Delaunay Stability via Perturbations

We present an algorithm that takes as input a finite point set in Euclidean space, and performs a perturbation that guarantees that the Delaunay triangulation of the resulting perturbed point set has quantifiable stability with respect to the metric and the point positions. There is also a guarantee on the quality of the simplices: they cannot be too flat. The algorithm provides an alternative tool to the weighting or refinement methods to remove poorly shaped simplices in Delaunay triangulations of arbitrary dimension, but in addition it provides a guarantee of stability for the resulting triangulation

Measuring Visual Consistency in 3D Rendering Systems

One of the major challenges facing a present day game development company is the removal of bugs from such complex virtual environments. This work presents an approach for measuring the correctness of synthetic scenes generated by a rendering system of a 3D application, such as a computer game. Our approach builds a database of labelled point clouds representing the spatiotemporal colour distribution for the objects present in a sequence of bug-free frames. This is done by converting the position that the pixels take over time into the 3D equivalent points with associated colours. Once the space of labelled points is built, each new image produced from the same game by any rendering system can be analysed by measuring its visual inconsistency in terms of distance from the database. Objects within the scene can be relocated (manually or by the application engine); yet the algorithm is able to perform the image analysis in terms of the 3D structure and colour distribution of samples on the surface of the object. We applied our framework to the publicly available game RacingGame developed for Microsoft(R) Xna(R). Preliminary results show how this approach can be used to detect a variety of visual artifacts generated by the rendering system in a professional quality game engine

Variational tetrahedral meshing

In this paper, a novel Delaunay-based variational approach to isotropic tetrahedral meshing is presented. To achieve both robustness and efficiency, we minimize a simple mesh-dependent energy through global updates of both vertex positions and connectivity. As this energy is known to be the ∠1 distance between an isotropic quadratic function and its linear interpolation on the mesh, our minimization procedure generates well-shaped tetrahedra. Mesh design is controlled through a gradation smoothness parameter and selection of the desired number of vertices. We provide the foundations of our approach by explaining both the underlying variational principle and its geometric interpretation. We demonstrate the quality of the resulting meshes through a series of examples

Conforming restricted Delaunay mesh generation for piecewise smooth complexes

A Frontal-Delaunay refinement algorithm for mesh generation in piecewise smooth domains is described. Built using a restricted Delaunay framework, this new algorithm combines a number of novel features, including: (i) an unweighted, conforming restricted Delaunay representation for domains specified as a (non-manifold) collection of piecewise smooth surface patches and curve segments, (ii) a protection strategy for domains containing curve segments that subtend sharply acute angles, and (iii) a new class of off-centre refinement rules designed to achieve high-quality point-placement along embedded curve features. Experimental comparisons show that the new Frontal-Delaunay algorithm outperforms a classical (statically weighted) restricted Delaunay-refinement technique for a number of three-dimensional benchmark problems.Comment: To appear at the 25th International Meshing Roundtabl