Resolution-independent method for displaying a three dimensional model in two-dimensional display space

DETAILED DESCRIPTION OF THE INVENTION Terminology A primitive is a mathematically defined portion of a model.
For the method of the present invention, primitives are bicubic patch meshes, a set of which defines the model.
A bicubic patch is well-known in the art and consists of a polynomial representation of a surface within bounds.
The bounds of a patch are formed by curves.
The curves are usually defined to correspond to straight lines in parametric space.
A bicubic patch mesh is a group of adjoining bicubic patches where at least the first derivatives are continuous across any two adjoining patches in the mesh.
Continuity of the derivatives means, generally, that the individual bicubic patches are joined smoothly into a mesh without apparent edges or "seams.
" In general, a bicubic patch mesh represents a curved surface, with a polygon being a special case of a bicubic patch.
Primitives are joined (without constraints on continuity of derivatives) to form a model.
A mapping is a correspondence between two spaces such that each point in one space corresponds to a point in the other space.
An example is the mapping of points on the surface of the earth to the points on a flat map of the earth established by, say, a Mercator projection.
A parametric space is a two-dimensional coordinate space having axes corresponding to two parameters defined on a two- or three-dimensional surface.
A parametric space is, therefore, a uniform coordinate system mapping of points from a surface.
Usually a three-dimensional surface is mapped to parameter space.
A parametric surface representation is a mathematical description of a surface where the points of the surface are defined by a mapping from a parameter space.
A shading function is a mathematical function in which a color or gray shade is defined for each point on the surface of a three-dimensional model.
The shading function typically depends upon the local orientation of the surface with respect to one or more pre-defined light sources, viewpoint and surface properties