scholarly journals Generalized Bernstein Polynomials and Bézier Curves: An Application of Umbral Calculus to Computer Aided Geometric Design

2001 ◽  
Vol 27 (1) ◽  
pp. 51-81 ◽  
Author(s):  
Rudolf Winkel
Keyword(s):  
Bernstein Polynomials ◽  
Geometric Design ◽  
Umbral Calculus ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Computer Aided Geometric Design ◽  
Computer Aided ◽  
Generalized Bernstein Polynomials

scholarly journals APLIKASI KURVA BEZIER PADA DESAIN BOTOL MINUMAN

2020 ◽  
Vol 20 (1) ◽  
pp. 1
Author(s):  
Muhammad Bagus Firman Triadi ◽  
Bagus Juliyanto ◽  
Firdaus Ubaidillah
Keyword(s):  
Research Method ◽  
Geometric Design ◽  
The Body ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Computer Aided Geometric Design ◽  
Symmetrical Shape ◽  
Computer Aided

The beverage bottle consists of several parts. There are mouth, neck, shoulders and body of the beverage bottle. This study aims to modeled the shape of the beverage bottles use Bezier curves with degrees less than or equal to six (n ≤ 6), for obtain a varied and symmetrical shape of the beverage bottles. This research method are divided into several stages. First, modeled the mouth of the beverage bottle. Second, modeled the neck of the beverage bottle. Third, modeled the body of the beverage bottle. Fifth, combined the parts of the beverage bottle. The results of this study was obtained a procedure for modeled varied and symmetrical beverage bottles using Bezier curves with degrees less than or equal to six (n ≤ 6). Keywords: Beverage Bottle, Bezier Curve, Computer Aided Geometric Design

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.

Topics in computer-aided geometric design-1990

1990 ◽  
Vol 25 (4) ◽  
pp. 7-16
Author(s):  
Richard Franke
Keyword(s):  
Geometric Design ◽  
Computer Aided Geometric Design ◽  
Computer Aided
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