Computer Aided Geometric Design

It has been recently proved that rational quadratic circles in standard Bezier form are parameterized by chord-length. If we consider that standard circles coincide with the isoparametric curves in a system of bipolar coordinates, this property comes as ...

We introduce a new method of solving C^1 Hermite interpolation problems, which makes it possible to use a wider range of PH curves with potentially better shapes. By characterizing PH curves by roots of their hodographs in the complex representation, we ...

We present a new semi-topological quantity, called the absolute hodograph winding number, that measures how close the quintic PH spline interpolating a given sequence of points is to the cubic spline interpolating the same sequence. This quantity then ...

The paper describes a method to join two circles with a C-shaped and an S-shaped transition curve, composed of a Pythagorean hodograph quintic segment, preserving G^2 continuity. It is considered desirable to have such a curve in satellite path planning,...

A constructive geometric approach to rational ovals and rosettes of constant width formed by piecewise rational PH curves is presented. We propose two main constructions. The first construction, models with rational PH curves of algebraic class 3 (T-...

The problem of specifying the two free parameters that arise in spatial Pythagorean-hodograph (PH) quintic interpolants to given first-order Hermite data is addressed. Conditions on the data that identify when the ''ordinary'' cubic interpolant becomes ...

We prove there is no rational rotation-minimizing frame (RMF) along any non-planar regular cubic polynomial curve. Although several schemes have been proposed to generate rational frames that approximate RMF's, exact rational RMF's have been only ...

We prove the Weierstrass-type approximation theorem that states every C^1 curve in the 2-dimensional or 3-dimensional Euclidean space or in the 3-dimensional Minkowski space can be uniformly approximated by Pythagorean hodograph curves in the ...

We 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 ...

A new branching blend between two natural quadrics (circular cylinders/cones or spheres) in many positions is proposed. The blend is a ring shaped patch of a PN surface (surface with rational offset) parametrized by rational bivariant functions of ...

In the present paper we investigate rational two-parameter families of spheres and their envelope surfaces in Euclidean R^3. The four dimensional cyclographic model of the set of spheres in R^3 is an appropriate framework to show that a quadratic ...