In this paper we shall introduce a simple, effective numerical method for finding differential operators for scalar and vector-valued functions on surfaces. The key idea of our algorithm is to develop an intrinsic and unified way to compute directly the partial derivatives of functions defined on triangular meshes which are the discretization of regular surfaces under consideration. Most import...

We describe a chain of algorithms for molecular surface and volumetric mesh generation. We take as inputs the centers and radii of all atoms of a molecule and the toolchain outputs both triangular and tetrahedral meshes that can be used for molecular shape modeling and simulation. Experiments on a number of molecules are demonstrated, showing that our methods possess several desirable propertie...

Data obtained by scanning 3D models typically contains missing pieces and holes. These can be caused due to scanning artifacts or artifacts in the surface due to wear and tear. We provide a method based on the Moving Least Squares projection to fill holes in triangular meshes obtained during the process of surface reconstruction . Our method can be applied to holes with non-planar geometry as w...

Shape analysis based on images and implicit surfaces has been an active area of research for the past several years. Particle systems have emerged as a viable solution to represent shapes for statistical analysis. One of the most widely used representations of shapes in computer graphics and visualization is the triangular mesh. It is desirable to provide a particle system representation for st...

The effects of mesh regularity on the accuracy of unstructured node-centered finite-volume discretizations are considered. The focus of this paper is on an edge-based approach that uses unweighted least-squares gradient reconstruction with a quadratic fit. Gradient errors and discretization errors for inviscid and viscous fluxes are separately studied according to a previously introduced method...

In recent years, several matrix-valued subdivisions have been proposed for triangular meshes. The matrix-valued subdivisions can simulate and extend the traditional scalar-valued subdivision, such as loop and 3 subdivision. In this paper, we study how to construct the matrix-valued subdivision wavelets, and propose the novel biorthogonal wavelet based on matrix-valued subdivisions on multiresol...

Navigation meshes are commonly employed as a practical representation for path planning and other navigation queries in animated virtual environments and computer games. This paper explores the use of triangulations as a navigation mesh, and discusses several useful triangulation–based algorithms and operations: environment modeling and validity, automatic agent placement, tracking moving obsta...

The shallow water equations model flows in rivers and coastal areas and have wide applications in ocean, hydraulic engineering, and atmospheric modeling. In [36], the authors constructed high order discontinuous Galerkin methods for the shallow water equations which can maintain the still water steady state exactly, and at the same time can preserve the nonnegativity of the water height without...

High quality meshes are crucial for the solution of partial differential equations (PDEs) via the finite element method (or other PDE solvers). The accuracy of the PDE solution, and the stability and conditioning of the stiffness matrix depend upon the mesh quality. In addition, the mesh must be untangled in order for the finite element method to generate physically valid solutions. Tangled mes...