scholarly journals A Bound on the Implicit Degree of Polygonal Bézier Surfaces

1994 ◽  
pp. 513-525 ◽  
Author(s):  
Joe Warren
Keyword(s):  
Bézier Surfaces ◽  
Implicit Degree ◽  
Bezier Surfaces

Interpolation of data in ℝ3 using quartic triangular Bézier surfaces

2021 ◽  
Author(s):  
Krassimira Vlachkova ◽  
Krum Radev
Keyword(s):  
Bézier Surfaces ◽  
Bezier Surfaces

Geometric Design and Fabrication of Developable Bezier Surfaces

1992 ◽  
Author(s):  
R. M. C. Bodduluri ◽  
B. Ravani
Keyword(s):  
Geometric Design ◽  
Developable Surface ◽  
Developable Surfaces ◽  
Surface Patches ◽  
Bézier Surfaces ◽  
Point Representation ◽  
Cad Cam ◽  
C2 Continuity ◽  
Type Construction ◽  
Bezier Surfaces

Abstract In this paper we study Computer Aided Geometric Design (CAGD) and Manufacturing (CAM) of developable surfaces. We develop direct representations of developable surfaces in terms of point as well as plane geometries. The point representation uses a Bezier curve, the tangents of which span the surface. The plane representation uses control planes instead of control points and determines a surface which is a Bezier interpolation of the control planes. In this case, a de Casteljau type construction method is presented for geometric design of developable Bezier surfaces. In design of piecewise surface patches, a computational geometric algorithm similar to Farin-Boehm construction used in design of piecewise parametric curves is developed for designing developable surfaces with C2 continuity. In the area of manufacturing or fabrication of developable surfaces, we present simple methods for both development of a surface into a plane and bending of a flat plane into a desired developable surface. The approach presented uses plane and line geometries and eliminates the need for solving differential equations of Riccatti type used in previous methods. The results are illustrated using an example generated by a CAD/CAM system implemented based on the theory presented.

scholarly journals Differentiable Piecewise-Bézier Surfaces on Riemannian Manifolds

2016 ◽  
Vol 9 (4) ◽  
pp. 1788-1828 ◽  
Author(s):  
P.-A. Absil ◽  
Pierre-Yves Gousenbourger ◽  
Paul Striewski ◽  
Benedikt Wirth
Keyword(s):  
Riemannian Manifolds ◽  
Bézier Surfaces ◽  
Bezier Surfaces

G1 Continuity of C-Bezier Rectangular Surfaces

2000 ◽  
Author(s):  
Manhong Wen ◽  
Kwun-Lon Ting
Keyword(s):  
Control Point ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Design Parameters ◽  
Control Points ◽  
Bézier Surfaces ◽  
G1 Continuity ◽  
Bezier Surfaces ◽  
Necessary And Sufficient

Abstract This paper probes G1 continuity between two adjacent c-Bezier rectangular patches. The necessary and sufficient conditions are derived. It shows that the coplanar condition for G1 continuity of two adjacent Bezier patches is not necessary for c-Bezier patches. Such a relaxation of constraints on control points is beneficial from vector weights of c-Bezier surfaces, which leads to two extra free design parameters for each control point. C-Bezier surfaces offer the possibility of obtaining G1 continuity by just adjusting the weights, which greatly simplifies the design to construct composite surfaces.

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