SURFACE MODELING:
The process of modeling is built much easier for a mathematical description of an object or at least on a part of the object might be applied. Surfaces might be described mathematically as in 3-dimensions space like parametric & non-parametric equations. There are two kinds of surfaces that are commonly utilized in modelling system - parametric & implicit. Parametric surfaces are indicated by a set of three functions one for each co-ordinates. Implicit surfaces are described by a polynomial of three variables. Parametric surfaces may represent sphere and ellipsoids where as spheres may easily be defined by implicit surfaces. In terms of expressive power, implicit surfaces are more powerful than parametric surfaces. Surface revolution is a method of generating as 3-D surface by revolving a 2-D entity. Such as a line, a curve, a plane, around an axis in space.
3-D surfaces are also attained by transversity an entity, for example a line polygone or a curve along a path in space. The resulting surfaces are known as sweep surfaces. The simplest sweep entity is any point. Difficult paths may be developed by combining simple paths, for example combining two paths of a point yield a single turn of a helical path. Several design tools originated from car companies, for example Bazier curves and surfaces were produced by Citroen and Renault, Coon's patches were built up for Ford Detroit and Gorden surfaces for General Motors Detroit. The primary step in design is the manual production of a model in wood or clay which is then digitised and records points whereas the sensor touches the model surface. From these degitised points, by using various design tools, surfaces in 3-D format are produced.