Added functions to perform 'octahedral' encoding and decoding of normals.

See http://jcgt.org/published/0003/02/01/paper-lowres.pdf

examples/Basic/main.cpp

@@ -50,14 +50,34 @@ void createSphereInVolume(SimpleVolume<uint8_t>& volData, float fRadius)
 				//And compute how far the current position is from the center of the volume
 				float fDistToCenter = (v3dCurrentPos - v3dVolCenter).length();
 
-				uint8_t uVoxelValue = 0;
+				// We actually want our volume to have high values in the center and low values as we move out, because our
+				// eath should be a solid sphere surrounded by empty space. If we invert the distance then this is a step in
+				// the right direction. We still have zero in the center, but lower (negative) values as we move out.
+				float density = -fDistToCenter;
 
-				//If the current voxel is less than 'radius' units from the center then we make it solid.
-				if(fDistToCenter <= fRadius)
-				{
-					//Our new voxel value
-					uVoxelValue = 255;
-				}
+				// By adding the 'planetRadius' we now have a function which starts at 'planetRadius' and still decreases as it
+				// moves out. The function passes through zero at a distance of 'planetRadius' and then continues do decrease
+				// as it gets even further out.
+				density += fRadius;
+
+				// Ideally we would like our final density value to be '255' for voxels inside the planet and '0' for voxels
+				// outside the planet. At the surface there should be a transition but this should occur not too quickly and
+				// not too slowly, as both of these will result in a jagged appearance to the mesh.
+				//
+				// We probably want the transition to occur over a few voxels, whereas it currently occurs over 255 voxels
+				// because it was derived from the distance. By scaling the density field we effectivly compress the rate
+				// at which it changes at the surface. We also make the center much too high and the outside very low, but
+				// we will clamp these to the corect range later.
+				//
+				// Note: You can try commenting out or changing the value on this line to see the effect it has.
+				density *= 50;
+
+				// Until now we've been defining our density field as if the threshold was at zero, with positive densities
+				// being solid and negative densities being empty. But actually Cubiquity operates on the range 0 to 255, and
+				// uses a threashold of 127 to decide where to place the generated surface.  Therefore we shift and clamp our
+				// density value and store it in a byte.
+				density += 127;
+				uint8_t uVoxelValue = (uint8_t)(clamp(density, 0.0f, 255.0f));
 
 				//Wrte the voxel value into the volume	
 				volData.setVoxelAt(x, y, z, uVoxelValue);
@@ -74,12 +94,12 @@ int main(int argc, char *argv[])
 	openGLWidget.show();
 
 	//Create an empty volume and then place a sphere in it
-	SimpleVolume<uint8_t> volData(PolyVox::Region(Vector3DInt32(0,0,0), Vector3DInt32(63, 63, 63)));
-	createSphereInVolume(volData, 30);
+	SimpleVolume<uint8_t> volData(PolyVox::Region(Vector3DInt32(0,0,0), Vector3DInt32(31, 31, 31)));
+	createSphereInVolume(volData, 15);
 
 	// Extract the surface for the specified region of the volume. Uncomment the line for the kind of surface extraction you want to see.
-	auto mesh = extractCubicMesh(&volData, volData.getEnclosingRegion());
-	//auto mesh = extractMarchingCubesMesh(&volData, volData.getEnclosingRegion());
+	//auto mesh = extractCubicMesh(&volData, volData.getEnclosingRegion());
+	auto mesh = extractMarchingCubesMesh(&volData, volData.getEnclosingRegion());
 
 	// The surface extractor outputs the mesh in an efficient compressed format which is not directly suitable for rendering. The easiest approach is to 
 	// decode this on the CPU as shown below, though more advanced applications can upload the compressed mesh to the GPU and decompress in shader code.

examples/common/example.frag

@@ -2,7 +2,7 @@
 
 // Passed in from the vertex shader
 in vec4 worldPosition;
-in vec4 worldNormal;
+in vec3 worldNormal;
 
 // the color that gets written to the display
 out vec4 outputColor;
@@ -15,5 +15,5 @@ void main()
 	
 	// We are just using the normal as the output color, and making it lighter so it looks a bit nicer. 
 	// Obviously a real shader would also do texuring, lighting, or whatever is required for the application.
-	outputColor = vec4(abs(normal) * 0.5 + vec3(0.5, 0.5, 0.5), 1.0);
+	outputColor = vec4(abs(worldNormal.xyz), 1.0);
 }

examples/common/example.vert

@@ -1,6 +1,7 @@
 #version 140
 
 in vec4 position; // This will be the position of the vertex in model-space
+in vec3 normal;
 
