Parameterized Curves and Surfaces

The geometry tool explained here has been developed in the years shortly before interactive graphic workstations became available, originally for input with data lists but increasingly laid out for interactive usage in the windows environment of the workstation. The list input still is the basic option and data for such usage will be presented here for explanation. Focusing on surface modelling of aerodynamically efficient aircraft components, we realize that the goal of shape generation requires much control over contour quality like slopes and curvature, while structural constraints require also comers, flat parts and other compromises against otherwise idealized shapes. When familiarity is gained with a set of simple analytic functions and the possibility is used to occasionally extend the existing collection of ID functions, ground is laid to compose these functions suitably to yield complex 2D curves and finally surfaces in 3D space. This way we intend to develop tools to define data for airframe components with a nearly unlimited variety within conventional, new and exotic configurations. A bncf illustration of the principle to start
with ID functions, define curses in 2D planes and vary them in 3D space to create surfaces is given: