Modeling the contour arc based on Dezargues configuration

Abstract

A new geometric algorithm for modeling the contour arc in the form of a curve of one relationship based on the Dezargues configuration, parameterization of which is performed using the mathematical apparatus "Point Calculus", is proposed. The analysis has shown that the obtained contour arc has interesting geometric properties, which can potentially be used for modeling one-dimensional and multidimensional outlines of high order smoothness, which constitutes a prospect for further research. A detailed description of the process of parametrization the contour arc in the point calculus based on the proposed geometric algorithm for its construction with the exception of cumbersome transformations is presented. The given methods of parametrization of geometrical objects in the point calculus on the basis of a simple relation of three points of a straight-line invariant concerning parallel projection, can be used by other researchers for the solution of a wide range of problems of engineering geometry and computer graphics. Examples of modeling spatial and planar, closed and unclosed arcs of the circumference, which can find their application as shape-forming elements of surfaces of technical forms, are given.

Keywords

• dezargues configuration
• contour arc
• geometric algorithm
• point calculus
• order of smoothness
• tangent