Octree-based decimation of marching cubes surfaces

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Abstract
The marching cubes (MC) algorithm is a method for generating isosurfaces. It also generates an excessively large number of triangles to represent an isosurface; this increases the rendering time. This paper presents a decimation method to reduce the number of triangles generated. Decimation is carried out before creating a large number of triangles. Four major steps comprise the algorithm: surface tracking, merging, crack patching and triangulation. Surface tracking is an enhanced implementation of the MC algorithm. Starting from a seed point, the surface tracker visits only those cells likely to compose part of the desired isosurface. The cells making up the extracted surface are stored in an octree that is further processed. A bottom-up approach is taken in merging the cells containing a relatively flat approximating surface. The finer surface details are maintained. Cells are merged as long as the error due to such an operation is within a user-specified error parameter, or a cell acquires more than one connected surface component in it. A crack patching method is described that forces edges of smaller cells to lie along those of the larger neighboring cells. The overall saving in the number of triangles depends both on the specified error value and the nature of the data. Use of the hierarchical octree data structure also presents the potential of incremental representation of surfaces. We can generate a highly smoothed surface representation which can be progressively refined as the user-specified error value is decreased.

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