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, Tsuzuki, Marcos Sales Guerra

FONTE

Journal of the Brazilian Society of Mechanical Sciences

DATA DE PUBLICAÇÃO

2000

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 .

Documentos Relacionados

• VISUALIZATION OF THE BOUNDARY BETWEEN FLUIDS USING THE SPH METHOD AND THE MARCHING CUBES ALGORITHM
• Curvas de Bezier em grupos de Lie e esferas S2 usando o algoritmo de De Casteljau
• Upper eyelid contour symmetry measurement with Bézier curves
• SIMPLE CURVES ON COMPACT SURFACES*
• A dynamic method for the calibration of dye dilution curves in a physiological system.