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Polygonal meshes have become the standard for discretely approximating 3D shapes, thanks to their efficiency and high flexibility in capturing non-uniform shapes. This non-uniformity, however, leads to irregularity in the mesh structure,…
Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, best known as a procedure to enable Quantifier Elimination over real-closed fields. However, it has a worst case complexity doubly exponential in…
An extension of the Method of Regularized Stokeslets (MRS) in three dimensions is developed for triangulated surfaces with a piecewise linear force distribution. The method extends the regularized Stokeslet segment methodology used for…
Finite element codes typically use data structures that represent unstructured meshes as collections of cells, faces, and edges, each of which require associated coordinate systems. One then needs to store how the coordinate system of each…
Some methods based on simple regularizing geometric element transformations have heuristically been shown to give runtime efficient and quality effective smoothing algorithms for meshes. We describe the mathematical framework and a…
Document dewarping, aiming to eliminate geometric deformation in photographed documents to benefit text recognition, has made great progress in recent years but is still far from being solved. While Cartesian coordinates are typically…
We present a novel algorithm to compute multi-scale curvature fields on triangle meshes. Our algorithm is based on finding robust mean curvatures using the ball neighborhood, where the radius of a ball corresponds to the scale of the…
While many algorithms exist for tracing various contours for illustrating a meshed object, few algorithms organize these contours into region-bounding closed loops. Tracing closed-loop boundaries on a mesh can be problematic due to…
We propose an image processing scheme based on reordering of its patches. For a given corrupted image, we extract all patches with overlaps, refer to these as coordinates in high-dimensional space, and order them such that they are chained…
For natural and artificial systems with some symmetry structure, computational understanding and manipulation can be achieved without learning by exploiting the algebraic structure. Here we describe this algebraic coordinatization method…
We prove a novel method for the embedding of a 3-fold rotationally symmetric sphere-type mesh onto a subset of the plane with 3-fold rotational symmetry. The embedding is free-boundary with the only additional constraint on the image set is…
Lattice structures have been widely used in applications due to their superior mechanical properties. To fabricate such structures, a geometric processing step called triangulation is often employed to transform them into the STL format…
With the increased availability of 3D scanning technology, point clouds are moving into the focus of computer vision as a rich representation of everyday scenes. However, they are hard to handle for machine learning algorithms due to their…
In this paper, we compare two optimization algorithms using full Hessian and approximation Hessian to obtain numerical spherical designs through their variational characterization. Based on the obtained spherical design point sets, we…
Image retargeting is a new image processing task that renders the change of aspect ratio in images. One of the most famous image-retargeting algorithms is seam-carving. Although seam-carving is fast and straightforward, it usually distorts…
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…
In molecular physics, it is often necessary to average over the orientation of molecules when calculating observables, in particular when modelling experiments in the liquid or gas phase. Evaluated in terms of Euler angles, this is closely…
We describe Mosaic, a computational geometry method for constructing the surface mosaic induced when a Cartesian volume grid intersects a spherical shell. The motivating application is conservative coupling between data produced on…
This article presents some aspects and experience in the use of algebraic manipulation software applied to general relativity. Some years ago certain results were reported using computer algebra platforms, but the growing popularity of…
This paper theoretically proposes a multichannel functional metasurface computer characterized by Generalized Sheet Transition Conditions (GSTCs) and surface susceptibility tensors. The study explores a polarization- and angle-multiplexed…