Related papers: BS-Patch: Constrained Bezier Parametric Patch
A new modification of the Hermite cubic rectangular patch is proposed: the S-Patch, which is based on the requirement that diagonal curves must be of degree 3 instead of degree 6 as it is in the case of the Hermite patch. Theoretical…
Bicubic four-sided patches are widely used in computer graphics, CAD/CAM systems etc. Their flexibility is high and enables to compress a surface description before final rendering. However, computer graphics hardware supports only…
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…
Properties of a parametric curve in R^3 are often determined by analysis of its piecewise linear (PL) approximation. For Bezier curves, there are standard algorithms, known as subdivision, that recursively create PL curves that converge to…
The affine space of all tensor product B\'ezier patches of degree nxn with prescribed main diagonal curves is determined. First, the pair of B\'ezier curves which can be diagonals of a B\'ezier patch is characterized. Besides prescribing…
A technique is described for constructing three-dimensional vector graphics representations of planar regions bounded by cubic B\'ezier curves, such as smooth glyphs. It relies on a novel algorithm for compactly partitioning planar B\'ezier…
Cage-based deformation is a fundamental problem in geometry processing, where a cage, a user-specified boundary of a region, is used to deform the ambient space of a given mesh. Traditional 3D cages are typically composed of triangles and…
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…
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…
Delineating the lesion area is an important task in image-based diagnosis. Pixel-wise classification is a popular approach to segmenting the region of interest. However, at fuzzy boundaries such methods usually result in glitches,…
In this paper, we introduce the BMT distribution as an unimodal alternative to continuous univariate distributions supported on a bounded interval. The ideas behind the mathematical formulation of this new distribution come from computer…
Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By…
We present a study of radially and azimuthally polarized Bessel-Gauss beams in both the paraxial and nonparaxial regimes. We discuss the validity of the paraxial approximation and the form of the nonparaxial corrections for Bessel-Gauss…
This paper derives strong relations that boundary curves of a smooth complex of patches have to obey when the patches are computed by local averaging. These relations restrict the choice of reparameterizations for geometric continuity. In…
Toric B\'ezier patches generalize the classical tensor-product triangular and rectangular B\'ezier surfaces, extensively used in $CAGD$. The construction of toric B\'ezier surfaces corresponding to multi-sided convex hulls for known…
The Cartesian coordinate system is the most commonly used system in computer visualization. This is due to its ease of use and processing speed. However, it is not always suitable for a given problem. Angular measures often allow us to…
Lower bounds on the generation of smooth bi-cubic surfaces imply that geometrically smooth ($G^1$) constructions need to satisfy conditions on the connectivity and layout. In particular, quadrilateral meshes of arbitrary topology can not in…
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…
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 B\'ezier surface. This is a big advantage compared to other multi-sided…
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…