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

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.

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Interpolation of data in ℝ3 using quartic triangular Bézier surfaces

10.1063/5.0040457 ◽

2021 ◽

Author(s):

Krassimira Vlachkova ◽

Krum Radev

Keyword(s):

Bézier Surfaces ◽

Bezier Surfaces

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Geometric Design and Fabrication of Developable Bezier Surfaces

18th Design Automation Conference: Volume 2 — Geometric Modeling, Mechanisms, and Mechanical Systems Analysis ◽

10.1115/detc1992-0172 ◽

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.

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