Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. The LIR space partitioning system applied to cartesian grids
 Floater, M.: Mathematical methods for curves and surfaces. 8th international conference, MMCS 2012 : Oslo, Norway, June 28  July 3, 2012; Revised selected papers Berlin: Springer, 2014 (Lecture Notes in Computer Science 8177) ISBN: 9783642543814 (Print) ISBN: 9783642543821 (Online) ISBN: 3642543812 pp.324340 
 International Conference on Mathematical Methods for Curves and Surfaces (MMCS) <8, 2012, Oslo> 

 English 
 Conference Paper 
 Fraunhofer ITWM () 
Abstract
We introduce a novel multidimensional space partitioning method. A new type of tree combines the advantages of the Octree and the KDtree without having their disadvantages. We present in this paper a new data structure allowing local refinement, parallelization and proper restriction of transition ratios between cells. Our technique has no dimensional restrictions at all. The tree's data structure is defined by a topological algebra based on the symbols A = {L, I, R} that encode the partitioning steps. The set of successors is restricted such that each cell has the partition of unity property to partition domains without overlap. With our method it is possible to construct a wide choice of spline spaces to compress or reconstruct scientific data such as pressure and velocity fields and multidimensional images. We present a generator function to build a tree that represents a voxel geometry. The space partitioning system is used as a framework to allow numerical computations. This work is triggered by the problem of representing, in a numerically appropriate way, huge threedimensional voxel geometries that could have up to billions of voxels.