The Marching Cubes Algorithm may return degenerate, zero area isosurface triangles, and often returns isosurface triangles with small areas, edges or angles. We show how to avoid both problems using an extended Marching Cubes lookup table. As opposed to the conventional Marching Cubes lookup table, the extended lookup table differentiates scalar values equal to the isovalue from scalar values g...

We present a method for extracting iso-surfaces and their intersections in 4D. Our work is a signiicant extension of the 3D Marching Lines algorithm with new orientation and implementation considerations. As a practical tool, it can be applied to track eeciently space curves, deened by diierential invariants, across increasing scale. Extraction d'iso-surfaces en 4D avec des applications la thho...

This paper presents an adaptive method for polygonisation of implicit surfaces. The method is based on the shape of triangles and the accuracy of resulting approximation. The main advantages of the triangulation presented are simplicity and the stable features that can be used for the next expansion. The presented algorithm is based on the surface tracking scheme, and it is compared with other ...

In this paper, an interactive segmentation method that combines fast marching and fast level set method is proposed. Level set segmentation involves solving the energybased active contour minimization problems by the computation of geodesics or minimal distance curves. First, by selecting the seed point, the fast marching method is used to extract rough boundaries of the interested object. We m...

This paper introduces the marching cube octree data structure, a new scheme for representing and generating the mesh of various level-of-details (LODs). The marching cube octree is based on the data structure of the Marching Cube algorithm [1 ], which is used to generate the mesh from the range data and the octree, this last widely used in computer graphics. Our LOD model can support adaptive s...

Chernyaev’s Marching Cubes 33 is one of the first algorithms intended to preserve the topology of the trilinear interpolant. In this work, we address three issues with the Marching Cubes 33 algorithm, two of which are related to its original description and one that is related to its variant. In particular, we solve a problem with the core disambiguation procedure of Marching Cubes 33 that prev...

Surface reconstruction from unorganized point set is a common problem in computer graphics. Generation of the signed distance field from the point set is a common methodology for the surface reconstruction. The reconstruction of implicit surfaces is made with the algorithm of marching cubes, but the distance field of a point set can not be processed with marching cubes because the unsigned natu...

This paper presents the basic principles for the visualization of objects which are defined by implicit functions and CSG trees. The basic principles (Marching cubes, Marching tetrahedra and Marching triangles) for iso-surfaces rendering of such objects are compared. A new fast modification of the Marching triangles algorithm is presented and compared with others algorithms. It is based on the ...

Parallel computers hold the promise of enabling interactive visualization of very large data sets. Ful lling this promise depends on the development of parallel algorithms and implementations which can e ciently utilize the power of a parallel computer. Fortunately, many visualization algorithms involve performing independent computations on a large collection of data items, making them particu...