Closes #7.

js/HyperSpace.js

@@ -156,10 +156,11 @@ var finishInit = function(fShader){
       maxSteps:{type:"i", value:maxSteps},
       sceneIndex:{type:"i", value: 1},
       halfCubeWidthKlein:{type:"f", value: hCWK},
+	  cut4:{type:"i", value:cut4},
       sphereRad:{type:"f", value:sphereRad},
       tubeRad:{type:"f", value:tubeRad},
-	    horosphereSize:{type:"f", value:horosphereSize},
-	    planeOffset:{type:"f", value:planeOffset}
+      horosphereSize:{type:"f", value:horosphereSize},
+      planeOffset:{type:"f", value:planeOffset}
     },
     vertexShader: document.getElementById('vertexShader').textContent,
     fragmentShader: fShader,

js/NonEuclideanMath.js

@@ -10,6 +10,19 @@ function PiOverNSafe(n)
 	return n == -1 ? 0 : Math.PI / n;
 }
 
+// Returns the geometry induced by a polygon with p sides, q meeting at each vertex.
+function GetGeometry2D(p,q)
+{
+	var test = 1.0 / p + 1.0 / q;
+	if( test > 0.5 )
+		return Geometry.Spherical;
+	else if( test == 0.5 )
+		return Geometry.Euclidean;
+
+	return Geometry.Hyperbolic;
+}
+
+// Returns the geometry induced by a {p,q{} polyhedron, r meeting at each edge.
 function GetGeometry(p, q, r)
 {
 	var t1 = Math.sin(PiOverNSafe(p)) * Math.sin(PiOverNSafe(r));

js/SceneManipulator.js

@@ -2,6 +2,7 @@ var gens;
 var invGens;
 var hCWH = 0.6584789485;
 var hCWK = 0.5773502692;
+var cut4 = 2;
 var sphereRad = 0.996216;
 var tubeRad = 0.15;
 var horosphereSize = -0.951621;
@@ -79,11 +80,11 @@ function updateUniformsFromUI()
 	// We want them to be slightly bigger than that so that they intersect.
 	// hOffset controls the thickness of edges at their smallest neck.
 	// (zero is a reasonable value, and good for testing.)
-	// Make hOffset a UI parameter??
+	var cut4 = GetGeometry2D( q, r );
 	var hOffset = guiInfo.edgeThickness / 10;
 
-  //Tube Radius
-  tubeRad = guiInfo.edgeThickness/10;
+	//Tube Radius
+	tubeRad = guiInfo.edgeThickness/10;
 
 	// sphereRad
 	sphereRad = midrad - hOffset;
@@ -104,17 +105,18 @@ function updateUniformsFromUI()
 	material.uniforms.generators.value = gens;
 	material.uniforms.invGenerators.value = invGens;
 	material.uniforms.halfCubeWidthKlein.value = hCWK;
+	material.uniforms.cut4.value = cut4;
 	material.uniforms.sphereRad.value = sphereRad;
-  material.uniforms.tubeRad.value = tubeRad;
+	material.uniforms.tubeRad.value = tubeRad;
 	material.uniforms.horosphereSize.value = horosphereSize;
 	material.uniforms.planeOffset.value = planeOffset;
-  material.uniforms.lightingModel.value = guiInfo.lightingModel;
+	material.uniforms.lightingModel.value = guiInfo.lightingModel;
 }
 
 //What we need to init our dat GUI
 var initGui = function(){
   var gui = new dat.GUI();
-  gui.add(material.uniforms.sceneIndex, 'value',{Sphere_horosphere: 1, Sphere_plane: 2, Edge_tubes: 3, Medial_surface: 4, Cube_planes: 5}).name("Scene");
+  gui.add(material.uniforms.sceneIndex, 'value',{Simplex_cuts: 1, Edge_tubes: 3, Medial_surface: 4, Cube_planes: 5}).name("Scene");
   var lightingController = gui.add(guiInfo, 'lightingModel', {"Standard":0, "Foo": 1}).name("Lighting Model");
   var edgeController = gui.add(guiInfo, 'edgeCase', {"5":1, "6":2, "7":3, "8":4, "9":5, "10":6, "11":7, "12":8}).name("Edge Degree");
   var thicknessController = gui.add(guiInfo, 'edgeThickness', 0, 5).name("Edge Thickness");

shaders/globalsInclude.glsl

@@ -34,6 +34,11 @@ uniform float tubeRad;
 uniform float horosphereSize;
 uniform float planeOffset;
 
