Related papers: Local Surface Parameterizations via Smoothed Geode…
This paper presents a spline-based parameterisation framework for plane graphs. The plane graph is characterised by a collection of curves forming closed loops that fence-off planar faces which have to be parameterised individually. Hereby,…
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…
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…
Randomly sampling points on surfaces is an essential operation in geometry processing. This sampling is computationally straightforward on explicit meshes, but it is much more difficult on other shape representations, such as widely-used…
Surface parametrization is a crucial part in various fields, having applications in computer graphic, medical imaging, scientific computing and computational engineering. The majority of surface parametrization approaches are performed on…
Domain discretization is an essential part of the solution procedure in numerical simulations. Meshless methods simplify the domain discretization to positioning of nodes in the interior and on the boundary of the domain. However, generally…
The advancements in neural rendering have increased the need for techniques that enable intuitive editing of 3D objects represented as neural implicit surfaces. This paper introduces a novel neural algorithm for parameterizing neural…
Inferring signed distance functions (SDFs) from sparse point clouds remains a challenge in surface reconstruction. The key lies in the lack of detailed geometric information in sparse point clouds, which is essential for learning a…
Surface-based data is commonly observed in diverse practical applications spanning various fields. In this paper, we introduce a novel nonparametric method to discover the underlying signals from data distributed on complex surface-based…
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…
Isothermic parameterizations} are synonyms of isothermal curvature line parameterizations, for surfaces immersed in Euclidean spaces. We provide a method of constructing isothermic coordinate charts on surfaces which admit them, starting…
Reconstruction of geometry based on different input modes, such as images or point clouds, has been instrumental in the development of computer aided design and computer graphics. Optimal implementations of these applications have…
In this paper we present a method for direct evaluation of generalized B-splines (GB-splines) via the local representation of these curves as piecewise functions. To accomplish this we introduce a local structure that makes GB-spline curves…
Surface parameterization is a fundamental concept in fields such as differential geometry and computer graphics. It involves mapping a surface in three-dimensional space onto a two-dimensional parameter space. This process allows for the…
Neural implicit surface representations have recently emerged as popular alternative to explicit 3D object encodings, such as polygonal meshes, tabulated points, or voxels. While significant work has improved the geometric fidelity of these…
In this paper we present an algorithm for computing a matrix representation for a surface in P^3 parametrized over a 2-dimensional toric variety T. This algorithm follows the ideas of [Botbol-Dickenstein-Dohm-09] and it was implemented in…
Conventional field parameters for surface measurement use all data points, while feature characterization focuses on subsets extracted by watershed segmentation. This approach enables the extraction of specific features that are potentially…
We present a computational scheme that derives a global polynomial level set parametrisation for smooth closed surfaces from a regular surface-point set and prove its uniqueness. This enables us to approximate a broad class of smooth…
Conformal surface parameterization is useful in graphics, imaging and visualization, with applications to texture mapping, atlas construction, registration, remeshing and so on. With the increasing capability in scanning and storing data,…
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…