ФОРМАЛІЗАЦІЯ ПРОЦЕСУ СТВОРЕННЯ ГЕОМЕТРИЧНИХ МОДЕЛЕЙ

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<ul><li><p> .., .., 2013 111 ISSN 1028-9763. , 2013, 1 </p><p> 681.5.015 </p><p>.. , .. </p><p>. . , . -, , . : , , -, . . -. - , . - , , - . : , , , . Abstract. The paper deals with the formalization of the process of geometric models creation and graphic representation of data and knowledge in the systems for automated learning. We presented examples of model building of bodies of simple shapes using binary operations; also we examined their properties and geometric interpretation. Morgan laws were presented and proved, distributive operations applied to op-erations with solids. Keywords: modeling of solids, modeling grammar, properties of binary operations, Model tree. 1. </p><p> - -, - . </p><p> -, . , , , [1]. </p><p> () . , - , () - [2]. </p><p> - (, ) . </p></li><li><p>112 ISSN 1028-9763. , 2013, 1 </p><p>2. </p><p> - , , -, , , . </p><p> -. - , . - . , . - , , , , . </p><p> 3D- - : </p><p> (Union) A B; , (. 1 ); </p><p> (Intersection) A B; , (. . 1 ); </p><p> (Subtraction) A \ B, B \ A; - (. 1 , ). </p><p> ) </p><p> ) </p><p> ) </p><p> ) </p><p> ) </p><p> ) </p><p>) </p><p>. 1. : ) ; ) ; ) ; ) A B; ) -</p><p> A B; ) A \ B; ) B / A </p><p>3. </p><p> CAD- - (. 2) ( feature manager, Model tree, Model Navigator). </p></li><li><p>ISSN 1028-9763. , 2013, 1 113 </p><p> . , . , , - . - . , . </p><p> [3]. (future-based design), - - . </p><p> ) ) ) ) </p><p>. 2. : ) -3D; ) SolidWorks; ) Autodesk Inventor 3D; ) Creo Elements/Pro </p><p> -</p><p> 3D- -, . . -, , - . , . </p><p> , . - . </p><p> , -, [4, 5]. . -, </p></li><li><p>114 ISSN 1028-9763. , 2013, 1 </p><p>, , , - , 3D- - . 4. </p><p> , . , , . . </p><p> , , . : , -. : , , , . . </p><p> - -. , - . , . , . 4.1. </p><p> { }|A B x x A x B = . - x A B x A x B . </p><p> . 3. </p><p> A B -: </p><p>) : A A A = ; </p><p>) : A B B A = ; </p><p>) -: ( ) ( )A B C A B C = ; . 3. </p><p>) A A = ; ) A B A B = = = . : x A A x A x A x A . . -</p><p>, . </p><p> x A B x A x B x B x A x B A . , x A B x B A . , A B B A = . </p><p> ( )x A B C x A B x C ( ) ( )x A x B x C x A x B x C ( ). </p><p>, ( ) ( )x A B C x A B C . </p></li><li><p>ISSN 1028-9763. , 2013, 1 115 </p><p> , ( ) ( )A B C A B C = . x A x A x x A . , -</p><p> x , . , A A = . A B= = , A B = = . . </p><p>A B = . , x A B x . . , x A B x A x B , - , . , x A x x B x , A B= = . 4.2. </p><p> { }|A B x x A x B = . . 4. </p><p> -: </p><p>) : A A A = ; </p><p>) : A B B A = ; </p><p>) : ( ) ( )A B C A B C = ; </p><p>) A A = . . 4. </p><p>: x A A x A x A x A . , A A A = . x A B x A x B x B x A x B A . , A B B A = . </p><p>( ) ( )x A B C x A B x C x A x B x C ( ) ( )x A x B x C x A x B C x A B C . </p><p> , ( ) ( )A B C A B C = . x A x A x x , x -</p><p>. 4.3. </p><p> , , . : ) </p><p>( ) ( ) ( )A B C A B A C = ; ) </p><p>( ) ( ) ( )A B C A B A C = . : </p><p>( ) ( )x A B C x A x B C x A x B x C </p></li><li><p>116 ISSN 1028-9763. , 2013, 1 </p><p>( ) ( ) ( ) ( ) ( )x A x B x A x B x A x C x A B x A C ( ) ( )x A B A C . </p><p> ( ) ( )x A B C x A x B C x A x B x C </p><p>( ) ( ) ( ) ( ) ( )x A x B x A x B x A x C x A B x A C ( ) ( )x A B A C . </p><p> 4.4. </p><p> { }\ |A B x x A x B= . . 5. </p><p> -: </p><p>) \A A = ; ) \A B A B= ; ) ( ) ( ) ( )\ \ \A B C A C B C = ; ) ( ) ( )\ \ \A B C A B C = . : </p><p>\x A A x A x A . 5. </p><p> . x , \A A = . </p><p> \A B = . x A , \A B = , \x A B , , Bx , BA . </p><p> ( ) ( )\x A B C x A B x C x A x B x C ( ) ( ) ( ) ( )\ \ \ \x A x C x B x C x A C x B C x A C B C ; </p><p> ( )\x A B C x A x B C x A x B x C x A x B x C ( ) ( )\ \ \x A B x C x A B C . </p><p> 4.5. </p><p>) ( ) ( ) ( )CABACBA \\\ = ; ) ( ) ( ) ( )CABACBA \\\ = . </p><p>: ( ) ( )\x A B C x A x B C x A x B x C </p><p>( ) ( ) ( ) ( )\ \ \ \x A x B x A x C x A B x A C x A B A C . ( )\x A B C x A x B C x A x B x C </p><p>( ) ( ) ( ) ( ) ( )\ \x A x B x C x A x B x A x C x A B A C . 5. </p><p> - . , -</p></li><li><p>ISSN 1028-9763. , 2013, 1 117 </p><p>. 6. </p><p> , , . , . </p><p> , , , x::=y - [6]. </p><p> : </p><p> ::= | ::= | | </p><p> -, , , -, , . - . - . </p><p> - (. . 6). , . -. </p><p>, . . </p><p> , . . . ( ) - . </p><p>6. </p><p> . - , - ; - . </p><p>1. .. : . . - / .. .: , 2011. 272 . 2. .. / .. .: - . .. , 2002. 336 . 3. http://www.ledas.com. 4. http://www.3ds.com/ru. 5. http://www.ptc.com. 6. .. : . . / .. , .. ; . .. . .: , 2001. 300 . </p><p> 08.01.2013 </p></li></ul>