Direct manipulations of NURBS surfaces subjected to geometric constraints

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• 作者：M. Pourazady and X. Xu
• 关键词：NURBS surfaces ; Deformable models ; Surface manipulations
• 刊名：Computers and Graphics
• 出版年：2006
• 出版时间：August 2006
• 年：2006
• 卷：30
• 期：4
• 页码：598-609
• 全文大小：294 K

文摘

Shape design is a complex process and requires interactive manipulations of curves and surfaces. This paper presents a deformable model for the direct manipulations of NURBS surfaces. A NURBS surface is modeled as a deformable plate subjected to specified constraints. Formulations of a deformable model results in a set of linear equations for a non-rational B-spline surface and a set of non-linear equations for a NURBS surface. A perspective mapping is introduced to convert NURBS formulations to B-spline formulations and linearize the deformable model defined for a NURBS surface. The final equations for a deformable model are similar to those obtained for the bending of a plate problem. These equations are defined by a stiffness matrix that is formulated in terms of the blending functions of a parametric surface and a force vector that is associated with the user-defined constraints. The solution of these equations results in the new locations of control points so that the deformed surface satisfies user-defined constraints. Several examples are presented to demonstrate the capabilities of this approach.