Related papers: BS-Patch: Constrained Bezier Parametric Patch
The isometric embedding of surfaces in three-dimensional space is fundamental to various physical systems, from elastic sheets to programmable materials. While continuous surfaces typically admit unique solutions under suitable boundary…
Approximating data points in three or higher dimension space based on cubic B-spline curve is presented. Representations for planar curves, are merged and extended to the higher dimension. The curve is fitted to the order of data points, or…
In this paper, we present a novel approach to the problem of merging of B\'ezier curves with respect to the $L_2$-norm. We give illustrative examples to show that the solution of the conventional merging problem may not be suitable for…
A new density field representation technique called the Bezier skeleton explicit density (BSED) representation scheme for topology optimization of stretchable metamaterials under finite deformation is proposed for the first time. The…
One key feature of isogeometric analysis is that it allows smooth shape functions. Indeed, when isogeometric spaces are constructed from $p$-degree splines (and extensions, such as NURBS), they enjoy up to $C^{p-1}$ continuity within each…
A class of quasi-distribution evaluation criteria based on piecewise Bezier curves is proposed to address the issue of the inability to objectively evaluate finite element models. During the optimization design of mechanical parts, finite…
The vast majority of mesh-based modelling applications iteratively transform the mesh vertices under prescribed geometric conditions. This occurs in particular in methods cycling through the constraint set such as Position-Based Dynamics…
Utilizing patch-based transformers for unstructured geometric data such as polygon meshes presents significant challenges, primarily due to the absence of a canonical ordering and variations in input sizes. Prior approaches to handling 3D…
In this paper, we propose a general framework for constructing IGA-suitable planar B-spline parameterizations from given complex CAD boundaries consisting of a set of B-spline curves. Instead of forming the computational domain by a simple…
Three-dimensional (3-D) meshes are commonly used to represent virtual surfaces and volumes. Over the past decade, 3-D meshes have emerged in industrial, medical, and entertainment applications, being of large practical significance for 3-D…
In [1], the author considered the problem of the optimal approximation of symmetric surfaces by biquadratic B\'ezier patches. Unfortunately, the results therein are incorrect, which is shown in this paper by considering the optimal…
This paper presents a new approach to computation of geometric continuity for parametric bi-cubic patches, based on a simple mathematical reformulation which leads to simple additional conditions to be applied in the patching computation.…
We solve the following problem: given a polynomial of order $n$ and the corresponding $B\'ezier$ tensor product patches over an unstructured regular quadrilateral mesh of any valence, find a solution to the $G^{1}1$ or $C^{1}1$…
We introduce a Bernstein-Bezier basis for the pyramid, whose restriction to the face reduces to the Bernstein-Bezier basis on the triangle or quadrilateral. The basis satisfies the standard positivity and partition of unity properties…
As a parametric polynomial curve family, B\'ezier curves are widely used in safe and smooth motion design of intelligent robotic systems from flying drones to autonomous vehicles to robotic manipulators. In such motion planning settings,…
We present a novel isogeometric collocation method for solving the Poisson's and the biharmonic equation over planar bilinearly parameterized multi-patch geometries. The proposed approach relies on the use of a modified construction of the…
The BPS spectrum of certain N=2 supersymmetric field theories can be determined algebraically by studying the representation theory of BPS quivers. We introduce methods based on BPS quivers to study line defects. The presence of a line…
In this paper, we give several simple methods for drawing a whole rational surface (without base points) as several Bezier patches. The first two methods apply to surfaces specified by triangular control nets and partition the real…
Stiffener layout optimization of complex surfaces is fulfilled within the framework of topology optimization. A combined parameterization method is developed in two aspects. One is to parameterize the material distribution of the stiffener…
B\'ezier curves provide the basic building blocks of graphic design in 2D. In this paper, we port B\'ezier curves to manifolds. We support the interactive drawing and editing of B\'ezier splines on manifold meshes with millions of…