Showing papers on "Marching tetrahedra published in 1997"

A Generalized Marching Cubes Algorithm Based On Non-Binary Classifications

Abstract: We present a new technique for generating surface meshes from a uniform set of discrete samples. Our method extends the well-known marching cubes algorithm used for computing polygonal isosurfaces. While in marching cubes each vertex of a cubic grid cell is binary classified as lying above or below an isosurface, in our approach an arbitrary number of vertex classes can be specified. Consequently the resulting surfaces consist of patches separating volumes of two different classes each. Similar to the marching cubes algorithm all grid cells are traversed and classified according to the number of different vertex classes involved and their arrangement. The solution for each configuration is computed based on a model that assigns probabilities to the vertices and interpolates them. We introduce an automatic method to find a triangulation which approximates the boundary surfaces - implicitly given by our model - in a topological correct way. Look-up tables guarantee a high performance of the algorithm. In medical applications our method can be used to extract surfaces from a 3D segmentation of tomographic images into multiple tissue types. The resulting surfaces are well suited for subsequent volumetric mesh generation, which is needed for simulation as well as visualization tasks. The proposed algorithm provides a robust and unique solution, avoiding ambiguities occuring in other methods. The method is of great significance in modeling and animation too, where it can be used for polygonalization of non-manifold implicit surfaces.

A note on computing the saddle values in isosurface polygonization

Abstract: The marching cubes method (Lorensen 1987) is a popular technique for visualizing a set of volume data. This method uses 15 base cases to construct polygons for each cube to approximate the isosurfaces F(x, y, z)"t for various values of t. The advantages of the polygon-based approach make it easy to adopt the technique on hardware platforms and to execute it efficiently. Unfortunately, the method has an ambiguity problem that causes anomalies in the rendered images (Durst 1988). Several improved approaches have been proposed (Montani et al. 1994; Nielson et al. 1991; Pasco 1988; Wilhelms and Gelder 1990). These methods try to resolve ambiguous situations by preventing possible ‘‘holes’’ in the isosurfaces. However, these approaches could introduce the topological inconsistency problem (Natarajan 1994), which confuses our perception of the observed objects, especially when supersampling the original data is necessary. In 1994, Natarajan developed a technique that computes topologically consistent isosurfaces by examining the saddle values of a trilinear interpolant. This technique also improves the method proposed by Pasco in 1988, which investigated saddle values for the bilinear interpolant only. In this note, we analyze the trilinear interpolant. We show that the cost for computing the body saddle value can be reduced.