Geometric Modelling

This text presents the nature, development and application of the basic concepts of geometric modeling. While this text is written for upper-division and graduate students in engineering, computer science, or applied mathematics, it is also useful for those already practicing in these and related fields. Readers should already be familiar with elementary calculus, analytical geometry and vectors and matrix methods, since the book simply reviews some results in these areas, without the burden of proofs, to emphasize certain important computational features. Geometric Modeling consists of three parts: parametric geometry, solid modeling, and applications. The first eight chapters lay the foundation with the parametric geometry of curves, surfaces and solids and show how particular formulations facilitate calculating geometric properties. The next three chapters explore the fundamentals of solid model construction and analysis from many points of view. The final chapters discuss three important areas of application: computer graphics, CAD and CAM. The last chapter is a broad view of the frontiers of geometric modeling.