Related papers: Ambient Isotopic Meshing of Implicit Algebraic Sur…
Polycube-maps are used as base-complexes in various fields of computational geometry, including the generation of regular all-hexahedral meshes free of internal singularities. However, the strict alignment constraints behind polycube-based…
This paper studies a problem of learning surface mesh via implicit functions in an emerging field of deep learning surface reconstruction, where implicit functions are popularly implemented as multi-layer perceptrons (MLPs) with rectified…
In this paper, we introduce the following problem in the theory of algorithmic self-assembly: given an input shape as the seed of a tile-based self-assembly system, design a finite tile set that can, in some sense, uniquely identify whether…
An implicit purification scheme is proposed for calculation of the temperature-dependent, grand canonical single-particle density matrix, given as a Fermi operator expansion in terms of the Hamiltonian. The computational complexity is shown…
We present a method for computing all the symmetries of a rational ruled surface defined by a rational parametrization which works directly in parametric rational form, i.e. without computing or making use of the implicit equation of the…
A technique is presented for the design of printed unit cells in aperiodic metasurface environments. The method begins with a solved matrix equation governing electromagnetic scattering from a homogenized metasurface design. The matrix…
We show that closed, immersed, minimal hypersurfaces in a compact symmetric space satisfy a lower bound on the index plus nullity, which depends linearly on their first Betti number. Moreover, if either the minimal hypersurface satisfies a…
Mutual localization is essential for coordination and cooperation in multi-robot systems. Previous works have tackled this problem by assuming available correspondences between measurements and received odometry estimations, which are…
We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using…
We prove a correspondence theorem for singular tropical surfaces in real three space, which recovers singular algebraic surfaces in an appropriate toric three-fold that tropicalize to a given singular tropical surface. Furthermore, we…
In this paper, we give algorithms for determining the existence of isomorphism between two finite-dimensional Lie algebras and compute such an isomorphism in the affirrmative case. We also provide algorithms for determining algebraic…
For generic maps from compact surfaces with boundary into the plane we develop an explicit algorithm for minimizing both the number of cusps and the number of components of the singular locus. More precisely, we minimize among maps with…
We consider a surface $M$ immersed in $\mathbb{R}^3$ with induced metric $g=\psi\delta_2$ where $\delta_2$ is the two dimensional Euclidean metric. We then construct a system of partial differential equations that constrain $M$ to lift to a…
The purpose of this paper is to explore the question "to what extent could we produce formal, machine-verifiable, proofs in real algebraic geometry?" The question has been asked before but as yet the leading algorithms for answering such…
Implicit curve and surface reconstruction attracts the attention of many researchers and gains a wide range of applications, due to its ability to describe objects with complicated geometry and topology. However, extra zero-level sets or…
This paper proposes a method for computing the visible occluding contours of subdivision surfaces. The paper first introduces new theory for contour visibility of smooth surfaces. Necessary and sufficient conditions are introduced for when…
We propose a novel meshless method to compute harmonic maps and conformal maps for surfaces embedded in the Euclidean 3-space, using point cloud data only. Given a surface, or a point cloud approximation, we simply use the standard cubic…
We present a series of examples of pairs of singular semialgebraic surfaces (real semialgebraic sets of dimension two) in ${\mathbb R}^3$ and ${\mathbb R}^4$ which are bi-Lipschitz equivalent with respect to the outer metric, ambient…
The ruled surface is a typical modeling surface in computer aided geometric design. It is usually given in the standard parametric form. However, it can also be in the forms than the standard one. For these forms, it is necessary to…
In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent implicit fixed-point…