Surface patch techniques for computational geometry

A method for creating an optically smooth geometric model, comprising:

• forming a loop from a plurality of parametrically defined curves;
• creating a plurality of ribbons along each of the plurality of parametrically defined curves of the loop, each ribbon between a preceding parametrically defined curve of the loop and a subsequent parametrically defined curve of the loop;
• and
• blending the ribbons to form a multi-sided surface patch between the parametrically defined curves, wherein a portion of each ribbon is Gk geometric continuous with a portion of another ribbon of the plurality of ribbons, wherein k is dependent upon one or more criteria for optical smoothness of the geometric model.

A method for creating an optically smooth geometric model, comprising:

• forming a loop from a plurality of parametrically defined curves;
• creating a plurality of ribbons along each of the plurality of parametrically defined curves of the loop, each ribbon between a preceding parametrically defined curve of the loop and a subsequent parametrically defined curve of the loop;
• and
• blending the ribbons to form a multi-sided surface patch between the parametrically defined curves, wherein a portion of each ribbon is G2 geometric continuous and not G3 geometric continuous with a portion of another ribbon of the plurality of ribbons.