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Octrees == accordions

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In dual contouring, (as defined in here) terrain can be shown as an octree where the leaves contain a vertex of the mesh.

However in order to save memory the mesh needs to be minimized, or similar leaves are collapsed into a single, larger, leaf. The paper discusses this and it makes sense, however another problem arises;


if you want to modify the mesh, by carving it using some sort of shape, then you may need to split that larger node down again. The issue with this step is that when a node is split again, how would you then rebuild the 'hermite data' that those smaller nodes use?


The far edges of the larger node would already contain 'hermite data'; however the new edges, on that are inside of the larger node, would need to be generated somehow.


Please let me know if I'm doing this wrong or if you have any ideas!

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So, take two.


The terrain is generated into an octree that looks like this:


Now this is a quadtree, but it is the same idea can is easily applied to three dimensions.

With this image the red line is the terrain surface, what you actually stand on. The green is leaf nodes, that contains part of the mesh. In this process each leaf would contain one point, or vertex, that is connected to its neighbors creating the actual terrain.


To show this a bit better than the previous general image, here is a snip from the dual contouring paper.


With this you can see each vertex, and how it would connect to form a mesh. Now with this you can see that there that many of the vertices are not really needed, they link to other points in a nearly straight line. So in order to optimize the mesh we can collapse a leaf into this:


As you can see there is only one vertex here, rather than 4. This is a save on both memory and processing time and therefore a very good idea to do. However there is an issue with doing this; To generate the original node, with all five vertices, you need some data that looks like this:


Where each edge contains a position, and a normal pointing outwards from where the surface will be. Using this it positions the vertices to build the surface.

Please note that once those points are generated though, they are merged into a matrix that looks like this:


Now this is after some operations were applied to it, and the data (represented where each row was the normal in the first three columns, and the dot of the normal to an average of the positions in the fourth column) has been pulled up into this triangle through some fancy operations. Most of this you don't really need, the only important bit is that this is generated from the arrows above, and once it is made the arrows are only needed if the matrix needs to be rebuilt.


Now this matrix is used for simplification and leaf compression, you can see the process in detail through the link in the top post. The issue is that when you compress a leaf you only need use that matrix to compress it. And if the arrows are kept then each collapsed node would take more and more memory as it has to store more and more arrows.


If the mesh was never changing this would not be a problem; However if say you wanted to change the terrain, carve it or shape it, you would need to get those arrows back in order to build that matrix again with really small leaves, then compress back up.


In a few general cases this would not be a problem, the original arrows are made using a noise function and can easily be replicated. However if you modify a surface (cut out a shape, fill a shape), the surface is simplified, and then you modify again; where will it get the arrows from?


I am just trying to find a good way to solve this without killing the memory usage. I get a feeling there is a trick with the matrix that I just don't understand.... if you have any ideas please let me know.

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As I understand from the paper and your drawing, you have to start from the surface and take samples at cube edges to gets positions and normals to turn into the dual contour. I see no reason why you could not use the same sampling on the compressed version of your surface inside of the oct tree leaf. You'll lose the original uncompressed version, but you should be able to resample and perform CSG operations on the resampled cubes.


Oh, I see, you're starting with noise, so you never had to perform the step of creating a dual contour from a surface?


If you're going to carve up that shape, you're going to have to be able to figure out where your surface intersects with other shapes, and what the normals are at those intersections. So, you may as well start out with cubes.

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