Adaptive marching cubes

Abstract

The Marching Cubes algorithm (MC) is a powerful surface rendering technique which can produce very high quality images. However, it is not suitable for interactive manipulation of the 3D surfaces constructed from high resolution volume data sets in terms of both space and time. In this paper, we present an adaptive version of MC called Adaptive Marching Cubes (AMC). It significantly reduces the number of triangles representing the surface by adapting the size of the triangles to the shape of the surface. This improves the performance of the manipulation of the 3D surfaces.A typical example with the volume data set of size shows that the number of triangles is reduced by 55%. The quality of images produced by AMC is similar to that of MC. One of the fundamental problems encountered with adaptive algorithms is the crack problem. Cracks may be created between two neighboring cubes processed with different levels of subdivision. We solve the crack problem by patching the cracks using polygons of the same shape as those of the cracks. We propose a simple but complete method by first abstracting 22 basic configurations of arbitrary sized cracks and then reducing the handling of these configurations to a simple rule. It requires only O(n 2 ) working memory for a volume data set.

Efficient representation and extraction of 2-manifold isosurfaces using kd-trees

“…Marching Cubes based adaptive approaches [13,14,15,16] have to deal with the fact that applying Marching Cubes to cells of different sizes lead to cracks in the generated surface since the Marching Cubes algorithm handles neighboring cells independently. In these approaches the cracks are patched either by closing them with polygons of the same shape as those cracks or by forcing the polyline on the common faces of neighboring cells to fall together.…”

Component-based polygonal approximation of soft objects

“…As well, the adaptive decomposition of space, which leads to an adaptive polygonization, may create holes called cracks on the polygons [29,30].…”

“…Tetrahedral decomposition [27,32], the approximation of ambiguous faces [21,25], and the use of information of neighboring cells [11] have been suggested for disambiguation. For adaptive polygonization, most work focused on decomposing space adaptively by considering the geometry of the object [12,24,29,30,34]. To enhance efficiency, the exact intersection point is replaced by the mid-point of the intersecting edge [15,23].…”

Interactive Curvature Tensor Visualization on Digital Surfaces

“…Hence, adaptive approaches have been proposed in order to optimize the triangulated mesh resolution according to the object geometry or the viewpoint. In this topic, many solutions have been developed in Computer Graphics [15,14,6,9,10]. The method developed by Lengyel et al [6] suits best our needs.…”