COMPARISON OF METHODS OF DESCRIPTIVE GEOMETRY AND COMPUTER 3D GEOMETRIC SIMULATION ACCORDING TO THE ACCURACY, COMPLEXITY AND EFFECTIVENESS

Abstract

Urgent educational problem of inconsistency of content of the course of descriptive geometry
(DG) with the trends in the development of CAD and geometric simulation is considered.
While the development is aimed at expanding the scope of computer 3D geometric simulation
the teaching of descriptive geometry projection methods continues despite the fact that they are
in no demand in practical applications. To compare the estimations of versions of solutions in descriptive
geometry and 3D five specific problems of the nomination in descriptive geometry
of All-Russian Olympiad 2014 are considered. They are the construction of sphere, tangent to the
paraboloid; determining the points of intersection of the ellipse defined by the axes, with a circle
(without the ellipse); finding the reference points of the ellipse section and its projections; construction
of a tetrahedron by one projection of its face; as well as the defining the points of intersection of
the circle with an elliptical cone. The detailed versions of solutions of descriptive geometry and 3D
are given for each problem.
The comparison of versions of the solution according to the geometrical accuracy is done.
It is offered to estimate not an abstract accuracy which corresponds to constructions made
by aperfect caliper and a ruler but the real accuracy independently of methods of its achievement.
It’s shown that with the computer realization of both variants their real accuracy is either equal or
3D is much better than DG.
The estimation of the complexity of task solutions is given. The amount of information needed
for the solution is taken as a criterion. The author makes the conclusion that generally 3D versions
are easier than DG.
The examples show that 3D solutions can be easily supplemented with researches of a solvable
problem. Much higher visualization, accessibility and universality of 3D versions are highlighted.
The author makes the conclusion about much higher general effectiveness of computer
3D variants and methods of solving the structural problems and the necessity of transfer
to new training course of 3d theory.
Keywords: descriptive geometry, computer graphics, 3D modeling, structural problems, geometrical
accuracy, complexity and effectiveness of structural problems.