The Problem of Visualizing Solid Models as a Three-Parameter Point Set
Evgeniy V. Konopatskiy, A. A. Bezditnyi · Scientific Visualization · 2022
This paper describes a new concept of defining geometric solids as a three-parameter set of points in three-dimensional space.An analytical description of such a three-parameter set of points is realized in the point calculus.The analysis of existing approaches to the visualization of a three-parameter set of points, which is described by a system of parametric equations, showed the absence of software solutions that are capable of visualizing threedimensional solids in accordance with the proposed concept.In this connection the problem of visualization of solid-state models of geometrical objects parametrized in the point calculus is set.One solution to this problem is to adapt the existing way of visualization of threedimensional objects in various simulation systems.Thus, on the basis of the point equation of a geometric solid, several surfaces are formed, the totality of which defines a closed envelope around the solid.Each of these surfaces corresponds to the limit state of one of the current parameters.Alternately fixing these parameters determines the point and parametric equations for their construction.Examples of visualization of face and curvilinear solids are given, which have shown the possibility of using computer algebra systems to visualize models of geometric solids in the form of a three-parameter set of points.