 // The usual matrices are provided
 uniform mat4 cameraToClipMatrix;
@@ -10,11 +11,15 @@ uniform mat4 modelToWorldMatrix;
 // This will be used by the fragment shader to calculate flat-shaded normals. This is an unconventional approach
 // but we use it in this example framework because not all surface extractor generate surface normals.
 out vec4 worldPosition;
+out vec3 worldNormal;
 
 void main()
 {
 	// Standard sequence of OpenGL transformations.
 	worldPosition = modelToWorldMatrix * position;
 	vec4 cameraPosition = worldToCameraMatrix * worldPosition;
+	
+	worldNormal = normal;
+	
 	gl_Position = cameraToClipMatrix * cameraPosition;
 }

library/PolyVoxCore/include/PolyVoxCore/MarchingCubesSurfaceExtractor.h

@@ -50,7 +50,7 @@ namespace PolyVox
 		// Each component of the normal is encoded using 5 bits of this variable.
 		// The 16 bits are -xxxxxyyyyyzzzzz (note the left-most bit is currently 
 		// unused). Some extra shifting and scaling is required to make it signed.
-		uint16_t encodedNormal;
+		Vector2DFloat encodedNormal;
 
 		// User data
 		DataType data;
@@ -64,7 +64,7 @@ namespace PolyVox
 		return result;
 	}
 
-	inline uint16_t encodeNormal(const Vector3DFloat& normal)
+	/*inline uint16_t encodeNormal(const Vector3DFloat& normal)
 	{
 		Vector3DFloat v3dNormal = normal;
 		v3dNormal += Vector3DFloat(1.0f, 1.0f, 1.0f);
@@ -96,6 +96,64 @@ namespace PolyVox
 		result -= Vector3DFloat(1.0f, 1.0f, 1.0f);
 
 		return result;
+	}*/
+
+	// Returns ±1
+	float signNotZero(float v)
+	{
+		return v >= 0.0 ? +1.0 : -1.0;
+	}
+
+	Vector2DFloat signNotZero(Vector2DFloat v)
+	{
+		return Vector2DFloat((v.getX() >= 0.0) ? +1.0 : -1.0, (v.getY() >= 0.0) ? +1.0 : -1.0);
+	}
+
+	// Assume normalized input. Output is on [-1, 1] for each component.
+	Vector2DFloat float32x3_to_oct(Vector3DFloat v)
+	{
+		// Project the sphere onto the octahedron, and then onto the xy plane
+		Vector2DFloat p(v.getX(), v.getY());			
+		p = p * (1.0f / (abs(v.getX()) + abs(v.getY()) + abs(v.getZ())));
+
+		float refX = ((1.0f - abs(p.getY())) * signNotZero(p.getX()));
+		float refY = ((1.0f - abs(p.getX())) * signNotZero(p.getY()));
+
+		Vector2DFloat ref(refX, refY);
+
+		// Reflect the folds of the lower hemisphere over the diagonals
+		return (v.getZ() <= 0.0) ? ref : p;
+	}
+
+	Vector3DFloat oct_to_float32x3(Vector2DFloat e)
+	{
+		Vector3DFloat v = Vector3DFloat(e.getX(), e.getY(), 1.0 - abs(e.getX()) - abs(e.getY()));
+
+		float refX = ((1.0f - abs(v.getY())) * signNotZero(v.getX()));
+		float refY = ((1.0f - abs(v.getX())) * signNotZero(v.getY()));
+
+		Vector2DFloat ref(refX, refY);
+
+		if (v.getZ() < 0.0f)
+		{
+			//v.xy = (1.0 - abs(v.yx)) * signNotZero(v.xy);
+			v.setX(refX);
+			v.setY(refY);
+		}
+
+		v.normalise();
+
+		return v;
+	}
+
+	inline Vector2DFloat encodeNormal(const Vector3DFloat& normal)
+	{
+		return float32x3_to_oct(normal);
+	}
+
+	inline Vector3DFloat decode(const Vector2DFloat& encodedNormal)
+	{
+		return oct_to_float32x3(encodedNormal);
 	}
 
 	/// Decodes a MarchingCubesVertex by converting it into a regular Vertex which can then be directly used for rendering.