Interpolation and Intersection Algorithms and GPU

Abstract

Interpolation and intersection methods are closely related and used in computer graphics, visualization, computer vision etc. The Euclidean representation is used nearly exclusively not only in computational methods, but also in education despite it might lead to instability in computation in many cases. The projective geometry, resp. projective extension of the Euclidean space, offers many positive features from the computational and educational points of view with higher robustness and stability of computation. This paper presents simple examples of projective representation advantages, especially from the educational point of view. In particular, how interpolation and intersection can be applied to fundamental algorithms, which are becoming more robust, stable and faster due to compact formulation. Another advantage of the proposed approach is a simple implementation on vector-vector architectures, e.g. GPU, as it is based on matrixvector operations.