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- research-articleFebruary 2021
Representing planar domains by polar parameterizations with parabolic parameter lines
Computer Aided Geometric Design (CAGD), Volume 85, Issue Chttps://doi.org/10.1016/j.cagd.2021.101966AbstractPolar parameterizations of star-shaped domains are based on the line segments that connect a suitably chosen center point with the points on the domain's boundary. Valid (i.e., regular everywhere except at the center point) polar ...
- research-articleMay 2019
Arc fibrations of planar domains
Computer Aided Geometric Design (CAGD), Volume 71, Issue CPages 105–118https://doi.org/10.1016/j.cagd.2019.04.010AbstractIt is well known that star-shaped domains possess particularly simple polar parameterizations, which are formed by the line segments that connect a suitably chosen center with the points on the domain's boundary. The polar ...
- articleJune 2012
Curves and surfaces with rational chord length parameterization
Computer Aided Geometric Design (CAGD), Volume 29, Issue 5Pages 231–241https://doi.org/10.1016/j.cagd.2011.04.003The investigation of rational varieties with chord length parameterization (shortly RCL varieties) was started by Farin (2006) who observed that rational quadratic circles in standard Bezier form are parametrized by chord length. Motivated by this ...
- articleFebruary 2011
Spherical quadratic Bézier triangles with chord length parameterization and tripolar coordinates in space
Computer Aided Geometric Design (CAGD), Volume 28, Issue 2Pages 127–134https://doi.org/10.1016/j.cagd.2010.11.001We consider special rational triangular Bezier surfaces of degree two on the sphere in standard form and show that these surfaces are parameterized by chord length. More precisely, it is shown that the ratios of the three distances of a point to the ...
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- articleDecember 2008
A construction of rational manifold surfaces of arbitrary topology and smoothness from triangular meshes
Computer Aided Geometric Design (CAGD), Volume 25, Issue 9Pages 801–815https://doi.org/10.1016/j.cagd.2008.08.003Given a closed triangular mesh, we construct a smooth free-form surface which is described as a collection of rational tensor-product and triangular surface patches. The surface is obtained by a special manifold surface construction, which proceeds by ...
- articleMay 2008
On rationally supported surfaces
Computer Aided Geometric Design (CAGD), Volume 25, Issue 4-5Pages 320–331https://doi.org/10.1016/j.cagd.2007.10.005We analyze the class of surfaces which are equipped with rational support functions. Any rational support function can be decomposed into a symmetric (even) and an antisymmetric (odd) part. We analyze certain geometric properties of surfaces with odd ...
- articleAugust 2007
Evolution-based least-squares fitting using Pythagorean hodograph spline curves
Computer Aided Geometric Design (CAGD), Volume 24, Issue 6Pages 310–322https://doi.org/10.1016/j.cagd.2007.04.001The problem of approximating a given set of data points by splines composed of Pythagorean hodograph (PH) curves is addressed. We discuss this problem in a framework that is not only restricted to PH spline curves, but can be applied to more general ...
- articleApril 2007
Computing roots of polynomials by quadratic clipping
Computer Aided Geometric Design (CAGD), Volume 24, Issue 3Pages 125–141https://doi.org/10.1016/j.cagd.2007.01.003We present an algorithm which is able to compute all roots of a given univariate polynomial within a given interval. In each step, we use degree reduction to generate a strip bounded by two quadratic polynomials which encloses the graph of the ...
- articleOctober 2006
On the existence of biharmonic tensor-product Bézier surface patches
A tensor-product Bezier surface patch x of degree (m,n) is called biharmonic if it satisfies @D^2x=0. As shown by Monterde and Ugail (2004), these surface patches are fully determined by their four boundaries. In this note we derive necessary conditions ...
- articleJuly 2006
G1 Hermite interpolation by Minkowski Pythagorean hodograph cubics
As observed by [Choi, H.I., Han, Ch.Y., Moon, H.P., Roh, K.H., Wee, N.S., 1999. Medial axis transform and offset curves by Minkowski Pythagorean hodograph curves. Computer-Aided Design 31, 59-72], curves in Minkowski space R^2^,^1 are very well suited ...
- articleJuly 2006
G1 Hermite interpolation by Minkowski Pythagorean hodograph cubics
As observed by [Choi, H.I., Han, Ch.Y., Moon, H.P., Roh, K.H., Wee, N.S., 1999. Medial axis transform and offset curves by Minkowski Pythagorean hodograph curves. Computer-Aided Design 31, 59-72], curves in Minkowski space R2,1 are very well suited to ...
- articleFebruary 2006
Rational surfaces with linear normals and their convolutions with rational surfaces
It is shown that polynomial (or rational) parametric surfaces with a linear field of normal vectors are dual to graphs bivariate polynomials (or rational functions). We discuss the geometric properties of these surfaces. In particular, using the dual ...
- articleNovember 2005
Euclidean and Minkowski Pythagorean hodograph curves over planar cubics
Starting with a given planar cubic curve [x(t),y(t)]^T, we construct Pythagorean hodograph (PH) space curves of the form [x(t),y(t),z(t)]^T in Euclidean and in Minkowski space, which interpolate the tangent vector at a given point. We prove the ...
- articleDecember 2003
The shape of spherical quartics
Computer Aided Geometric Design (CAGD), Volume 20, Issue 8-9Pages 621–636https://doi.org/10.1016/j.cagd.2003.07.003We discuss the problem of interpolating C1 Hermite data on the sphere (two points with associated first derivative vectors) by spherical rational curves. With the help of the generalized stereographic projection (Dietz et al., 1993), we construct a two-...
