Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide (Gerald Farin)

SIAM Review ◽  
1991 ◽  
Vol 33 (2) ◽  
pp. 301-302
Author(s):  
Tony DeRose
Keyword(s):  
Geometric Design ◽  
Computer Aided Geometric Design ◽  
Practical Guide ◽  
Curves And Surfaces ◽  
Computer Aided

Multiresolution Curve Editing With Linear Constraints*

2001 ◽  
Vol 1 (4) ◽  
pp. 347-355 ◽  
Author(s):  
Gershon Elber
Keyword(s):  
Linear Constraints ◽  
Geometric Design ◽  
Computer Aided Geometric Design ◽  
Freeform Surfaces ◽  
Modeling Tool ◽  
B Spline ◽  
Curves And Surfaces ◽  
Orthogonality Constraints ◽  
Spline Curves ◽  
Computer Aided

The use of multiresolution control toward the editing of freeform curves and surfaces has already been recognized as a valuable modeling tool [1–3]. Similarly, in contemporary computer aided geometric design, the use of constraints to precisely prescribe freeform shape is considered an essential capability [4,5]. This paper presents a scheme that combines multiresolution control with linear constraints into one framework, allowing one to perform multiresolution manipulation of nonuniform B-spline curves, while specifying and satisfying various linear constraints on the curves. Positional, tangential, and orthogonality constraints are all linear and can be easily incorporated into a multiresolution freeform curve editing environment, as will be shown. Moreover, we also show that the symmetry as well as the area constraints can be reformulated as linear constraints and similarly incorporated. The presented framework is extendible and we also portray this same framework in the context of freeform surfaces.

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