Related papers: Fast Disk Conformal Parameterization of Simply-con…
Several problems in magnetically confined fusion, such as the computation of exterior vacuum fields or the decomposition of the total magnetic field into separate contributions from the plasma and the external sources, are best formulated…
When two bodies get into contact, only a small portion of the apparent area is actually involved in producing contact and friction forces, because of the surface roughnesses. It is therefore crucial to accurately describe the morphology of…
Surface parameterization plays an essential role in numerous computer graphics and geometry processing applications. Traditional parameterization approaches are designed for high-quality meshes laboriously created by specialized 3D…
This work introduces a novel method for surface normal estimation from rectified stereo image pairs, leveraging affine transformations derived from disparity values to achieve fast and accurate results. We demonstrate how the rectification…
The notion of discrete conformality proposed by Luo and Bobenko-Pinkall-Springborn on triangle meshes has rich mathematical theories and wide applications. Gu et al. proved that the discrete uniformizations approximate the continuous…
We present a systematic, algebraically based, design methodology for efficient implementation of computer programs optimized over multiple levels of the processor/memory and network hierarchy. Using a common formalism to describe the…
Discrete conformal mappings based on circle packing, vertex scaling, and related structures has had significant activity since Thurston proposed circle packing as a way to approximate conformal maps in the 1980s. The first convergence…
With the rapid development of high-resolution 3D vision applications, the traditional way of manipulating surface detail requires considerable memory and computing time. To address these problems, we introduce an efficient surface detail…
Acquiring an anatomical map from position data is important for medical applications where catheters interact with soft tissues. To improve autonomous navigation in these settings, we require information beyond nonparametric maps typically…
We use a conformal mapping method introduced in a companion paper to study the properties of bi-harmonic fields in the vicinity of rough boundaries. We focus our analysis on two different situations where such bi-harmonic problems are…
Isothermic parameterizations} are synonyms of isothermal curvature line parameterizations, for surfaces immersed in Euclidean spaces. We provide a method of constructing isothermic coordinate charts on surfaces which admit them, starting…
We fully generalize a previously-developed computational geometry tool [1] to perform large-scale simulations of arbitrary two-dimensional faceted surfaces $z = h(x,y)$. Our method uses a three-component facet/edge/junction storage model,…
Point discretization of curved surfaces is required in many applications ranging from object rendering to the solution of surface partial differential equations (PDEs). These applications often impose that surfaces are sampled with local…
We present a novel shape-approximating anisotropic re-meshing algorithm as a geometric generalization of the adaptive moving mesh method. Conventional moving mesh methods reduce the interpolation error of a mesh that discretizes a given…
Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…
Computational analysis with the finite element method requires geometrically accurate meshes. It is well known that high-order meshes can accurately capture curved surfaces with fewer degrees of freedom in comparison to low-order meshes.…
We propose a fast bivariate smoothing approach for symmetric surfaces that has a wide range of applications. We show how it can be applied to estimate the covariance function in longitudinal data as well as multiple additive covariances in…
We introduce decorated piecewise hyperbolic and spherical surfaces and discuss their discrete conformal equivalence. A decoration is a choice of circle about each vertex of the surface. Our decorated surfaces are closely related to…
In the calculation of thermodynamic properties and three dimensional structures of macromolecules, such as proteins, it is important to have a good algorithm for computing solvent accessible surface area of macromolecules. Here we propose a…
To produce cartographic maps, simplification is typically used to reduce complexity of the map to a legible level. With schematic maps, however, this simplification is pushed far beyond the legibility threshold and is instead constrained by…