Improvement And Implementation Of Automatic Geometric Reasoning Of The Dm-decomposition Algorithm

Automated geometric deduction is the core of intelligence CAD technology. By using computer, the automated geometric deduction generates graphs satisfying the aim of designer automatically , and can provide the graph which is created automatically when the constraints are changed with the modifying of some results. The DM-decomposition algorithm is an automated geometric deduction method based on the DM- decomposition of bigraphs.The main idea of DM-decomposition algorithm is to separate a automated geometric deduction problem into some small automated geometric deduction problems. Its purpose is reducing the difficulty of solutions, that is, decomposing a geometry on bigraph to some small geometric rigids, then assembling and getting the geometry graph according to the primary problem of automated geometric deduction. DM-decomposition algorithm obtains a series of subgraphs by decomposing the representative bigraph of the automated geometric deduction, and these subgraphs represent a series of small rigids correspondingly. In the representing bigraph of automated geometric deduction, every rigid owns at least one knot. In the view of intuitive geometry, these knots should be decomposed to the same subbigraphs. I give the proof of the theorem. I prove this problem by using diagram theory, i.e. the decomposed bigraph knots in the same rigid will lie in the same subgraphs. And I verify the accuracy and validity of the DM- decomposition algorithm by the uniform results between experimental programming and computing and the theoretical conclusion.