Related papers: A package for computing implicit equations of para…
Boundary representation (B-rep) is the industry standard for computer-aided design (CAD). While deep learning shows promise in processing B-rep models, existing methods suffer from a representation gap: continuous approaches offer…
A novel algorithm for creating a mathematical model of curved shapes is introduced. The core of the algorithm is based on building a graph representation of the contoured image, which occupies less storage space than produced by raster…
The non-linear transformations incurred by the rays in an optical system can be suitably described by matrices to any desired order of approximation. In systems composed of uniform refractive index elements, each individual ray refraction…
A stochastic method is introduced for geometric modeling aerosol surface roughness with random field and discrete differential geometry theory. Optical scattering properties are computed for randomly oriented spheroidal particles with…
Neural implicit representations, which encode a surface as the level set of a neural network applied to spatial coordinates, have proven to be remarkably effective for optimizing, compressing, and generating 3D geometry. Although these…
When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…
Rough sets were proposed to deal with the vagueness and incompleteness of knowledge in information systems. There are may optimization issues in this field such as attribute reduction. Matroids generalized from matrices are widely used in…
Mirror symmetry suggests unexpected relationships between arithmetic properties of distinct families of algebraic varieties. For example, Wan and others have shown that for some mirror pairs, the number of rational points over a finite…
Implicit surface representations, such as signed-distance functions, combined with deep learning have led to impressive models which can represent detailed shapes of objects with arbitrary topology. Since a continuous function is learned,…
Simplified representations of macromolecules help in rationalising and understanding the outcome of atomistic simulations, and serve to the construction of effective, coarse-grained models. The number and distribution of coarse-grained…
This paper presents a spline-based parameterisation framework for plane graphs. The plane graph is characterised by a collection of curves forming closed loops that fence-off planar faces which have to be parameterised individually. Hereby,…
We present some algorithms that provide useful topological information about curves in surfaces. One of the main algorithms computes the geometric intersection number of two properly embedded 1-manifolds $C_1$ and $C_2$ in a compact…
Computing offsets of curves on parametric surfaces is a fundamental yet challenging operation in computer aided design and manufacturing. Traditional analytical approaches suffer from time-consuming geodesic distance queries and complex…
Whereas dedicated scene representations are required for each different task in conventional robotic systems, this paper demonstrates that a unified representation can be used directly for multiple key tasks. We propose the Log-Gaussian…
We construct a matrix representation of compact membranes analytically embedded in complex tori. Brane configurations give rise, via Bergman quantization, to U(N) gauge fields on the dual torus, with almost-anti-self-dual field strength.…
Tube-like surfaces are widely encountered in geometry processing, engineering structures, and medical anatomy, yet their intrinsic longitudinal and circumferential topology is not well preserved by conventional planar annular or rectangular…
The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate…
We contribute a new algebraic method for computing the orthogonal projections of a point onto a rational algebraic surface embedded in the three dimensional projective space. This problem is first turned into the computation of the finite…
We present the Macaulay2 package TropicalToric.m2 for toric intersection theory computations using tropical geometry.
We introduce a conceptually simple and efficient algorithm for seamless parametrization, a key element in constructing quad layouts and texture charts on surfaces. More specifically, we consider the construction of parametrizations with…