The importance of properly implemented isosurface extraction for verifiable visualization led to a previously published paper on the general Method of Manufactured Solutions (MMS), inclusive of a supportive software infrastructure. This work builds upon that foundation, while significantly extending it. Specifically, we extend previous work on verification of geometrical properties to ensuring correctness of considerably more subtle topological characteristics that are crucial for the extracted surfaces. We first show a new theoretical synthesis of results from stratified Morse theory and digital topology for algorithms created to verify topological invariants and then we demonstrate how the MMS approach can be extended to embrace topology, consistent with the design intent for MMS. The transition to topological verification motivated these considerable theoretical advances and algorithmic development, consistent with general MMS principles. The methodology reported reveals unexpected behavior and even coding mistakes in publicly available popular isosurface codes, as presented in a case study for visualization tools that documents the

Abstract not found

The Hermite Radial Basis Functions (HRBF) Implicits reconstruct an implicit function which interpolates or approximates scattered multivariate Hermite data (i.e., unstructured points and their corresponding normals). Experiments suggest that HRBF Implicits allow the reconstruction of surfaces rich in details and behave better than previous related methods under coarse and/or nonuniform samplings, even in the presence of close sheets. HRBF Implicits theory unifies a recently introduced class of surface reconstruction methods based on radial basis functions (RBF) which incorporate normals directly in their problem formulation. Such class has the advantage of not depending on manufactured offset-points to ensure existence of a non-trivial implicit surface RBF interpolant. In fact, we show that HRBF Implicits constitute a particular case of Hermite-Birkhoff interpolation with radial basis functions, whose main results we present here. This framework not only allows us to show connections between the present method and others but also enable us to enhance the flexibility of our method by ensuring well-posedness of an interesting combined interpolation/regularisation approach.

Abstract not found