Geometric construction of quintic parametric B-splines

Geometric Modelling with Beta-function B-splines, I: Parametric Curves

This is the first one in a sequence of several papers dedicated to the development of applications of Euler Beta-function B-splines (BFBS) to Computer-aided Geometric Design (CAGD) and, in particular, for geometric modelling of parametric curves, surfaces and volume deformations. This study is an analogue of the study conducted in [12, 10] for the case of expo-rational Bsplines (ERBS). An impor...

Construction of ECT - B - splines , a survey ∗

s-dimensional generalized polynomials are linear combinations of functions forming an ECT-system on a compact interval with coefficients from R. ECT-spline curves in R are constructed by glueing together at interval endpoints generalized polynomials generated from different local ECT-systems via connection matrices. If they are nonsingular, lower triangular and totally positive there is a basis...

Data Interpolation by C 2 Quintic Splines

An Evolution Model of B-splines Parametric Surface

The study of the motion of deformable objects is one of the most important topics in computer animation, computer modelling, and so on. This paper presents an evolution model which deform a parametric surface with a linear complexity and nearly stability. The deformation model is based on an associated energy to one surface, that it check the shape of it. The associated variational formulation ...

A parametric family of quintic Thue equations

For an integral parameter t ∈ Z we investigate the family of Thue equations F (x, y) = x + (t− 1)xy − (2t + 4t + 4)xy + (t + t + 2t + 4t − 3)xy + (t + t + 5t+ 3)xy + y = ±1 , originating from Emma Lehmer’s family of quintic fields, and show that for |t| ≥ 3.28 ·1015 the only solutions are the trivial ones with x = 0 or y = 0. Our arguments contain some new ideas in comparison with the standard ...