An algorithmic approach to degree reduction of Bezier 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 generalised least squares method. The computations are carried out by minimising the Z/2 a n d discrete 1% distance between the two curves.
We study the relationship of transformations between Legendre and Bernstein basis. Using the relationship, we present a simple and efficient method for optimal multiple degree reductions of Bézier curves with respect to the L 2 -norm.
The error analysis of an algorithm for generating an approximation of degree n -1 to an nth degree Be'zier curve is presented. The algorithm is based on observations of the geometric properties of Be'zier curves which allow the development of detailed error analysis. By combining subdivision with a degree reduction algorithm, a piecewise approximation can be generated, which is within some preset error tolerance of the original curve. The number of subdivisions required can be determined a priori and a piecewise approximation of degree m can be generated by iterating the scheme.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.