Related papers: On the CAD-compatible conversion of S-patches
The recent surge of utilizing deep neural networks for geometric processing and shape modeling has opened up exciting avenues. However, there is a conspicuous lack of research efforts on using powerful neural representations to extend the…
A parameterized surface can be represented as a projection from a certain toric surface. This generalizes the classical homogeneous and bihomogeneous parameterizations. We extend to the toric case two methods for computing the implicit…
It is shown that there are examples of distinct polyhedra, each with a Hamiltonian path of edges, which when cut, unfolds the surfaces to a common net. In particular, it is established for infinite classes of triples of tetrahedra.
The one-sided offset surface Fd of a given surface F is, roughly speaking, obtained by shifting the tangent planes of F in direction of its oriented normal vector. The conchoid surface Gd of a given surface G is roughly speaking obtained by…
In this paper we show that a surface in P^3 parametrized over a 2-dimensional toric variety T can be represented by a matrix of linear syzygies if the base points are finite in number and form locally a complete intersection. This…
Every bi-uniform matroid is representable over all sufficiently large fields. But it is not known exactly over which finite fields they are representable, and the existence of efficient methods to find a representation for every given…
Many innovative applications require establishing correspondences among 3D geometric objects. However, the countless possible deformations of smooth surfaces make shape matching a challenging task. Finding an embedding to represent the…
Subdivision surfaces are proven to be a powerful tool in geometric modeling and computer graphics, due to the great flexibility they offer in capturing irregular topologies. This paper discusses the robust and efficient implementation of an…
This paper presents the generalization of weighted distances to modules and their computation through the chamfer algorithm on general point lattices. The first part is dedicated to formalization of definitions and properties (distance,…
We introduce trimmed NURBS surfaces with accurate boundary control, briefly called ABC-surfaces, as a solution to the notorious problem of constructing watertight or smooth ($G^1$ and $G^2)$ multi-patch surfaces within the function range of…
In this article we describe an algorithm that can be applied for the generation of various classes of maps on orientable surfaces. It uses existing generators for abstract graphs and combines them with an efficient embedding and isomorphism…
This thesis surveys the research in patch-based synthesis and algorithms for finding correspondences between small local regions of images. We additionally explore a large kind of applications of this new fast randomized matching technique.…
Reconstructing 3D shape from 2D sketches has long been an open problem because the sketches only provide very sparse and ambiguous information. In this paper, we use an encoder/decoder architecture for the sketch to mesh translation. When…
A piecewise Chebyshevian spline space is good for design when it possesses a B-spline basis and this property is preserved under knot insertion. The interest in such kind of spaces is justified by the fact that, similarly as for polynomial…
A pants decomposition of an orientable surface S is a collection of simple cycles that partition S into pants, i.e., surfaces of genus zero with three boundary cycles. Given a set P of n points in the plane, we consider the problem of…
Given a small polygon S, a big simple polygon B and a positive integer k, it is shown to be NP-hard to determine whether k copies of the small polygon (allowing translation and rotation) can be placed in the big polygon without overlap.…
Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…
G-frames are generalized frames which include ordinary frames, bounded invertible linear operators, as well as many recent generalizations of frames, e.g., bounded quasi-projectors and frames of subspaces. G-frames are natural…
We present a bottom-up differentiable relaxation of the process of drawing points, lines and curves into a pixel raster. Our approach arises from the observation that rasterising a pixel in an image given parameters of a primitive can be…
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…