A Symbolic Approach to Freeform Parametric Surface Blends

✍ Scribed by KIM, KWANSIK ;ELBER, GERSHON

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 755 KB
• Volume: 8
• Category: Article
• ISSN: 1049-8907
• DOI: 10.1002/(sici)1099-1778(199703)8:2<69::aid-vis162>3.0.co;2-d

✦ Synopsis

This paper presents a symbolic approach to the computation of blend surfaces across piecewise polynomial and rational surfaces. Curves in the parameter space of the primary surfaces can be specified as the rail curves, also known as trimlines, of the blend. Several techniques which require various levels of user interaction are presented for defining the cross-boundary tangent curves along the rail curves. The resulting blend is represented as a polynomial surface having tangent plane continuity with the primary surfaces to an accuracy bounded only by the machine precision. Also presented is a normalization method that approximates unit vector fields, an approach that might benefit other applications such as offset approximation and animation curve construction.