Pyramid Algorithms

Foreword

About forty years ago, the development of computer-aided design and manufacturing created the strong need for new ways to mathematically represent curves and surfaces: the new representations should possess enough flexibility to describe almost arbitrary geometric shapes; be compatible with efficient algorithms; and be readily accessible to designers who could manipulate them simply and intuitively. Although these new requirements presented a difficult challenge, the search for appropriate mathematical tools has been very successful within a relatively short period of time. Curves and surfaces with a piecewise polynomial or rational parametric representation have become the favorites, in particular if they are represented in so-called ...