Searcharxiv⌕ Search

arXiv subjects

Péter Salvi

Publications and source records attributed to Péter Salvi.

9 recordsLinked to original sources
arXiv2026

Polyhedral design with blended $n$-sided interpolants

A new parametric surface representation is proposed that interpolates the vertices of a given closed mesh of arbitrary topology. Smoothly connecting quadrilateral patches are created by blending local, multi-sided quadratic interpolants. In the non-four-sided case, this requires a special parameterization technique involving rational curves. Appropriate handling of triangular subpatches and alternative subpatch representations are also discussed.

cs.CG↗
arXiv2023

A circular parameterization for multi-sided patches

Most genuine multi-sided surface representations depend on a 2D domain that enables a mapping between local parameters and global coordinates. The shape of this domain ranges from regular polygons to curved configurations, but the simple circular domain - to the best of our knowledge - has not been investigated yet. Here we fill this gap, and introduce a parameter mapping ideal for use with periodic boundaries. It is based on circular arcs and satisfies constraints often needed in actual surface formulations. The proposed method is demonstrated through a corner-based variant of Generalized Bézier patches.

cs.CG↗
arXiv2022

Approximating triangular meshes by implicit, multi-sided surfaces

The I-patch is a multi-sided surface representation, defined as a combination of implicit ribbon and bounding surfaces, whose pairwise intersections determine the natural boundaries of the patch. Our goal is to show how a collection of smoothly connected I-patches can be used to approximate triangular meshes. We start from a coarse, user-defined vertex graph which specifies an initial subdivision of the surface. Based on this, we create ribbons that tightly fit the mesh along its edges in both positional and tangential sense, then we optimize the free parameters of the patch to better approximate the interior. If the surfaces are not sufficiently accurate, the network needs to be refined; here we exploit that the I-patch construction naturally supports T-nodes. We also describe a normalization method that nicely approximates the Euclidean distance field, and can be efficiently evaluated. The capabilities and limitations of the approach are analyzed through several examples.

cs.CG↗
arXiv2022

Creating good quality meshes from smooth implicit surfaces

Visualization of implicit surfaces is an actively researched topic. While raytracing can produce high quality images, it is not well suited for creating a quick preview of the surface. Indirect algorithms (e.g. Marching Cubes) create an easily renderable triangle mesh, but the result is often not sufficiently well-structured for a good approximation of differential surface quantities (normals, curvatures, etc.). Post-processing methods usually have a considerable computational overhead, and high quality is not guaranteed. We propose a tessellation algorithm to create nearly isotropic meshes, using multi-sided implicit surfaces.

cs.GR↗
arXiv2020

A multi-sided generalization of the $C^0$ Coons patch

Most multi-sided transfinite surfaces require cross-derivatives at the boundaries. Here we show a general $n$-sided patch that interpolates all boundaries based on only positional information. The surface is a weighted sum of $n$ Coons patches, using a parameterization based on Wachspress coordinates.

cs.GR↗
arXiv2020

$G^1$ hole filling with S-patches made easy

S-patches have been around for 30 years, but they are seldom used, and are considered more of a mathematical curiosity than a practical surface representation. In this article a method is presented for automatically creating S-patches of any degree or any number of sides, suitable for inclusion in a curve network with tangential continuity to the adjacent surfaces. The presentation aims at making the implementation straightforward; a few examples conclude the paper.

cs.GR↗
arXiv2020

On the CAD-compatible conversion of S-patches

S-patches have many nice mathematical properties. It is known since their first appearance, that any regular S-patch can be exactly converted into a trimmed rational Bézier surface. This is a big advantage compared to other multi-sided surface representations that have to be approximated for exporting them into CAD/CAM systems. The actual conversion process, however, remained at a theoretical level, with bits and pieces scattered in multiple publications. In this paper we review the entirety of the algorithm, and investigate it from a practical aspect.

cs.GR↗
arXiv2020

Computationally efficient transfinite patches with fullness control

Transfinite patches provide a simple and elegant solution to the problem of representing non-four-sided continuous surfaces, which are useful in a variety of applications, such as curve network based design. Real-time responsiveness is essential in this context, and thus reducing the computation cost is an important concern. The Midpoint Coons (MC) patch presented in this paper is a fusion of two previous transfinite schemes, combining the speed of one with the superior control mechanism of the other. This is achieved using a new constrained parameterization based on generalized barycentric coordinates and transfinite blending functions.

cs.GR↗