ABSTRACT
This chapter introduces the fundamentals to geometric modeling and mesh generation followed by geometric objects and transformations, curves and surfaces, as well as spline-based modeling. It presents two important iso-contouring methods: marching cubes and dual contouring. The chapter reviews the fundamentals to the representation and manipulation of sets of basic geometric elements such as points, line segments, polygons and polyhedra. There are three commonly used spaces: vector space, affine space and Euclidean space. The chapter provides some basic geometric objects like points, lines, planes, coordinate systems and transformations. General geometric objects include lines, polygons and polyhedra. Their relationships can be described using three fundamental types: scalars, points and vectors. In geometric modeling, convexity is an important property for geometric objects. Parametric forms have been used popularly in computer-aided geometric design due to its five important properties: local control of object shape; surface smoothness and continuity; being able to evaluate derivatives; stability; and ease of rendering.
