UBC Theses and Dissertations
Solid modelling using linear octree representation Ho, Sheung-Lai Sunny
Object representation is the backbone of any solid modelling system. Hierarchical spatial decompositions of objects called octrees introduced very efficient algorithms for boolean set operations and some restricted classes of geometric transformations. Linear octrees, a compact encoding of the octrees, result in a significant reduction of storage requirements, and lead simpler algorithms for most modelling operations. This thesis investigates some properties of linear octrees with emphasis on object generation. By interpreting linear octree node digits as binary numbers, some simple conversion and node trimming algorithms are found, which when combined with a node enumeration algorithm, generate the linear octrees of cuboidal volumes efficiently. A simple and uniform approach is devised to perform arbitrary geometric transformations by means of cuboid generation. Experiments shows these algorithms maintain the efficiency of special cases while degrading linearly with the number of intermediate nodes generated.
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