Collection of 3D models from projections Axonométricas
(1) Department of computer science and Industrial Engineering
Universitat de Lleida, Jaume II, 69, E - 25001 Lleida
e-mail: {ramon,alba,felip}@eup.udl.es}
(2) Department of graphical expression in engineering
Universitat Politècnica de Catalunya, Av. Víctor Balaguer, s/n, 08800 Vilanova i la Geltrú
e-mail:membrilla@Ege.UPC.es
01/12/2002The spatial interpretation of drawing lines is a topic studied by the communities of machine vision and structural geometry. They develop algorithms to automate the collection of 3D models from 2D drawings such that, as with human vision, capable of rejecting impossible images.
In this work will head off of the system of labelling of Huffman [1] and Clowes [2], which assigns to each line or edge of an oblique R representation a label denoting whether the edge is convex, concave or border or occlusion. The system assigns a tag of type + to those edges which are convex and that faces present in the edge are visible in the representation R; It is assigned a tag of type - to those edges which are concave and that faces present in the edge are visible in the representation R; assigns a label type (Æ, ¨) those edges which is only visible to one side of which concur on the ridge. The latter will be the border edges and the faces that concur in the edge presented occlusion.
On the other hand, depending on the number of edges that meet at a vertex and its position in the representation, the system of Huffman and Clowes classifies joints at the vertices. Joints can be of four types: fork, T, L and arrow. In addition, as the edges that meet at a vertex have label, these four types of links give rise to a catalog that is composed of 18 unions representing all the unions that are physically realizable in a polyhedral 3D scene. If an oblique projection is supported by a consistent labelling of the edges with the unions of the catalogue of Huffman and Clowes, then we can get a 3D model. On the other hand, if the labelling is inconsistent, the projection corresponds to a physically unrealizable 3D polyhedral object.
Given an oblique R of a 3D object representation, our method starts by represent restrictions of joints by a set of propositional logic formulas F and R, so R corresponds to a 3D object if, and only if F is satisfactible (i.e., is not contradictory). Then determines the first of F using Satz [3], which is a first that incorporates artificial intelligence techniques. Finally, if F is satisfactible, build a correct labelling of the 3D object from the logical model of F which has derived Satz.
In the experiments have observed that our method of 3D models, from projections axonométricas, is a highly efficient approximation from point computational view.
References
[2] Moniteur belge Clowes, "On seeing things", Artificial Intelligence 2: 79-116, 1971.
[3] Chu Min Li and Anbulagan, "Heuristics based on unit propagation for satisfiabiliy problems", Proceedings of the Fifteenth International Joint Conference on Artificial Intelligence (IJCAI'97), 366-371, Nagoya (Japan), 1997
