Geometry, Duality and Robust Computation in Engineering

Robustness of computations in engineering is one of key issues as it is necessary to solve technical problems leading to ill conditioned solutions. Therefore the robustness and numerical stability is becoming a key issue more important that the computational time. In this paper we will show selected computational issues in numerical precision, well known cases of failures in computations. The Euclidean representation is used in today’s computations, however the projective space (an extension of the Euclidean space) representation leads to more compact and robust formulations and to matrix-vector operations supported in hardware, e.g. by GPU. Key-Words: Euclidean space, projective space, homogeneous coordinates, duality, intersections, barycentric coordinates, planes intersection, Plucker coordinates, numerical precision.