Related papers: B/Surf: Interactive B\'ezier Splines on Surfaces
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…
We integrate smoothing B-splines into a standard differentiable vector graphics (DiffVG) pipeline through linear mapping, and show how this can be used to generate smooth and arbitrarily long paths within image-based deep learning systems.…
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…
Bspline solids are used for solid objects modeling in R3. Mathematica incorporates a several commands to manipulate symbolic and graphically Bspline basis functions and to graphically manipulate Bsplines curves and surfaces; however, it…
We introduce B\'{e}zier projection as an element-based local projection methodology for B-splines, NURBS, and T-splines. This new approach relies on the concept of B\'{e}zier extraction and an associated operation introduced here, spline…
Bilevel optimization has gained prominence in various applications. In this study, we introduce a framework for solving bilevel optimization problems, where the variables in both the lower and upper levels are constrained on Riemannian…
The smoothing spline is one of the most popular curve-fitting methods, partly because of empirical evidence supporting its effectiveness and partly because of its elegant mathematical formulation. However, there are two obstacles that…
Parametric boundary representation models (B-Reps) are the de facto standard in CAD, graphics, and robotics, yet converting them into valid meshes remains fragile. The difficulty originates from the unavoidable approximation of high-order…
We unify and extend previous bijections on plane quadrangulations to bipartite and quasibipartite plane maps. Starting from a bipartite plane map with a distinguished edge and two distinguished corners (in the same face or in two different…
3D Computer-Aided Design (CAD) users need to overcome several obstacles to benefit from the flexibility of programmatic interface tools. Besides the barriers of any programming language, users face challenges inherent to 3D spatial…
Lane detection has made significant progress in recent years, but there is not a unified architecture for its two sub-tasks: 2D lane detection and 3D lane detection. To fill this gap, we introduce B\'{e}zierFormer, a unified 2D and 3D lane…
For large-scale data fitting, the least-squares progressive iterative approximation is a widely used method in many applied domains because of its intuitive geometric meaning and efficiency. In this work, we present a randomized progressive…
As a parametric motion representation, B\'ezier curves have significant applications in polynomial trajectory optimization for safe and smooth motion planning of various robotic systems, including flying drones, autonomous vehicles, and…
In this paper, we give an efficient algorithm of degree reduction of B\'ezier curves with box constraints. The idea is to combine the previous iterative approach, that has been presented recently in (P. Gospodarczyk, Comput. Aided Des. 62…
Polygonal meshes are ubiquitous, but have only played a relatively minor role in the deep learning revolution. State-of-the-art neural generative models for 3D shapes learn implicit functions and generate meshes via expensive iso-surfacing.…
Recently, many methods have been proposed for face reconstruction from multiple images, most of which involve fundamental principles of Shape from Shading and Structure from motion. However, a majority of the methods just generate discrete…
The novel Locally Refined B-spline (LR B-spline) surface format is suited for representing terrain and seabed data in a compact way. It provides an alternative to the well know raster and triangulated surface representations. An LR B-spline…
In this paper, we propose a linear method for $C^{(r,s)}$ approximation of rational B\'{e}zier curve with arbitrary degree polynomial curve. Based on weighted least-squares, the problem be converted to an approximation between two…
We present CUBE (Control-based Unified B-spline Encoding), a new geometric representation for human faces that combines B-spline volumes with learned features, and demonstrate its use as a decoder for 3D scan registration and monocular 3D…
Calculations of properties of materials require performing numerical integrals over the Brillouin zone (BZ). Integration points in density functional theory codes are uniformly spread over the BZ (despite integration error being…