(new Mass(50, 5, 1));
-var m5 = v.AddMass(new Mass(65, 5, 1));
-var m6 = v.AddMass(new Mass(80, 5, 1));
-m6.Active = false;
+var cable = new Cable(v, 5, 5, 500, 5);
 
-var t1 = v.AddMass(new Mass(20, 15, 2));
-var t2 = v.AddMass(new Mass(0, 45, 2));
-var t3 = v.AddMass(new Mass(40, 45, 2));
-v.AddConstraint(new Constraint(m1, m2));
-v.AddConstraint(new Constraint(m2, m3));
-v.AddConstraint(new Constraint(m3, m4));
-v.AddConstraint(new Constraint(m4, m5));
-v.AddConstraint(new Constraint(m5, m6));
-
-v.AddConstraint(new Constraint(t1, t2));
-v.AddConstraint(new Constraint(t1, t3));
-v.AddConstraint(new Constraint(t3, t2));
-v.AddConstraint(new Constraint(m1, t1));
 
 var c = document.getElementById("main");
 var ctx = c.getContext('2d');
@@ -177,30 +225,21 @@ setInterval(function()
 
     v.Update(1/50);
 
+    cable.Render(ctx);
     ctx.fillStyle = '#FFFFFF';
-    for (k in v.Masses)
-    {
-        var m = v.Masses[k];
-        if (typeof(m) == "function")
-            continue;
 
-        ctx.beginPath();
-        ctx.arc(m.X, m.Y, 5, 0, Math.PI*2, true);
-        ctx.closePath();
-        ctx.fill();
-    }
-    ctx.strokeStyle = '#FFFFFF';
-    for (k in v.Constraints)
-    {
-        var c = v.Constraints[k];
-        if (typeof(c) == "function")
-            continue;
+    var First = v.Masses[0];
+    var Last = v.Masses[v.Masses.length - 1];
+    
+    ctx.beginPath();
+    ctx.arc(First.X, First.Y, 5, 0, Math.PI*2, true);
+    ctx.closePath();
+    ctx.fill();
 
-        ctx.beginPath();
-        ctx.moveTo(c.Mass1.X, c.Mass1.Y);
-        ctx.lineTo(c.Mass2.X, c.Mass2.Y);
-        ctx.stroke();
-    }
+    ctx.beginPath();
+    ctx.arc(Last.X, Last.Y, 5, 0, Math.PI*2, true);
+    ctx.closePath();
+    ctx.fill();
 }, 1000/50);