Efficient Algorithms for Octree-Based Geometric Modelling
Year: 2009
Type: conference-paper
Abstract: \n Dealing with surface-oriented models - e.g. B-Rep models - is very\n popular and appropriate for many applications. They can be read by\n most CAD programs and they provide all freedom of modelling.\n Concerning a lot of other tasks - consistency checks, collision\n detection, structural analysis, flow simulation, e.g. - these models\n become difficult to handle, and a volume-oriented model has to be\n derived from the existing surface-oriented one. Hierarchical\n volume-oriented models, represented by octrees for example, provide\n an easy access to solve the latter tasks with respect to their\n spatial decomposition of the underlying geometry. This paper deals\n with fast and efficient algorithms to generate and process octrees -\n even on-the-fly - from surface-oriented models for applications in\n civil engineering. Encoding these octrees as binary streams makes\n them suitable to get multiplexed with other octree-coded objects or\n for the usage in pipe-like constructs.\n\n Conventional algorithms for octree generation or processing\n don't exploit the full potential of these structures. In spite\n of the principal advantages of octrees concerning complexity,\n objects of a higher resolution typically still entail too high\n run-time and memory requirements. Usually, an expensive\n floating-point-based decision whether or not to refine the structure\n has to be taken in each voxel (cell) successively. In our approach,\n instead, the refinement decision is done by a simple parameter\n comparison of plane equations, avoiding all these costs.\n\n By treating each face of the surface-oriented model as a plane that\n divides the whole space into two half spaces - inside and outside -,\n the volume-oriented model can be built from intersecting all\n inside-attributed half spaces. The steps for generating an octree\n presentation for each corresponding plane, intersecting these\n octrees, and encoding the result as a binary stream can be done at\n once - thus, the octree generation is free of any redundant\n calculations, and the overall memory requirements are reduced to a\n minimum due to the usage of stacks. The highest gain can be achieved\n in run-time, e.g. an octree generation for an average geometry with\n more than 1.5 billion voxels can be done in best time on a standard\n PC. Several of these binary streams can be multiplexed to perform\n further Boolean or more sophisticated operations (e.g. collision\n detection), while one always has the choice to perform this\n operations on-the-fly or to perform consecutive operations - like\n with Unix pipes - on binary streams written to the hard disk.\n\n One target application of this method deals with consistency checks\n for CAD models in the scope of simplifying and unifying planning\n processes in civil engineering. Before a connection model for\n structural analysis is created out of an (Eurostep) IFC model, any\n modelling errors (geometric inconsistencies) - wrong intersections\n or gaps between parts of the model - can be detected fast and\n easily. Hence, this proceeding enables us to obtain a reliable\n volume-oriented attributed model that can serve for numerical\n simulations as well as to determine relations between parts of the\n model to ensure global consistency, which brings us one step closer\n to the long-term objective of completely embedded simulation\n processes.\n
Source: Civil-comp proceedings
DOI: 10.4203/ccp.77.10
Language: English
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2748761888