Rapid zippering for real time tesselation of bicubic surfaces

A computer readable medium containing program instructions for rendering bicubic surfaces of an object on a computer system, the surface defined by sixteen control points and bounded by four boundary curves, wherein each boundary curves is formed by boundary box of line segments formed between four control points, the program instructions for:

• (a) transforming only the control points of the surface given a view of the object;
• (b) using the four boundary edges for purposes of subdivision;
• (c) selecting an additional pair of orthogonal internal curves to process;
• (d) iteratively subdividing the four boundary edges and the pair of orthogonal internal curves, wherein two new curves are generated with each subdivision;
• and
• (e) terminating the subdivision of each of the curves when the curves satisfy a flatness threshold expressed in screen coordinates, thereby minimizing a number of computations required to render the object.

A computer system for rendering curved surfaces of an object, comprising:

• a communication path;
• a random access memory (RAM) coupled to the communication path containing program instructions for defining a curved surface of an object and instructions for rendering the object, wherein the curved surface is defined by sixteen control points and bounded by four boundary curve edges, wherein each boundary curve edges is formed by boundary box of line segments formed between four control points, and wherein a corner is the point where two boundary curve edges meet;
• at least one processor coupled to the communication path;
• a graphics controller coupled to the communication path for receiving commands from the processor and generating display signals therefrom;
• and
• a display unit coupled to the graphics controller for displaying images defined by the display signals,
• wherein when the program instructions are executed, the program instructions render the curved surfaces of the object by,
• (a) transforming only the control points of the surface given a view of the object;
• (b) using the four boundary edges for purposes of subdivision;
• (c) selecting an additional pair of orthogonal internal curves to process;
• (d) iteratively subdividing the four boundary edges and the pair of orthogonal internal curves, wherein two new curves are generated with each subdivision;
• (e) terminating the subdivision of each of the curves when the curves satisfy a flatness threshold expressed in screen coordinates, thereby minimizing a number of computations required to render the object;
• and
• (f) for each of the 4 boundary edges,
• leaving a strip of 1 subdivision parametric step between the boundary edge and the interior;
• for each strip,
• zippering the strip within the subdivision parametric steps;
• for each of the 4 corners,
• tesselating an area not covered by the two strips joining at the corner;
• and
• tesselating an interior parametric rectangle.