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Object representation by means of nonminimal division quadtrees and octrees
Ayala Vallespí, M. Dolors; Brunet Crosa, Pere; Juan, R.; Navazo Álvaro, Isabel
Universitat Politècnica de Catalunya. Departament de Llenguatges i Sistemes Informàtics; Universitat Politècnica de Catalunya. MOVING - Grup de Recerca en Modelatge, Interacció i Visualització en Realitat Virtual; Universitat Politècnica de Catalunya. GIE - Grup d´Informàtica a l´Enginyeria
Quadtree representation of two-dimensional objects is performed with a tree that describes the recursive subdivision of the more complex parts of a picture until the desired resolution is reached. At the end, all the leaves of the tree are square cells that lie completely inside or outside the object. There are two great disadvantages in the use of quadtrees as a representation scheme for objects in geometric modeling system: The amount of memory required for polygonal objects is too great, and it is difficult to recompute the boundary representation of the object after some Boolean operations have been performed. In the present paper a new class of quadtrees, in which nodes may contain zero or one edge, is introduced. By using these quadtrees, storage requirements are reduced and it is possible to obtain the exact backward conversion to boundary representation. Algorithms for the generation of the quadtree, Boolean operations, and recomputation of the boundary representation are presented, and their complexities in time and space are discussed. Three-dimensional algorithms working on octrees are also presented. Their use in the geometric modeling of three-dimensional polyhedral objects is discussed.
Peer Reviewed
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica::Algorísmica i teoria de la complexitat
Àrees temàtiques de la UPC::Informàtica::Infografia
Geometrical models -- Data processing
Geometric modeling
Octrees
Quadtrees
Modelatge
Geometria computacional
info:eu-repo/semantics/publishedVersion
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