Marching Cubes' methods first offered visual access to experimental and theoretical data. The implementation of this method usually relies on a small lookup table. Many enhancements and optimizations of Marching Cubes still use it. However, this lookup table can lead to cracks and inconsistent topology. This paper introduces a full implementation of Chernyaev's technique to ensure a topologically correct result, i.e. a manifold mesh for any input data. It completes the original paper for the ambiguity resolution and for the feasibility of the implementation. Moreover, the cube interpolation provided here can be used in a wider range of methods. The source code is available online.

The paper goal is to fit trilinear iso-surfaces out of volume data, by adopting an adaptive mesh refinement approach and therefore supporting a higher accuracy with respect to standard MC solutions. In order to be correct, adaptive refinement must be applied to a topologically correct initial mesh patch. For this reason, we designed a new, Exhaustive Look Up Table (ELUT) which encodes multi-entry patterns for each ambiguous configuration. Following the solution proposed by Natarajan, for each ambiguous configuration we choose, at run time, the actual pattern by evaluating the corresponding set of saddle points. Once the corresponding starting patch has been read from the ELUT, it is adaptively refined to fulfill a user-selected accuracy. Refinement is adaptive to ensure that the complexity of the fitted mesh will not become excessive. An evaluation of the results produced on some volume dataset is reported, both in terms of accuracy and complexity of the meshes obtained. Contact autho...

This paper addresses the problem of piecewise linear approximation of implicit surfaces. We first give a criterion ensuring that the zero-set of a smooth function and the one of a piecewise linear approximation of it are isotopic. Then, we deduce from this criterion an implicit surface meshing algorithm certifying that the output mesh is isotopic to the actual implicit surface. This is the first algorithm achieving this goal in a provably correct way. 1

This paper describes a method for constructing isosurface triangulations of sampled, volumetric, three-dimensional scalar fields. The resulting meshes consist of triangles that are of consistently high quality, making them well suited for accurate interpolation of scalar and vector-valued quantities, as required for numerous applications in visualization and numerical simulation. The proposed method does not rely on a local construction or adjustment of triangles as is done, for instance, in advancing wavefront or adaptive refinement methods. Instead, a system of dynamic particles optimally samples an implicit function such that the particles ’ relative positions can produce a topologically correct Delaunay triangulation. Thus, the proposed method relies on a global placement of triangle vertices. The main contributions of the paper are the integration of dynamic particles systems with surface sampling theory and PDE-based methods for controlling the local variability of particle densities, as well as detailing a practical method that accommodates Delaunay sampling requirements to generate sparse sets of points for the production of high-quality tessellations. Index Terms—Isosurface extraction, particle systems, Delaunay triangulation.

In this paper we present a method for applying 2D textures onto composite and articulated objects defined by implicit functions. The method generates a particle system associated with the gradient vector field of an implicit function which acquires texture coordinates at a support surface. By extending this method to composite objects, an implicit surface may change its shape in time, while maintaining texture consistency. This approach prevents the appearance of undesirable effects such as ghosting and artifacts at the blending parts of an implicit object.

In this paper, we propose a solution to adapt the differential point rendering technique developed by Kalaiah and Varshney to implicit surfaces. Differential point rendering was initially designed for parametric surfaces as a twostage sampling process that strongly relies on an adjacency relationship for the samples, which does not naturally exist for implicit surfaces. This fact made it particularly challenging to adapt the technique to implicit surfaces. To overcome this difficulty, we extended the particle sampling technique developed by Witkin and Heckbert in order to locally account for the principal directions of curvatures of the implicit surface. The final result of our process is a curvature driven anisotropic sampling where each sample "rules" a rectangular or elliptical surrounding domain and is oriented according to the directions of maximal and minimal curvatures. As in the differential point rendering technique, these samples can then be efficiently rendered using a specific shader on a programmable GPU.

We address the problem of isosurface meshing with topological guaranties. Assuming the critical points of the considered function are given, we give a certified algorithm for this problem. This seems to be the first one in the literature.

In this work, we introduce a new algorithm for direct and progressive encoding of isosurfaces extracted from volumetric data. A binary multi– triangulation is used to represent and adapt the 3D scalar grid. This simplicial scheme provides geometrical and topological control on the decoded isosurface. The resulting algorithm is an efficient and flexible isosurface compression scheme. 1

Automatic blending has characterized the major advantage of implicit surface modeling systems. Recently, the introduction of deformations based on space warping and boolean operations between primitives has increased the usefulness of such systems. We propose a further enhancement which will greatly enhance the range of models that can be easily and intuitively defined with a skeletal implicit surface system. We decribe a hierarchical method which allows arbitrary compositions of models that make use of blending, warping and boolean operations. We call this structure the BlobTree. Blending and space warping are treated in the same way as union, difference and intersection, i.e. as nodes in the BlobTree. The traversal of the BlobTree is described along with two rendering algorithms; a polygonizer and a ray tracer. We present some examples of interesting models which can be made easily using our approach that would be very difficult to represent with conventional systems. Key words: blending, implicit surfaces, polygonizing, raytracing, warping.

A method for ray casting implicit surfaces, defined with procedural noise models, is presented. The method is robust in that it is able to guarantee correct intersections at all image pixels and for all types of implicit surfaces. This robustness comes from the use of an affine arithmetic representation for the quantity that expresses the variation of the implicit function along a ray. Affine arithmetic provides a bounding interval estimate which is tighter than the interval estimates returned by conventional interval arithmetic. Our ray casting method is also efficient due to a proposed modification in the data structure used to hold affine arithmetic quantities. This modified data structure ultimately leads to a reduced affine arithmetic model. We show that such a reduced affine arithmetic model is able to retain all the tight estimation capabilities of standard affine arithmetic, in the context of ray casting implicit procedural noises, while being faster to compute and more efficient to store. We also show that, without this reduced model, affine arithmetic would not have any advantage over the more conventional interval arithmetic for ray casting the class of implicit procedural surfaces that we are interested in visualizing.