Blending Vertex Normals In A Quad Tree

Ogre 3D Vertex Normal Blending from petrocket on Vimeo.

I’ve finally had some time to work on blending the mesh normals and can post a video – my FIRST video of the app so go easy – and talk about what works about it and where the idea came from.

As it turns out there is/was another excellent planetary LOD program based on geo clipmaps and I read that Lutz Justen (the author, now an engineer at Red 5 Studios!) had blended his normal maps and done some other fancy things like cloud map shadows. I contacted Lutz and he responded with this:

“Vertex normals: I don’t think there is *any* way to make vertex normals not pop – UNLESS you change the way geo morphing works. You probably interpolate a vertex to the position between the two higher-level verts, i.e.
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The upper vertex is interpolated to the average of the lower 2 vertices. In that case, you’ll always have lighting pops. If you instead interpolate the upper vertex to either the left or the right vertex, you’d get rid of the pops because the limit of the finer triangles as you interpolate to the coarser triangles actually match the coarser triangles. I hope that makes sense. If you interpolate to the average of the lower vertices, the limit doesn’t match the coarser representation. It’s the same geometry, but a different triangulation.

If you store per-patch normals as Ysaneya does, there’s another way. You can store your normal maps in object space (instead of tangent space) because they are unique anyway. Then you can lerp between a fine-level normal map and the corresponding coarse-level normal map. That’d make your lighting completely smooth. That’s what I did in my demo, although the resolution of the normal map was very low – it was the same resolution as the vertices! But nevertheless, the lighting was completely continuous.”

And that’s what I tried to do, only right now my normal map calculations for the “coarse” map are not entirely correct because there is still a pop when the mesh level changes – although a MUCH smaller pop than before, it is still there as you can see in the video. Maybe sometime I will post a video of the transitions without normal blending so you can see the improvement.

Here’s how I implemented the normal map blending in Ogre (cooking directions style!)
6 quad trees
4 quad tree meshes per node
2 sets of normals per mesh (for blending)
1 blend start distance for each level/depth in the quad tree
1 blend end distance for each level/depth in the quad tree
1 GLSL vertex shader to take these values and do something with them

1. prepare your meshes by creating the 3d vertex positions from your 3d noise function
2. calculate your end normals based on those positions and save them – these are the normals we will blend to.
3. get the outer edge vertices for the “coarser” mesh
4. calculate the normals for each vertex that exists in the “coarser” mesh
5. calculate all the interpolated normals for each vertex that exists in the “finer” mesh but not in the “coarser” mesh.
6. in the vertex shader blend between the “finer” and “coarser” normals based on the camera’s distance to the vertex. Each level of the quad tree will have a different distance based on the split distance for that level – the split distance is the distance from the camera to a node at which it must split into 4 sub nodes, one for each quadrant.

Right now my calculations are not completely correct for step 5 because there is still a visible transition or “pop” when the finer mesh is displayed. I don’t know where my calculations are wrong, but if I figure it out I will post the solution.