Procedures of modeling nonparametric surfaces based on proportional development are explained.
Proportional development techniques have been widely used in descriptive geometry to graphically generate a 3D surface from its four boundary curves. When used as a surface modeling tool, the existing method of proportional development basically is a single patch technique generating a parametric surface of the form ir=(x(u,v),y(u,v),z(u,v)). The proportional development technique proporsed by Duncan and Mair is extended in order to construct $VC^1$ composite nonparametric surfaces from a network of cross-section curves. A nonparametric surface is a surface that can be represented as z=f(x,y), and is very useful in CAGD.
Two different schemes of modeling $VC^1$ composite nonparametric surfaces are proposed. The first scheme follows the basic idea of proportional development and is applicable to the type of surfaces where the range of a boundary curve is limited by its end points. If the trajectory of a boundary curve exceeds the end points range, the proportionally developed surface becomes out of proportion. This drawback of proportional development is overcomed in the second scheme where the idea of sweeping cross-section curves is employed. In both schemes, Brown's interpolants are used to obtain $VC^1$ composite surfaces.
