A ternary subdivision scheme for generating trigonometric splines and its application to geometric modeling

Author(s):  
Sunita Daniel
Author(s):  
Shanglong Wang ◽  
Kwun-Lon Ting

This paper proposes a subdivision scheme that is capable of expressing arcs and circles in a consistent form. This curve scheme is based on the unified subdivision rules for cubic B-splines, splines-in-tension, and some trigonometric splines that are capable of generating circles. The most important feature of the scheme is to change the end point rule such that the end points are forced to locate on lines connecting the center to the start point as well as the end point. With the proposed scheme, generating arcs and circles also becomes much more intuitive.


Author(s):  
Denis Voloshinov ◽  
K. Solomonov ◽  
Lyudmila Mokretsova ◽  
Lyudmila Tishchuk

The application of constructive geometric modeling to pedagogical models of teaching graphic disciplines today is a promising direction for using computer technology in the educational process of educational institutions. The essence of the method of constructive geometric modeling is to represent any operation performed on geometric objects in the form of a transformation, as a result of which some constructive connection is established, and the transformation itself can be considered as a result of the action of an abstract cybernetic device. Constructive geometric modeling is a popular information tool for information processing in various applied areas, however, this tool cannot be appreciated without the presence of appropriate software systems and developed design techniques. Traditionally, constructive geometric modeling is used in the design of mechanical engineering, energy, aircraft and shipbuilding facilities, in architectural and design engineering. The need to study descriptive geometry at the university in recent years has something in common with the issues of mastering graphic packages of computer programs in the framework of the new discipline "Engineering and Computer Graphics". The well-known KOMPAS software product is considered the simplest and most attractive for training. It should be noted the important role of graphic packages in the teaching of geometric disciplines that require a figurative perception of the material by students. Against the background of a reduction in classroom hours, computer graphics packages are practically the only productive teaching methodology, successfully replacing traditional tools - chalk and blackboard.


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