Reconstruction of helices from their orthogonal projection
We describe a method for modeling helices from planar curves. Given a polygonal curve in the ( x , y ) plane, the method computes a helix such that its orthogonal projection onto the ( x , y ) plane fits the polygonal curve. The helix curve is first ...
On degree elevation of T-splines
A degree elevation algorithm is presented for T-splines. We also provide two optimized degree elevation algorithms to restrict the resulting T-splines to be analysis-suitable. A recursive algorithm for general T-spline degree elevation is developed.Two ...
Anamorphic Free-Form Deformation
In an optical anamorphosis, an object is seen distorted unless the viewer is positioned at a specific point, where the object appears normal. We describe how to endow a rational Free-Form Deformation with an anamorphic character in a simple manner, ...
On a generalization of Bernstein polynomials and Bézier curves based on umbral calculus (III)
The investigation of a ź -Bernstein polynomials and a ź -Bézier curves is continued in this paper. It is shown that convolution of the parameters a ź = ( a ź 1 , ź , a ź n ) is fundamental for (1) the definition of a ź -Bernstein polynomials, (2) a ...
Construction of G1 planar Hermite interpolants with prescribed arc lengths
The problem of constructing a plane polynomial curve with given end points and end tangents, and a specified arc length, is addressed. The solution employs planar quintic Pythagorean-hodograph (PH) curves with equal-magnitude end derivatives. By ...
Area-preserving mesh parameterization for poly-annulus surfaces based on optimal mass transportation
This work proposes a novel method for computing area-preserving parameterization for genus zero surfaces with multiple boundaries (poly-annuli), which is based on discrete optimal mass transportation and surface Ricci Flow. We first begin with a ...
Medial axis transforms yielding rational envelopes
Minkowski Pythagorean hodograph (MPH) curves provide a means for representing domains with rational boundaries via the medial axis transform. Based on the observation that MPH curves are not the only curves that yield rational envelopes, we define and ...
High quality local interpolation by composite parametric surfaces
In CAGD the design of a surface that interpolates an arbitrary quadrilateral mesh is definitely a challenging task. The basic requirement is to satisfy both criteria concerning the regularity of the surface and aesthetic concepts.With regard to ...
Computing µ-bases from algebraic ruled surfaces
We find a µ-basis for a rational ruled surface, starting from its implicit representation. A parametrization for this ruled surface is then deduced form this µ-basis. This parametrization does not have any non-generic base points and its directrix has ...