Algorithm to Determine the Intersection Curves between Bezier Surfaces by the Solution of Multivariable Polynomial System and the Differential Marching Method

Autor(es)

Faustini, Mário Carneiro ^[1] ; Tsuzuki, Marcos Sales Guerra

Afiliação do(s) autor(es)

^[1] Universidade de São Paulo (USP). Escola Politécnica - Brasil

• Tipo de documento: Artigo Científico
• Fonte: Journal of the Brazilian Society of Mechanical Sciences; v. 22, n. 2, p. 251-263, 2000.
• Área do conhecimento: Engenharias - Engenharia Mecânica
• Assunto(s): Teoria de sistemas e controle

Resumo

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. (AU)

• Processo FAPESP: 97/02939-8 - Proposta de algoritmo para determinação da curva de intersecção entre superfícies NURBS
• Beneficiário: Mário Carneiro Faustini
• Modalidade de apoio: Bolsas no Brasil - Mestrado