Related papers: B/Surf: Interactive B\'ezier Splines on Surfaces
We study configurations of immersed curves in surfaces and surfaces in 3-manifolds. Among other results, we show that primitive curves have only finitely many configurations which minimize the number of double points. We give examples of…
The adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an…
Bayesian learning with Gaussian processes demonstrates encouraging regression and classification performances in solving computer vision tasks. However, Bayesian methods on 3D manifold-valued vision data, such as meshes and point clouds,…
We introduce a numerical method for reconstructing a multidimensional surface using the gradient of the surface measured at some values of the coordinates. The method consists of defining a multidimensional spline function and minimizing…
The goal of this study is to provide a method for computing the following: Given a network of curves in 3d (satisfying a condition at the intersection points), compute efficiently a smooth surface such that the curves are geodesics on it.…
Crowd-sourced mapping offers a scalable alternative to creating maps using traditional survey vehicles. Yet, existing methods either rely on prior high-definition (HD) maps or neglect uncertainties in the map fusion. In this work, we…
Professional software offers immense power but also presents significant learning challenges. Its complex interfaces, as well as insufficient built-in structured guidance and unfamiliar terminology, often make newcomers struggle with task…
Farin proposed a method for designing Bezier curves with monotonic curvature and torsion. Such curves are relevant in design due to their aesthetic shape. The method relies on applying a matrix M to the first edge of the control polygon of…
This paper derives strong relations that boundary curves of a smooth complex of patches have to obey when the patches are computed by local averaging. These relations restrict the choice of reparameterizations for geometric continuity. In…
Computing the gradients of a rendering process is paramount for diverse applications in computer vision and graphics. However, accurate computation of these gradients is challenging due to discontinuities and rendering approximations,…
Bezier parametric patches are used in engineering practice quite often, especially in CAD/CAM systems oriented to mechanical design. In many cases quadrilateral meshes are used for tessellation of parameters domain. We propose a new…
This paper develops a computational framework with unfitted meshes to solve linear piezoelectricity and flexoelectricity electromechanical boundary value problems including strain gradient elasticity at infinitesimal strains. The high-order…
Measuring the similarity of curves is a fundamental problem arising in many application fields. There has been considerable interest in several such measures, both in Euclidean space and in more general setting such as curves on Riemannian…
We present a novel multi-view implicit surface reconstruction technique, termed StreetSurf, that is readily applicable to street view images in widely-used autonomous driving datasets, such as Waymo-perception sequences, without necessarily…
Converting quad meshes to smooth manifolds, guided subdivision offers a way to combine the good highlight line distributions of recent G-spline constructions with the refinability of subdivision surfaces. Specifically, we present a C2…
In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential…
We present an approach to finding the implicit equation of a planar rational parametric cubic curve, by defining a new basis for the representation. The basis, which contains only four cubic bivariate polynomials, is defined in terms of the…
This paper will appear in the Santa Cruz proceedings. An overview of the braid group techniques in the theory of algebraic surfaces, from Zariski to the latest results, is presented. An outline of the Van Kampen algorithm for computing…
We present Spline-based Convolutional Neural Networks (SplineCNNs), a variant of deep neural networks for irregular structured and geometric input, e.g., graphs or meshes. Our main contribution is a novel convolution operator based on…
New differential-recurrence relations for B-spline basis functions are given. Using these relations, a recursive method for finding the Bernstein-B\'{e}zier coefficients of B-spline basis functions over a single knot span is proposed. The…