3D visualisation of cylindrical bodies in the Maple CAS: Original methods and techniques

Abstract

The relevance of this topic stems the growing need to utilise modern tools of computational mathematics to enhance the efficiency of analysing, modelling and visualising complex spatial objects. The aim of this work was to develop an original method for the three-dimensional visualisation of cylindrical solids within the Maple computer algebra system. The proposed approach was based on structuring the mathematical model of a cylindrical body into separate elements – a projection plane, guide curves, generatrix segments and boundary surfaces – with their subsequent integration into a single 3D model. The study employed the basic Maple tools (plot3d, spacecurve, plottools[line], display), which enabled the software implementation of individual elements of the spatial object and their step-by-step combination into a complete model of a cylindrical body in order to create a clear three-dimensional representation. A number of original techniques were developed for constructing planar and spatial guides defined by a pair of intersecting curves forming a closed region, families of generators in the form of straight-line segments to create a transparent lateral cylindrical surface, as well as methods for surface visualisation that allow adaptive modification of model parameters, display of intermediate construction stages, and control over the relative arrangement of its elements. Examples of the practical implementation of the method for constructing cylindrical bodies based on typical higher mathematics problems were presented, confirming the effectiveness and convenience of the developed approach. It was shown that the proposed method has a universal character and may be used not only in the educational process but also in scientific research and applied engineering tasks requiring accurate and clear 3D visualisation of multicomponent bodies. The practical value of the work lies in the fact that the developed approach may be regarded as a component of information technology for the three-dimensional visualisation of geometric objects in computer algebra systems, combining ease of implementation, flexibility of modelling, and high informational value of graphical results.