Marching Cubes in Four and Higher Dimensions (Extended Abstract)

Praveen Bhaniramka Roger Craws Ho-Seok Kang DongLin Liang Rephael Wenger Zhi Yao The Ohio State University Columbus, Ohio Abstract The marching cubes algorithm is a popular visualization algorithm for constructing a 2D isosurface from a regular 3D grid. We generalize the marching cubes algorithm to four dimensions and higher. For each hypercube in the grid, we identify the edges which intersect the isosurface. We construct the isosurface within the hypercube by taking the convex hull of the midpoints of these edges and choosing a subset of the boundary of that convex hull. 1 Introduction Given a scalar eld, i.e., a scalar function on R d , an isosurface is a set of points with identical scalar values. The marching cubes algorithm by Lorensen and Cline is a popular, simple, and eÆcient algorithm for constructing isosurfaces from scalar values in a three dimensional regular grid[1]. The regular grid divides the volume into cubes whose vertices are the grid vertices and the isosurfa..