scholarly journals On Bézier surfaces in three-dimensional Minkowski space

2011 ◽  
Vol 62 (8) ◽  
pp. 2899-2912 ◽  
Author(s):  
H. Ugail ◽  
M.C. Márquez ◽  
A. Yılmaz
Keyword(s):  
Minkowski Space ◽  
Three Dimensional ◽  
Bézier Surfaces ◽  
Dimensional Minkowski Space ◽  
Bezier Surfaces

scholarly journals The Algebraic Surfaces of the Enneper Family of Maximal Surfaces in Three Dimensional Minkowski Space

Axioms ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 4
Author(s):  
Erhan Güler
Keyword(s):  
Minkowski Space ◽  
Three Dimensional ◽  
Algebraic Surfaces ◽  
Cartesian Coordinates ◽  
Maximal Surfaces ◽  
Dimensional Minkowski Space ◽  
The Family

We consider the Enneper family of real maximal surfaces via Weierstrass data (1,ζm) for ζ∈C, m∈Z≥1. We obtain the irreducible surfaces of the family in the three dimensional Minkowski space E2,1. Moreover, we propose that the family has degree (2m+1)2 (resp., class 2m(2m+1)) in the cartesian coordinates x,y,z (resp., in the inhomogeneous tangential coordinates a,b,c).

Hamilton–Jacobi theory in three-dimensional Minkowski space via Cartan geometry

2009 ◽  
Vol 50 (5) ◽  
pp. 053507 ◽  
Author(s):  
Joshua T. Horwood ◽  
Raymond G. McLenaghan ◽  
Roman G. Smirnov
Keyword(s):  
Minkowski Space ◽  
Three Dimensional ◽  
Cartan Geometry ◽  
Dimensional Minkowski Space

scholarly journals Numerical Calculation of Three-Dimensional Euler Flow Through a Transonic Test Turbine Stage

1998 ◽  
Author(s):  
Harald Paßrucker ◽  
Wolfgang Sanz ◽  
Herbert Jericha
Keyword(s):  
Boundary Conditions ◽  
Hyperbolic Systems ◽  
Three Dimensional ◽  
Linearized Euler Equations ◽  
Viscosity Term ◽  
University Of Technology ◽  
Bézier Surfaces ◽  
Boundary Treatment ◽  
Bezier Surfaces ◽  
The One

The objective of this work is the development of an implicit block-structured central-differencing scheme with implicit treatment of the boundary conditions for the calculation of three-dimensional inviscid compressible steady flow, primarily through transonic turbomachinery stages. The implicit boundary treatment is based on the mathematical theory of characteristics for hyperbolic systems of equations. Steady-state non-reflecting boundary conditions at the inflow and outflow boundaries and at the stator/rotor interface based on Fourier analysis applied to the linearized Euler equations are also used. Getting a monotonous resolution of shocks, a non-linear additive viscosity term of 2nd and 4th order with pressure-controlled factors is implemented. The three-dimensional blade geometry consists of Bézier-surfaces which are determined by two-dimensional blade profiles based on Bézier-curves. The grid for the flow calculation is obtained by parameterizing special Bézier-surfaces, respectively Bézier-volumes. Finally, the aerodynamic design of the one-stage highly loaded transonic test turbine of Institute of Thermal Turbomachinery and Machine Dynamics - Graz University of Technology) with these tools described above is illustrated with detailed presentation of the specific aerodynamic features, the design technology and the computational results.

Constructions of spacelike Bézier Surfaces in the Three-dimensional Minkowski space

2009 ◽  
Author(s):  
Georgi H. Georgiev ◽  
George Venkov ◽  
Ralitza Kovacheva ◽  
Vesela Pasheva
Keyword(s):  
Minkowski Space ◽  
Three Dimensional ◽  
Dimensional Minkowski Space

Parametric Modeling Method for Truss Structures

2002 ◽  
Author(s):  
Hongqing Wang ◽  
David W. Rosen
Keyword(s):  
Dynamic Properties ◽  
Three Dimensional ◽  
Main Idea ◽  
Parametric Modeling ◽  
Modeling Method ◽  
Truss Structure ◽  
Truss Structures ◽  
Bézier Surfaces ◽  
Thick Part ◽  
Bezier Surfaces

This paper presents a parametric modeling method to create truss structures to enhance a part’s mechanical and/or dynamic properties. The main idea behind this method is to replace thick part sections with thinner sections that are reinforced by truss structure. Computational methods are presented to create truss structures that conform to a part’s shape. The methods utilize Bezier surfaces to approximate the part surface and to create the truss structure. Truss topologies can be created for a two-dimensional truss, a three-dimensional truss for single volume and a three-dimensional truss for multiple volumes. The decomposition of the part surfaces, the construction of approximating Bezier surfaces, and solid modeling of the truss structures are also shown. An example is presented to demonstrate the utility of conformal truss structures for a large part from the aerospace industry.

Accretive growth kinematics in Minkowski 3-space

2017 ◽  
Vol 14 (05) ◽  
pp. 1750069
Author(s):  
Gül Tuğ ◽  
Zehra Özdemi̇r ◽  
Selçuk Han Aydin ◽  
Fai̇k Nejat Ekmekci̇
Keyword(s):  
Minkowski Space ◽  
Analytical Approach ◽  
Three Dimensional ◽  
Dimensional Minkowski Space

In this study, a model of accretive growth for arbitrary surfaces in three-dimensional Minkowski space is formulated by evolving a curve. An analytical approach to surfaces is also given in terms of a few parameters which are effective in the accretive growth of surfaces. The proposed method is visualized on some test surfaces and displayed in terms of figures.

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