GeometryProcessing/Spring2009/Schedule/Surface Generation Extraction1

• John Meier

I liked the structure of Tuesday's lecture: 1) the build-up to the topic of marching cubes from marching tets, and 2) examination of the aspects of marching cubes that have been "solved", like how to prevent ambiguous surface extraction by automatically generating the intersection lookup table, and optimizing runtime with structures likes octrees or span spaces. The biggest mental hurdle for me among the lecture topics was the reason for building an octree of an implicit surface from the bottom up as a preprocessing step, which Carlos cleared up well (once the structure is built, it can be queried for any constant). The analogy to sorting an array before searching for elements was intuitive and appreciated.

Questions

What steps would take place when using Marching Cubes to extract a surface from an implicit representation?

(I'm not sure I understood the question, so feel free to tell me I didn't get it) If you already have a volumetric dataset stored as a 3D set of voxels in space, then you can just run Marching Cubes directly on that representation, one voxel being one cube. If what you have is an evaluation formula for each point in space, then you can first evaluate the function in a fixed volumetric grid, giving you the voxels and then running Marching Cubes.

Guidance Field - Not sure if this is something we've talked about or are going to talk about, but for an advancing front method to generate iso-surfaces, what's a guidance field? I would assume that it's some sort of function that guides the creation of new triangles, but how? And what's it look like?

The guidance field is the function that, for every point in space, tells you how big the triangle can be there. Remember that, in class, we looked at how one particular size constraint for a triangle (say, near a high-curvature region) induced a constraint over the entire space? And then we took the minimum of a lot of constraints, which looked like an upside-down "mountain range"? This is the guidance field.