No abstract

No abstract

No abstract

While it is usually not difficult to compute principal curvatures of a smooth surface of sufficient differentiability, it is a rather difficult task when only a polygonal approximation of the surface is available, because of the inherent ambiguity of such representation. A number of different approaches has been proposed in the past that tackle this problem using various techniques. Most papers tend to focus on a particular method, while an comprehensive comparison of the different approaches is usually missing. We present results of a large experiment, involving both common and recently proposed curvature estimation techniques, applied to triangle meshes of varying properties. It turns out that none of the approaches provides reliable results under all circumstances. Motivated by this observation, we investigate mesh statistics, which can be computed from vertex positions and mesh connectivity information only, and which can help in deciding which estimator will work best for a particular case. Finally, we propose a meta‐estimator, which makes a choice between existing algorithms based on the value of the mesh statistics, and we demonstrate that such meta‐estimator, despite its simplicity, provides considerably more robust results than any existing approach.

No abstract

The Connolly surface defines the boundary between a molecular structure and its environment. Its shape depends on the radius of the probe used to inspect the structure. The exploration of surface features is of great interest among chemists because it helps them to better understand and describe processes in the molecular structure. To help chemists better explore these features, we have combined two things together: a fast extraction of Connolly surfaces from a Voronoi diagram of atoms and a fast visualization based on GPU ray casting. Not only the surface but also the volume description is provided by the diagram. This enables to distinguish surface cavities one from another and compute their properties, e.g. the approximate volume, the maximal filling sphere or the maximal probe that can escape from the cavity to the outer environment. Cavities can be filtered out by applying restrictions to these properties. Views behind the surface and surface clipping improve the perception of the complex internal structure. The surface is quickly recomputed for any probe radius, so interactive changes of the probe radius show the development of cavities, especially how and where they merge together or with the outer environment.The contour-buildup algorithm was parallelized for both CPU [LBPH10] and GPU [KGE11]. The CPU variant runs in

No abstract

No abstract