scholarly journals Motion of Bishop Frenet Offsets of Ruled Surfaces inE3

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
H. N. Abd-Ellah
Keyword(s):  
Geometric Design ◽  
Ruled Surfaces ◽  
Computer Aided Geometric Design ◽  
Computer Aided

The main goal of this paper is to study the motion of two associated ruled surfaces in Euclidean 3-spaceE3. In particular, the motion of Bishop Frenet offsets of ruled surfaces is investigated. Additionally, the characteristic properties for such ruled surfaces are given. Finally, an application is presented and plotted using computer aided geometric design.

Rational Bézier Line-Symmetric Motions

1999 ◽  
Author(s):  
Shutian Li ◽  
Q. J. Ge
Keyword(s):  
Ruled Surface ◽  
Geometric Design ◽  
Ruled Surfaces ◽  
Line Geometry ◽  
Symmetric Motion ◽  
Computer Aided Geometric Design ◽  
De Casteljau Algorithm ◽  
Computer Aided ◽  
Kinematic Geometry

Abstract This paper brings together line geometry, kinematic geometry of line-symmetric motions, and computer aided geometric design to develop a method for geometric design of rational Bézier line-symmetric motions. By taking advantage of the kinematic geometry of a line-symmetric motion, the problem of synthesizing a rational Bézier line-symmetric motion is reduced to that of designing a rational Bézier ruled surface. In this way, a recently developed de Casteljau algorithm for line-geometric design of ruled surfaces can be applied. An example is presented in which the Bennet motion is represented as a rational Bézier line-symmetric motion whose basic surface is a hyperboloid.

On Representation and Interpolation of Line-Segments for Computer Aided Geometric Design

1994 ◽  
Author(s):  
Q. J. Ge ◽  
B. Ravani
Keyword(s):  
Line Segment ◽  
Geometric Design ◽  
Ruled Surfaces ◽  
Line Geometry ◽  
Computer Aided Geometric Design ◽  
Line Segments ◽  
Geometric Shapes ◽  
Computer Aided ◽  
On Line ◽  
New Algorithms

Abstract In this paper, three new representations of a line-segment are introduced that combine Plücker line coordinates with specifications of length and location of a line-segment. For each of the three line-segment representations, a right conoidal interpolant of two arbitrarily disposed line-segments is developed. These interpolants are then combined with deCasteljau-like algorithms for generating ruled surfaces. The results can be extended to develop new algorithms for computer aided geometric design of geometric shapes based on line geometry.

Rational Be´zier Line-Symmetric Motions

2005 ◽  
Vol 127 (2) ◽  
pp. 222-226 ◽  
Author(s):  
Shutian Li ◽  
Q. J. Ge
Keyword(s):  
Ruled Surface ◽  
Geometric Design ◽  
Ruled Surfaces ◽  
Line Geometry ◽  
Symmetric Motion ◽  
Computer Aided Geometric Design ◽  
De Casteljau Algorithm ◽  
Computer Aided ◽  
Kinematic Geometry

This paper brings together line geometry, kinematic geometry of line-symmetric motions, and computer aided geometric design to develop a method for geometric design of rational Be´zier line-symmetric motions. By taking advantage of the kinematic geometry of a line-symmetric motion, the problem of synthesizing a rational Be´zier line-symmetric motion is reduced to that of designing a rational Be´zier ruled surface. In this way, a recently developed de Casteljau algorithm for line-geometric design of ruled surfaces can be applied. An example is presented in which the Bennet motion is represented as a rational Be´zier line-symmetric motion whose basic surface is a hyperboloid.

scholarly journals Conversion Between Cubic Bezier Curves and Catmull–Rom Splines

2021 ◽  
Vol 2 (5) ◽  
Author(s):  
Soroosh Tayebi Arasteh ◽  
Adam Kalisz
Keyword(s):  
Computer Graphics ◽  
Geometric Design ◽  
The Other ◽  
Control Points ◽  
Complex Surfaces ◽  
Linear Transformations ◽  
Computer Aided Geometric Design ◽  
Cubic Curves ◽  
Original Curve ◽  
Computer Aided

AbstractSplines are one of the main methods of mathematically representing complicated shapes, which have become the primary technique in the fields of Computer Graphics (CG) and Computer-Aided Geometric Design (CAGD) for modeling complex surfaces. Among all, Bézier and Catmull–Rom splines are the most common in the sub-fields of engineering. In this paper, we focus on conversion between cubic Bézier and Catmull–Rom curve segments, rather than going through their properties. By deriving the conversion equations, we aim at converting the original set of the control points of either of the Catmull–Rom or Bézier cubic curves to a new set of control points, which corresponds to approximately the same shape as the original curve, when considered as the set of the control points of the other curve. Due to providing simple linear transformations of control points, the method is very simple, efficient, and easy to implement, which is further validated in this paper using some numerical and visual examples.

Kinematically Generated Dual Tensor-Product Surfaces

1998 ◽  
Author(s):  
Q. J. Ge ◽  
D. Kang ◽  
M. Sirchia
Keyword(s):  
Tensor Product ◽  
Geometric Design ◽  
Computer Aided Geometric Design ◽  
Freeform Surfaces ◽  
Computer Aided ◽  
Design And Manufacture ◽  
Two Parameter

Abstract This paper takes advantage of the duality between point and plane geometries and studies a class of tensor-product surfaces that can be generated kinematically as surfaces enveloped by a plane under two-parameter rational Bézier motions. The results of this cross-disciplinary work, between the field of Computer Aided Geometric Design and Kinematics, can be used as a basis for studying geometric and kinematic issues associated with the design and manufacture of freeform surfaces.

Computer Aided Geometric Design of Two-Parameter Freeform Motions

1999 ◽  
Vol 121 (4) ◽  
pp. 502-506 ◽  
Author(s):  
Q. J. Ge ◽  
M. Sirchia
Keyword(s):  
Computer Aided Design ◽  
Control Structure ◽  
Geometric Design ◽  
Computer Aided Geometric Design ◽  
Kinematic Control ◽  
Computer Aided ◽  
Cad Cam ◽  
Aided Design ◽  
Two Parameter ◽  
And Robotics

This paper brings together the notion of analytically defined two-parameter motion in Theoretical Kinematics and the notion of freeform surfaces in Computer Aided Geometric Design (CAGD) to develop methods for computer aided design of two-parameter freeform motions. In particular, a rational Be´zier representation for two-parameter freeform motions is developed. It has been shown that the trajectory surface of such a motion is a tensor-product rational Be´zier surface and that such a kinematically generated surface has a geometric as well as a kinematic control structure. The results have not only theoretical interest in CAGD and kinematics but also applications in CAD/CAM and Robotics.

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