Robust evaluation of differential geometry properties using interval arithmetic techniques

Abstract

This thesis presents a robust method for evaluating differential geometry properties of sculptured surfaces by using a validated ordinary differential equation (ODE) system solver based on interval arithmetic. Iso-contouring of curvature of a Bezier surface patch. computation of curvature lines of a Bezier surface patch and computation of geodesics of a Bezier surface patch are computed by the Validated Numerical Ordinary Differential Equations (VNODE) solver which employs rounded interval arithmetic methods. Then. the results generated from the VNODE program are compared with the results from Praxiteles code which uses non-validated ODE solvers operating in double precision floating point arithmetic for the solution of the same problems. From the results of these experiments, we find that the VNODE program performs these computations reliably, but at increased computational cost.