scholarly journals Generation Method of Bezier Curves and Surfaces on Lie Groups

2002 ◽  
Vol 9A (1) ◽  
pp. 99-104
Author(s):  
Jang-Hwan Im ◽  
Tae-Eun Kim
Keyword(s):  
Lie Groups ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Curves And Surfaces

Curvature of singular Bézier curves and surfaces

2011 ◽  
Vol 28 (4) ◽  
pp. 233-244 ◽  
Author(s):  
Thomas W. Sederberg ◽  
Hongwei Lin ◽  
Xin Li
Keyword(s):  
Bezier Curves ◽  
Bézier Curves ◽  
Curves And Surfaces

Bézier Curves on Riemannian Manifolds and Lie Groups With Kinematics Applications

1994 ◽  
Author(s):  
Frank C. Park ◽  
Bahram Ravani
Keyword(s):  
Riemannian Manifold ◽  
Rigid Body ◽  
Lie Groups ◽  
Riemannian Manifolds ◽  
Group Structure ◽  
Recursive Algorithm ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Spatial Displacements ◽  
Natural Way

Abstract In this article we generalize the concept of Bézier curves to curved spaces, and illustrate this generalization with an application in kinematics. We show how De Casteljau’s algorithm for constructing Bézier curves can be extended in a natural way to Riemannian manifolds. We then consider a special class of Riemannian manifold, the Lie groups. Because of their algebraic group structure Lie groups admit an elegant, efficient recursive algorithm for constructing Bézier curves. Spatial displacements of a rigid body also form a Lie group, and can therefore be interpolated (in the Bezier sense) using this recursive algorithm. We apply this algorithm to the kinematic problem of trajectory generation or motion interpolation for a moving rigid body.

Biquadratic TC-Bézier Curves with Shape Parameter

2011 ◽  
Vol 467-469 ◽  
pp. 57-62
Author(s):  
Xu Min Liu ◽  
Xian Peng Yang ◽  
Yan Ling Wu
Keyword(s):  
Shape Parameter ◽  
Free Form ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Curves And Surfaces ◽  
G1 Continuity ◽  
Shape Controlling

Shape controlling is a popular topic in curves and surfaces design with free form. In this paper, a new curve, to be called Biquadratic TC-Bézier curves with shape parameter , is constructed in the space . We show that such curves share the same properties as the traditional Bézier curves in polynomial spaces. The shape of new curves, representing circle and ellipse accurately, can be adjusted by changing the value of the parameter . Then we give the G1 continuity conditions of Biquadratic TC-Bézier curves with shape parameter and its application in surfaces modeling.

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