Drawing Rational Surfaces with Rational Bezier Triangles

Implicit Equations of Non-degenerate Rational Bezier Quadric Triangles

In this paper we review the derivation of implicit equations for non-degenerate quadric patches in rational Bézier triangular form. These are the case of Steiner surfaces of degree two. We derive the bilinear forms for such quadrics in a coordinate-free fashion in terms of their control net and their list of weights in a suitable form. Our construction relies on projective geometry and is groun...

Simple Methods For Drawing Rational Surfaces as Four or Six Bezier Patches

In this paper, we give several simple methods for drawing a whole rational surface (without base points) as several Bézier patches. The first two methods apply to surfaces specified by triangular control nets and partition the real projective plane RP into four and six triangles respectively. The third method applies to surfaces specified by rectangular control nets and partitions the torus RP ...

Rational Bezier Simplices

A gr'oup-theor'etic analysis is applied to find th e transf01'11wtion of the homogeneous control points of kdim ensional B ezier simplices {such as two dim ensional triangles and three dim ensional tetrah edra} under' a kdim ensional projec tive reparam eterization, This transf ormation has applications in the perspec tive projec ti on of textur'es represented as triangular spline intensity sur...

Variational design of rational Bezier curves and surfaces

The design of curves and surfaces in C.A.D. systems has many applications in car, plane or ship industry. Because they offer more flexibility, rational functions are often prefered to polynomial functions to modelize curves and surfaces. In this work, several methods to generate rational Bezier curves and surfaces which minimize some functionals are proposed. The functionals measure a technical...

5 Rational Bezier Curves Andrelief