ABSTRACT
This chapter introduces several classes of surface that can assist us in meeting some of the demanding dictates of realizing a form, and that possess desirable surface properties. It focuses on just three categories of classical surfaces – rotational, translational and ruled – as these suggest an alignment between their construction as modeled surfaces in a digital environment and their construction as built surfaces in the physical world. Like curves, surfaces are often constructed in the service of producing other geometries – such as when a base surface is used to position aggregations of smaller elements. A parametric representation is once again employed as a lower-level description that can encompass a range of common surfaces. In software, surfaces are often constructed from lower-level objects, such as curves. Many classical surfaces may be described in terms of the lower-level curves that comprise them. A common way of identifying special types of surfaces is by considering restrictions on the Gaussian curvatures.
