Process for creating a parametric surface having a required...

Details Process for creating a parametric surface having a required... Process for creating a parametric surface having a required...

2005-08-04

2008-07-15

Chauhan, Ulka (Department: 2628)

Computer graphics processing and selective visual display system

Computer graphics processing

Three-dimension

Reexamination Certificate

active

07400323

ABSTRACT:
Creating a parametric surface having a required geometrical continuity Gi from a set of parametric elementary surfaces includes providing a set of parametric elementary surfaces, each elementary surface having edges, with vertices joining adjacent edges, each elementary surface having an internal continuity Cj at least equal to the required continuity Gi, the geometrical continuity between at least two elementary surfaces across their common edge being less than the required continuity Gi. For each singular vertex, the process can include defining a system of equations linking the parameters (including control points) of the parametric elementary surfaces across edges joined to the vertex and enforcing the required geometrical continuity across the joined edges and solving the system of equations to obtain the parameters.

REFERENCES:
patent: 6037949 (2000-03-01), DeRose et al.
patent: 6806874 (2004-10-01), Biermann et al.
patent: 6950099 (2005-09-01), Stollnitz et al.
patent: 7170516 (2007-01-01), Stollnitz et al.
patent: 2004/0189633 (2004-09-01), Sederberg
Charles Loop, “Second Order Smoothness Over Extraordinary Vertices,” Jul. 8, 2004, Proceedings of the 2004 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, p. 165-174.
Jörg Peters, “C2 free-form surfaces of degree (3,5),” Feb. 2002, Computer Aided Geometric Design, vol. 19, Issue 2, p. 113-126.

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