scholarly journals A novel method for planning liver resections using deformable Bézier surfaces and distance maps

2017 ◽  
Vol 144 ◽  
pp. 135-145 ◽  
Author(s):  
Rafael Palomar ◽  
Faouzi A. Cheikh ◽  
Bjørn Edwin ◽  
Åsmund Fretland ◽  
Azeddine Beghdadi ◽  
...  
Keyword(s):  
Liver Resections ◽  
Bézier Surfaces ◽  
Novel Method ◽  
Bezier Surfaces

scholarly journals G3 Shape Adjustable GHT-Bézier Developable Surfaces and Their Applications

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2350
Author(s):  
Samia BiBi ◽  
Md Yushalify Misro ◽  
Muhammad Abbas ◽  
Abdul Majeed ◽  
Tahir Nazir
Keyword(s):  
Shape Control ◽  
Duality Principle ◽  
Developable Surface ◽  
Control Parameters ◽  
Shape Parameters ◽  
Developable Surfaces ◽  
Bézier Surfaces ◽  
Canal Surfaces ◽  
Novel Method ◽  
Bezier Surfaces

In this article, we proposed a novel method for the construction of generalized hybrid trigonometric (GHT-Bézier) developable surfaces to tackle the issue of modeling and shape designing in engineering. The GHT-Bézier developable surface is obtained by using the duality principle between the points and planes with GHT-Bézier curve. With different shape control parameters in their domain, a class of GHT-Bézier developable surfaces can be established (such as enveloping developable GHT-Bézier surfaces, spine curve developable GHT-Bézier surfaces, geodesic interpolating surfaces for GHT-Bézier surface and developable GHT-Bézier canal surfaces), which possess many properties of GHT-Bézier surfaces. By changing the values of shape parameters the effect on the developable surface is obvious. In addition, some useful geometric properties of GHT-Bézier developable surface and the G1, G2 (Farin-Boehm and Beta) and G3 continuity conditions between any two GHT-Bézier developable surfaces are derived. Furthermore, various useful and representative numerical examples demonstrate the convenience and efficiency of the proposed method.

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
Sign in / Sign up

Export Citation Format

Share Document