Related papers: Influence of control polygon on the generalization…
In this paper, general conversion equations are derived between Absolute Nodal Coordinates Formulation (ANCF) finite surface elements and B-spline surfaces, an extension of our previous work on the conversion between ANCF cable elements and…
Splines are one of the main methods of mathematically representing complicated shapes, which have become the primary technique in the fields of Computer Graphics (CG) and Computer-Aided Geometric Design (CAGD) for modeling complex surfaces.…
The control polygon of a Bezier curve is well-defined and has geometric significance---there is a sequence of weights under which the limiting position of the curve is the control polygon. For a Bezier surface patch, there are many possible…
In this paper we address the issue of designing developable surfaces with Bezier patches. We show that developable surfaces with a polynomial edge of regression are the set of developable surfaces which can be constructed with Aumann's…
Quadratic surfaces gain more and more attention among the Geometric Algebra community and some frameworks were proposed in order to represent, transform, and intersect these quadratic surfaces. As far as the authors know, none of these…
This paper proposes a simple technique of curve and surface construction with B-splines. Given a control polygon or a control mesh together with node ordinates corresponding to all control points, a rational curve or surface is obtained by…
Two different aspects of formation control of multiple agents subjected to linear transformation have been addressed in this paper. We consider a set of complex single integrator systems so that the dimension of the system reduces to half…
When observing the surface patterns of objects delimited by smooth surfaces, the projections of the surface patterns to the image domain will be subject to substantial variabilities, as induced by variabilities in the geometric viewing…
We study surface effects in amorphous polymer systems by means of computer simulation. In the framework of molecular dynamics, we present two different methods to prepare such surfaces. {\em Free} surfaces are stabilized solely by…
In this paper, we use the blending functions of Bernstein polynomials with shifted knots for construction of Bezier curves and surfaces. We study the nature of degree elevation and degree reduction for Bezier Bernstein functions with…
The construction of parametric curve and surface plays important role in computer aided geometric design (CAGD), computer aided design (CAD), and geometric modeling. In this paper, we define a new kind of blending functions associated with…
This paper introduces a watertight technique to deal with the boundary representation of surface-surface intersection in CAD. Surfaces play an important role in today's geometric design. The mathematical model of non-uniform rational…
In this article we study the deformation of finite maps and show how to use this deformation theory to construct varieties with given invariants in a projective space. Among other things, we prove a criterion that determines when a finite…
Graph Transformers, which incorporate self-attention and positional encoding, have recently emerged as a powerful architecture for various graph learning tasks. Despite their impressive performance, the complex non-convex interactions…
In this paper the interface between two transformation media or between a transformation medium and vacuum is studied. Strictly from the transformation optics point of view the consequences of the boundary conditions at such interfaces are…
Metasurface optical elements enable wavefront control and polarization manipulation with subwavelength resolution. Metasurfaces made of linearly birefringent meta-atoms such as rectangular nano-posts are commonly used to control phase and…
We argue that for a smooth surface S, considered as a ramified cover over the projective plane branched over a nodal-cuspidal curve B one could use the structure of the fundamental group of the complement of the branch curve to understand…
The one-sided offset surface Fd of a given surface F is, roughly speaking, obtained by shifting the tangent planes of F in direction of its oriented normal vector. The conchoid surface Gd of a given surface G is roughly speaking obtained by…
In a well-known paper by Bruna, Nagel and Wainger [BNW], Fourier transform decay estimates were proved for smooth hypersurfaces of finite line type bounding a convex domain. In this paper, we generalize their results in the following ways.…
A new global basis of B-splines is defined in the space of generalized quadratic splines (GQS) generated by Merrien subdivision algorithm. Then, refinement equations for these B-splines and the associated corner-cutting algorithm are given.…