An extended triangulation to the Marching Cubes 33 algorithm

Lis Custodio,Claudio Silva,Sinesio Pesco

doi:10.1186/s13173-019-0086-6

Abstract

The Marching Cubes algorithm is arguably the most popular isosurface extraction algorithm. Since its inception, two problems have lingered, namely, triangle quality and topology correctness. Although there is an extensive literature to solve them, topology correctness is achieved in detriment of triangle quality and vice versa. In this paper, we present an extended version of the Marching Cubes 33 algorithm (a variation of the Marching Cubes algorithm which guarantees topological correctness), called Extended Marching Cubes 33. In the proposed algorithm, the grid vertex are labeled with “+,” “ −,” and “=,” according to the relationship between its scalar field value and the isovalue. The inclusion of the “=” grid vertex label naturally avoids degenerate triangles. As an application of our method, we use the proposed triangulation to improve the quality of the triangles in the generated mesh while preserving its topology as much as possible.

Highlights

The isosurface extraction algorithms are a powerful tool in the interpretation and visualization of volumetric data
To solve the problem of degenerate triangles and to preserve the topological correctness of the resulting mesh as much as possible, we propose a method to construct an extended triangulation to the Marching Cubes 33
We propose a specific triangulation process to construct an extended triangulation to the Marching Cubes 33

Summary

Introduction

The isosurface extraction algorithms are a powerful tool in the interpretation and visualization of volumetric data. To avoid the creation of degenerate triangles by the Marching Cubes algorithm, Raman and Wenger [10] in 2008 propose a lookup table that includes grid vertices with labels “+,” “−,” and “=,” according to the relationship of the isovalue with its scalar value. Related work In 2000, Lachaud and Montanvert [12] and Bhaniramka et al [13] independently proposed an algorithm to generate a Marching Cubes lookup table in higher dimension In both methods, the ambiguities of the trilinear interpolant in the interior of the cube are not considered in constructing the triangulation, which leads to topological inconsistencies in the generated mesh. In 2008, Raman and Wenger [10], based on the Bhaniramka et al.’s [14] work, proposed an algorithm to construct an extended lookup table which allows the vertices of the grid to be part of the triangulation.

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