Open AccessAlgorithm to determine the intersection curves between bezier surfaces by the solution of multivariable polynomial system and the differential marching method
Author(s) -
Mário Carneiro Faustini,
Marcos de Sales Guerra Tsuzuki
Publication year - 2000
Publication title -
revista brasileira de ciências mecânicas
Language(s) - English
Resource type - Journals
ISSN - 0100-7386
DOI - 10.1590/s0100-73862000000200010
Subject(s) - bézier curve , mathematics , intersection (aeronautics) , multivariable calculus , polynomial , bernstein polynomial , parametric equation , basis function , parametric statistics , basis (linear algebra) , parametric surface , mathematical analysis , geometry , statistics , control engineering , engineering , aerospace engineering
The determination of the intersection curve between Bézier Surfaces may be seen as the composition of two separated problems: determining initial points and tracing the intersection curve from these points. The Bézier Surface is represented by a parametric function (polynomial with two variables) that maps a point in the tridimensional space from the bidimensional parametric space. In this article, it is proposed an algorithm to determine the initial points of the intersection curve of Bézier Surfaces, based on the solution of polynomial systems with the Projected Polyhedral Method, followed by a method for tracing the intersection curves (Marching Method with differential equations). In order to allow the use of the Projected Polyhedral Method, the equations of the system must be represented in terms of the Bernstein basis, and towards this goal it is proposed a robust and reliable algorithm to exactly transform a multivariable polynomial in terms of power basis to a polynomial written in terms of Bernstein basis