We present an algorithm for interactive display of trimmed NURBS surfaces. The algorithm converts the NURBS surfaces to B ezier surfaces, tessellates each trimmed B ezier surface into triangles and renders them using the triangle rendering capabilities common in current graphics systems. It makes use of tight bounds for uniform tessellation of B ezier surfaces into cells and traces the trimming...

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...

Many papers describe techniques for evaluating spline curves and surfaces. While each paper provides some theoretical or empirical evidence with which to compare techniques, there exist few global comparisons Peters94]. Also, papers describing particular algorithms often provide few details, making implementation of the technique presented diicult or impossible. This report attempts to illumina...

This paper first shows how the B ezier coefficients of a given degree n polynomial are perturbed so that it can be reduced to a degree m ð< nÞ polynomial with the constraint that continuity of a prescribed order is preserved at the two endpoints. The perturbation vector, which consists of the perturbation coefficients, is determined by minimizing a weighted Euclidean norm. The optimal degree n ...

An algorithmic approach to degree reduction of B ezier curves is presented. The algorithm is based on the matrix representations of the degree elevation and degree reduction processes. The control points of the approximation are obtained by the generalized least square method. The computations are carried out by minimizing the L2 and discrete l2 distance between the two curves.

We present an algorithm to approximate the variable radius ooset curves by cubic B ezier curves. The ooset curve is approximated by a cubic B ezier curve which interpolates the positions and derivatives of the exact ooset curve at both end points. Thus, it approximates the exact ooset curve very closely near the curve end points, but not necessarily in the middle of the curve. Given a xed base ...

A group-theoretic analysis is applied to nd the transformation of the homogeneous control points of k-dimensional B ezier simplices (such as two dimensional triangles and three dimensional tetrahedra) under a k-dimensional projective reparameterization. This transformation has applications in the perspective projection of textures represented as triangular spline intensity surfaces , in arbitra...

We present an algorithm to approximate the variable radius ooset curves by cubic B ezier curves. The ooset curve is approximated by a cubic B ezier curve which interpolates the positions and derivatives of the exact ooset curve at both end points. Thus, it approximates the exact ooset curve very closely near the curve end points, but not necessarily in the middle of the curve. Given a xed base ...

New algorithm for evaluating a point on a Bézier curve and on a rational Bézier curve is given. The method has a geometric interpretation and a convex hull property. The computational complexity of the new algorithm is linear with respect to the degree of the considered curve, and its memory complexity is O(1).