+// The type of cut (1=sphere, 2=horosphere, 3=plane) for the vertex opposite the fundamental simplex's 4th mirror.
+// These integers match our values for the geometry of the honeycomb vertex figure.
+// We'll need more of these later when we support more symmetry groups.
+uniform int cut4;		
+
 //Quaternion Math
 vec3 qtransform( vec4 q, vec3 v ){
   return v + 2.0*cross(cross(v, -q.xyz ) + q.w*v, -q.xyz);

shaders/hyperbolicScene.glsl

@@ -28,20 +28,20 @@ float geodesicCylinderHSDFends(vec4 samplePoint, vec4 lightPoint1, vec4 lightPoi
 
 
 float localSceneHSDF(vec4 samplePoint){
-  if(sceneIndex == 1){  // sphere and horosphere
+  if(sceneIndex == 1){  // cuts into the simplex
      float sphere = sphereHSDF(samplePoint, ORIGIN, sphereRad);
-     float horosphere = horosphereHSDF(abs(samplePoint), idealCubeCornerKlein, horosphereSize);
-     float final = -unionSDF(horosphere, sphere);
+     float vertexSphere = 0.0;
+     if(cut4 == 2) {
+        vertexSphere = horosphereHSDF(abs(samplePoint), idealCubeCornerKlein, horosphereSize);
+     }
+	 if(cut4 == 1 || cut4 == 3) {	// Interesting that this works for finite spheres as well.
+        vec4 dualPoint = lorentzNormalize(vec4(halfCubeWidthKlein,halfCubeWidthKlein,halfCubeWidthKlein,1.0));
+        vertexSphere = geodesicPlaneHSDF(abs(samplePoint), dualPoint, planeOffset);
+     }
+     float final = -unionSDF(vertexSphere,sphere);
      return final;
   }
-  else if(sceneIndex == 2){  // sphere and plane
-   float sphere = sphereHSDF(samplePoint, ORIGIN, sphereRad);
-   vec4 dualPoint = lorentzNormalize(vec4(halfCubeWidthKlein,halfCubeWidthKlein,halfCubeWidthKlein,1.0));
-   float plane0 = geodesicPlaneHSDF(abs(samplePoint), dualPoint, planeOffset);
-   float final = -unionSDF(plane0, sphere);
-   return final;
-  }
-  else if(sceneIndex == 3){  // edge tubes
+  else if(sceneIndex == 2){  // edge tubes
     samplePoint = abs(samplePoint);
     // //now reflect until smallest xyz coord is z, and largest is x
     if(samplePoint.x < samplePoint.z){
@@ -62,7 +62,7 @@ float localSceneHSDF(vec4 samplePoint){
     float final = edgesDistance;
     return final;
   }
-  else if(sceneIndex == 4){  // edge medial surfaces
+  else if(sceneIndex == 3){  // edge medial surfaces
     samplePoint = abs(samplePoint);
     // //now reflect until smallest xyz coord is z, and largest is x
     if(samplePoint.x < samplePoint.z){
@@ -91,7 +91,7 @@ float localSceneHSDF(vec4 samplePoint){
     float final = 0.5*edgesDistance - 0.5*dualEdgesDistance;
     return final;
   }
-  else if(sceneIndex == 5){  // cube sides
+  else if(sceneIndex == 4){  // cube sides
     /// draw sides of the cube fundamental domain
     vec4 dualPoint0 = lorentzNormalize(vec4(1.0/halfCubeWidthKlein,0.0,0.0,1.0));
     vec4 dualPoint1 = lorentzNormalize(vec4(0.0,1.0/halfCubeWidthKlein,0.0,1.0));