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Preserving Zeros in Surface Construction using Marching Cubes

Liu S., Li J.

Machine Graphics and Vision

2010

Vol. 19, No. 1

97-123

In surface construction, existing marching cubes (MC) methods require sample values at cell vertices to be non-zero after thresholding, or modify them otherwise. The modification may introduce problems in the constructed surface, such as topological changes, representation errors, and preference for positive or negative values. This paper presents a generalized MC algorithm. It constructs surface patches by exploiting cycles in cells without changing the sample values at vertices, and thus allows cell vertices with zero sample values to lie on the constructed surface. The simulation results show that the proposed Zero-Crossing MC method preserves better topologies of implicit surfaces that pass through cell vertices, and represents the surfaces more accurately. Its efficiency is comparable to existing MC methods in constructing surfaces.

Higher Order Approximating Normals and Their Impact on Isosurface Shading Accuracy

Wood B. A., Lee J. K., Maskey M., Newman T. S.

Machine Graphics and Vision

2010

Vol. 19, No. 2

201-221

Two alternatives to the standard (central differencing) method for estimating normals of Marching Cubes isosurfaces are considered. The methods are based on higher order approximations of dataset gradients. Of primary concern here are the effects of these methods on rendering quality, which is evaluated here through pixel-by-pixel comparisons of typical-fidelity isosurfaces versus high-fidelity rendering achievable from analytically derived formulae. The evaluations also consider effects of noise on isosurface rendering quality for renderings based on standard versus higher order gradients.

Two methods for iso-surface extraction from vlumetric data and their comparison

Skala V., Brusi A.

Machine Graphics and Vision

2000

Vol. 9, No. 1/2

149-166

There are various methods for extracting iso-surfaces from volumetric data. Marching cubes or tetrahedra or raytracing methods are mostly used. There are many specific techniques to increase speed of computation and decrease memory requirements. Although a precision of iso-surface extraction is very important, too, it is not mentioned usually. A comparison of the selected method was made in different aspects: iso-surface extraction process time, number of triangles generated and estimation of radius, area and volume errors based on approximation of a sphere. Surprisingly, experiments proved that there is no direct relation between precision of extracted and human perception of the extracted iso-surface.