Added fixed point drawing

js/mobius.js

@@ -94,6 +94,14 @@ function update_vector_field(a,b,c,d){
             ctx.stroke();
         }   
     }
+    fp = fixedpts(a,b,c,d);
+    ctx.beginPath();
+    ctx.arc(remap(fp[0].re,-2,2,0,600),remap(fp[0].im,-2,2,600,0),5,0,Math.PI*2);
+    ctx.stroke();
+
+    ctx.beginPath();
+    ctx.arc(remap(fp[1].re,-2,2,0,600),remap(fp[1].im,-2,2,600,0),5,0,Math.PI*2)
+    ctx.stroke();
 }
 
 function render(a,b,c,d){
@@ -118,10 +126,6 @@ function renderGL(texture) {
     gl.enableVertexAttribArray(positionLocation);
     gl.vertexAttribPointer(positionLocation, 2, gl.FLOAT, false, 0, 0);
 
-
-
-
-
     gl.uniform2f(gl.getUniformLocation(program, "a"),a.re,a.im);
     gl.uniform2f(gl.getUniformLocation(program, "b"),b.re,b.im);
     gl.uniform2f(gl.getUniformLocation(program, "c"),c.re,c.im);
@@ -208,6 +212,25 @@ var mobius_inv = function(a,b,c,d,z){
     return c.multiply(Complex(-1,0)).multiply(z).add(a).reciprocal().multiply(b.multiply(Complex(-1,0)).add(z.multiply(d)));
 }
 
+function cpxSqrt(z) {
+    x = z.re;
+    y = z.im;
+    factor = Math.pow(x*x+y*y,0.25);
+    re = Math.cos(0.5*Math.atan2(y,x))*factor;
+    im = Math.sin(0.5*Math.atan2(y,x))*factor;
+    return new Complex(re,im);
+}
+
+var fixedpts = function(a,b,c,d){
+    fp = [1000,1000];
+    ad = a.add(new Complex(-1,0).multiply(d));
+    discr = ad.multiply(ad).add(new Complex(4,0).multiply(b).multiply(c));
+    den = new Complex(2,0).multiply(c).reciprocal();
+    fp[0] = ad.add(cpxSqrt(discr)).multiply(den);
+    fp[1] = ad.add(cpxSqrt(discr).multiply(new Complex(-1,0))).multiply(den);
+    return fp;
+}
+
 remap = function(x,a,b,c,d){
     //maps x from [a,b] to [c,d]
     return (x - a) * (d - c) / (b - a) + c;