Related papers: Smooth surface interpolation using patches with ra…
This paper proposes a simple technique of curve and surface construction with B-splines. Given a control polygon or a control mesh together with node ordinates corresponding to all control points, a rational curve or surface is obtained by…
We introduce an information-theoretic framework for smooth structures on topological manifolds, replacing coordinate charts with small-scale entropy data of local probability probes. A concise set of axioms identifies admissible coordinate…
In this paper we describe a parallel implicit method based on radial basis functions (RBF) for surface reconstruction. The applicability of RBF methods is hindered by its computational demand, that requires the solution of linear systems of…
We examine the use of domain decomposition for potentially more efficient mean curvature flow of surface meshes, whose faces are arbitrary simple polygons. We first test traditional domain decomposition methods with and without overlap of…
Oriented normals are common pre-requisites for many geometric algorithms based on point clouds, such as Poisson surface reconstruction. However, it is not trivial to obtain a consistent orientation. In this work, we bridge orientation and…
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,…
This is an expanded version of the two papers "Interpolation of Varieties of Minimal Degree" and "Interpolation Problems: Del Pezzo Surfaces." It is well known that one can find a rational normal curve in $\mathbb P^n$ through $n+3$ general…
It is constructed a formal normal form, using an iterative normalization procedure, for a large class of Real-Smooth Hypersurfaces in Complex Spaces.
Implicit neural networks have been successfully used for surface reconstruction from point clouds. However, many of them face scalability issues as they encode the isosurface function of a whole object or scene into a single latent vector.…
In this paper, we propose an effective point cloud generation method, which can generate multi-resolution point clouds of the same shape from a latent vector. Specifically, we develop a novel progressive deconvolution network with the…
A procedure for interpolating between specified points of a curve or surface is described. The method guarantees slope continuity at all junctions. A surface panel divided into p x q contiguous patches is completely specified by the…
We present a learning-based method for interpolating and manipulating 3D shapes represented as point clouds, that is explicitly designed to preserve intrinsic shape properties. Our approach is based on constructing a dual encoding space…
We analyze surface patches with a corner that is rounded in the sense that the partial derivatives at that point are antiparallel. Sufficient conditions for $G^1$ smoothness are given, which, up to a certain degenerate case, are also…
In applications that involve interactive curve and surface modeling, the intuitive manipulation of shapes is crucial. For instance, user interaction is facilitated if a geometrical object can be manipulated through control points that…
We present an isogeometric analysis technique that builds on manifold-based smooth basis functions for geometric modelling and analysis. Manifold-based surface construction techniques are well known in geometric modelling and a number of…
Embedded WENO methods utilize all adjacent smooth substencils to construct a desirable interpolation. Conventional WENO schemes under-use this possibility close to large gradients or discontinuities. We develop a general approach for…
Modern shape design and capture techniques often lead to the geometric data presented in the form of serial rows of data points. In general, the number of data points varies from row to row. Lofted or skinned B-spline surface interpolation…
Spline interpolation has been used in several applications due to its favorable properties regarding smoothness and accuracy of the interpolant. However, when there exists a discontinuity or a steep gradient in the data, some artifacts can…
Thin surfaces, such as the leaves of a plant, pose a significant challenge for implicit surface reconstruction techniques, which typically assume a closed, orientable surface. We show that by approximately interpolating a point cloud of the…
We introduce new manifold-based splines that are able to exactly reproduce B-splines on unstructured surface meshes. Such splines can be used in isogeometric analysis (IGA) to represent smooth surfaces of arbitrary topology. Since prevalent…