Modifying the shape of NURBS surfaces with geometric constraints
نویسندگان
چکیده
NURBS surfaces are among the most commonly used parametric surfaces in CAGD and Computer Graphics. This paper investigates shape modi®cation of NURBS surfaces with geometric constraints, such as point, normal vector, and curve constraints. Two new methods are presented by constrained optimization and energy minimization. The former is based on minimizing changes in control net of surfaces, whereas the latter is based on strain energy minimization. By these two methods, we change control points and weights of an original surface, such that the modi®ed surface satis®es the given constraints. Comparison results and practical examples are also given. q 2001 Elsevier Science Ltd. All rights reserved.
منابع مشابه
Hierarchical D-NURBS Surfaces and Their Physics-Based Sculpting
In this paper, we present Hierarchical D-NURBS as a new shape modeling representation that generalizes powerful, physics-based D-NURBS for interactive geometric design. Our Hierarchical D-NURBS can be viewed as a collection of standard D-NURBS finite elements, organized hierarchically in a tree structure and subject to continuity constraints across the shared boundaries of adjacent D-NURBS elem...
متن کاملDynamic NURBS Swung Surfaces for Physics - Based Shape Design
We develop a dynamic, free-form surface model which is useful for representing a broad class of objects with symmetries and topological variability. The new model is based upon swung NURBS surfaces, and it inherits their desirable cross-sectional design properties. It melds these geometric features with the demonstrated conveniences of surface design within a physics-based framework. We demonst...
متن کاملDynamic Non-Uniform Rational B=Splines
Non-uniform rational B-splines (NURBS) have become a de facto standard in commercial modeling systems because of their power to represent both free-form shapes and some common analytic shapes. To date, however, NURBS have been viewed as purely geometric primitives, which require the designer to interactively adjust many degrees of freedom (DOFs )-control points and associated weights-to achieve...
متن کاملD NURBS A Physics Based Geometric Design Framework
This paper presents dynamic NURBS or D NURBS a physics based generalization of non uniform ra tional B splines NURBS have become a de facto standard in commercial modeling systems because of their power to represent both free form and common analytic shapes Traditionally however NURBS have been viewed as purely geometric primitives which require the designer to interactively adjust many degrees...
متن کاملD-NURBS: A Physics-Based Framework for Geometric Design
This paper presents dynamic NURBS or D NURBS a physics based generalization of Non Uniform Rational B Splines NURBS have become a de facto stan dard in commercial modeling systems because of their power to represent both free form shapes and common analytic shapes Traditionally however NURBS have been viewed as purely geometric primitives which require the designer to interactively adjust many ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Computer-Aided Design
دوره 33 شماره
صفحات -
تاریخ انتشار 2001