Geometrical accuracy of computer algorithms for constructive problems
Kheifetc Aleksandr Lvovich
Аbstract
The criteria of geometrical accuracy (GA) of algorithms intended for solving problems of constructive geometry are considered. The existing in descriptive geometry criterion of GA requires using a pair of compasses and a ruler. The historical background of developing this criterion as abstract accuracy which doesn’t meet current requirements for applied problems is given. The author suggests estimating a true GA which is assessed by solution errors in terms of quantity. The true GA of computer algorithms is considered. A number of tests for its assessment are developed and the testing results are given.
The classic Fermat problem on spheres is considered. On its basis comparative evaluation of methods of descriptive geometry (DG), 3D and parameterization is conducted. It’s shown that the requirement of abstract GA (pair of compasses and ruler) hinders the development of educational process.
