Generalized Bézier volumes over simple convex polyhedra
In recent years, there has been growing interest in the representation of volumes within the field of geometric modeling (GM). While polygonal patches for surface modeling have been extensively studied, there has been little focus on the ...
Graphical abstract Highlights
- We propose a novel polyhedral volumetric representation method, called Generalized Bézier (GB) volume.
- A GB volume behaves as a tensor-product Bézier volume along each quadrilateral boundary surface and a tensor-product GB volume along ...
pκ-Curves: Interpolatory curves with curvature approximating a parabola
This paper introduces a novel class of fair and interpolatory planar curves called pκ-curves. These curves are comprised of smoothly stitched Bézier curve segments, where the curvature distribution of each segment is made to closely resemble a ...
Highlights
- Introduce fair and interpolatory pκ-curves with parabolic-like curvature distribution.
- Customize energy functionals to guide pκ-curve construction.
- Develop an efficient and practical algorithm to solve the tailored optimization ...
Hermite subdivision schemes for manifold-valued Hermite data
This paper introduces a family of subdivision schemes that generate curves over manifolds from manifold-Hermite data. This data consists of points and tangent directions sampled from a curve over a manifold. Using a manifold-Hermite average based ...