Generalizations of fuzzy linguistic control points in geometric design

2014 ◽  
Author(s):  
M. H. Sallehuddin ◽  
A. F. Wahab ◽  
R. U. Gobithaasan
Keyword(s):  
Geometric Design ◽  
Control Points ◽  
Linguistic Control ◽  
Fuzzy Linguistic

scholarly journals Fuzzy linguistic in geometric modeling

2015 ◽  
Vol 11 (1) ◽  
Author(s):  
Mohd Sallehuddin Husain ◽  
Abd Fatah Wahab ◽  
R.U. Gobithasaan
Keyword(s):  
Set Theory ◽  
Fuzzy Set Theory ◽  
Geometric Modeling ◽  
Control Point ◽  
Control Points ◽  
Linguistic Variables ◽  
Numerical Examples ◽  
Basic Functions ◽  
Linguistic Control ◽  
Fuzzy Linguistic

Fuzzy Linguistic is an extension of fuzzy set theory was introduced by Zadeh. Normally fuzzy linguistic is often associated with linguistic variables generated by a function modifier is also known as a hedges. This paper discusses the theorems and definitions of fuzzy linguistic perspective geometric modeling to produce Fuzzy Linguistic Control Point (FLCP). Fuzzy Linguistic Control Points have been blended in with the spline basic functions of the model to produce a few splines’s model are characterized by fuzzy linguistics. At the end of this article will discuss some numerical examples of Fuzzy Linguistic Bezier Model. 

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.

Geometric Design of Uniform Developable B-Spline Surfaces

2004 ◽  
Author(s):  
Chih-Hsing Chu ◽  
Jang-Ting Chen
Keyword(s):  
Degrees Of Freedom ◽  
Solution Process ◽  
Boundary Curve ◽  
Geometric Design ◽  
Constrained Systems ◽  
Control Points ◽  
B Spline ◽  
Cubic Surface ◽  
De Boor Algorithm ◽  
Spline Surfaces

This paper studies geometric design of uniform developable B-spline surfaces from two boundary curves. The developability constraints are geometrically derived from the de Boor algorithm and expressed as a set of equations that must be fulfilled by the B-spline control points. These equations help characterize the number of degrees of freedom (DOF’s) for the surface design. For a cubic B-spline surface with a first boundary curve freely chosen, five more DOF’s are available for a second boundary curve when both curves contain four control points. There remain (7-2m) DOF’s for a cubic surface consisting of m consecutive patches with C2 continuity. The results are in accordance with previous findings for equivalent composite Be´zier surfaces. Test examples are illustrated to demonstrate design methods that fully utilize the DOF’s without leading to over-constrained systems in the solution process. Providing a foundation for systematic implementation of a CAGD system for developable B-spline surfaces, this work has substantial improvements over past studies.

scholarly journals A new approach to design the ruled surface

2019 ◽  
Vol 16 (06) ◽  
pp. 1950093
Author(s):  
Ferhat Taş ◽  
Kazım İlarslan
Keyword(s):  
Unit Sphere ◽  
Ruled Surface ◽  
Geometric Design ◽  
Control Points ◽  
Computer Aided Geometric Design ◽  
New Approach ◽  
Transference Principle ◽  
Integral Invariants ◽  
Computer Aided ◽  
Novel Method

This paper considers a kind of design of a ruled surface. The design interconnects some concepts from the fields of computer-aided geometric design (CAGD) and kinematics. Dual unit spherical Bézier-like curves on the dual unit sphere (DUS) are obtained by a novel method with respect to the control points. A dual unit spherical Bézier-like curve corresponds to a ruled surface by using Study’s transference principle and closed ruled surfaces are determined via control points and also, integral invariants of these surfaces are investigated. Finally, the results are illustrated by several examples and the motion interpolation was shown as an embodiment of this method.

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