ABSTRACT
This chapter will combine a discussion on fundamental modeling techniques with an introduction to our Geometrical Modeling Package (GMP). We present the idea of a manifold and parametrizations, and discuss the fundamental requirement of compatibility of parametrizations. Then we demonstrate how the condition is met in practice by using the techniques of transfinite interpolation, and implicit parametrizations. Finally, we discuss the use of the projection-based interpolation for the initial mesh generation, geometry updates following mesh refinements, as well as the approximation of Dirichlet data.
