Related papers: Implicitization of tensor product surfaces via vir…
The following is an extended version of a talk given at the Kinosaki Symposium on Algebraic Geometry in October 2011. The aim is to give an overview of product-quotient surfaces, the results that have been proven so far in collaboration…
Chen, Sederberg, and Zheng introduced the notion of a $\mu$-basis for a rational ruled surface in Chen et al. (2001) and showed that its resultant is the implicit equation of the surface, if the parametrization is generically injective. We…
In this paper, based on the theory of surfaces in the four-dimensional Euclidean space which generalizes the theory of surfaces in three-dimensional Euclidean space, beside other results, we will give a characterization of points on…
In this paper we further develop the theory of geometric tropicalization due to Hacking, Keel and Tevelev and we describe tropical methods for implicitization of surfaces. More precisely, we enrich this theory with a combinatorial formula…
Algebraic hyperbolicity serves as a bridge between differential geometry and algebraic geometry. Generally, it is difficult to show that a given projective variety is algebraically hyperbolic. However, it was established recently that a…
Implicit Neural Representations (INRs) have been demonstrated to achieve state-of-the-art compression of a broad range of modalities such as images, videos, 3D surfaces, and audio. Most studies have focused on building neural counterparts…
We present the basic concepts of tensor products of vector spaces, emphasizing linear algebraic and combinatorial techniques as needed for applied areas of research. The topics include (1) Introduction; (2) Basic multilinear algebra; (3)…
We have developed a new embedding method for solving scalar hyperbolic conservation laws on surfaces. The approach represents the interface implicitly by a signed distance function following the typical level set method and some embedding…
Consider a rational family of planar rational curves in a certain region of interest. We are interested in finding an approximation to the implicit representation of the envelope. Since exact implicitization methods tend to be very costly,…
Elliptic problems along smooth surfaces embedded in three dimensions occur in thin-membrane mechanics, electromagnetics (harmonic vector fields), and computational geometry. In this work, we present a parametrix-based integral equation…
Given a rational projective parametrization $\cP(\ttt,\sss,\vvv)$ of a rational projective surface $\cS$ we present an algorithm such that, with the exception of a finite set (maybe empty) $\cB$ of projective base points of $\cP$,…
We generate abstractions of buildings, reflecting the essential aspects of their geometry and structure, by learning to invert procedural models. We first build a dataset of abstract procedural building models paired with simulated point…
Surface extraction from implicit neural representations modelling a single class surface is a well-known task. However, there exist no surface extraction methods from an implicit representation of multiple classes that guarantee topological…
Articulated objects and their representations pose a difficult problem for robots. These objects require not only representations of geometry and texture, but also of the various connections and joint parameters that make up each…
Converting a parametric curve into the implicit form, which is called implicitization, has always been a popular but challenging problem in geometric modeling and related applications. However, the existing methods mostly suffer from the…
We advocate the use of implicit fields for learning generative models of shapes and introduce an implicit field decoder, called IM-NET, for shape generation, aimed at improving the visual quality of the generated shapes. An implicit field…
Tensor diagrams are a handy way to depict complicated relationships between objects in projective geometry. One of the simpler ones takes two copies of a $3\times 3$ matrix and computes its adjugate. In this paper, we give a geometric…
We introduce a new way to implicitly represent swept volumes in 3D. We first implicitize the base volume and then apply the time-dependent rigid transformation to build an implicit representation of the swept volume. This way, we build a…
We discretize a tangential tensor field equation using a surface-finite element approach with a penalization term to ensure almost tangentiality. It is natural to measure the quality of such a discretization intrinsically, i.e., to examine…
Mastering dexterous, contact-rich object manipulation demands precise estimation of both in-hand object poses and external contact locations$\unicode{x2013}$tasks particularly challenging due to partial and noisy observations. We present…