19. 4 Cell decompositions 19. 4.1 Motivation The motivation for cell decomposition methods is Use of elements other than cubes, see Figure 19.7 for an example Applications such as design of inhomogeneous(eg. composites) and functionally graded materials, finite element analysis methods, scientific visualization of scalar and vector fields Cells are parametrized instances of a generic cell type, eg. a cell bounded by quadratic curves and surfaces Cells are homeomorphic to spheres Cells meet at a vertex, edge, face otherwise the representation is invalid Cells are disjoint and non-overlapping Cells may belong to different cell types, eg. box-like, tetrahedra-like, etc Figure 19.7: A cell decomposition(finite element mesh) 19. 4.2 Cell tuple data structure A cell decomposition can be represented using the cell-tuple data structure 2 which applies for n-D models, see also 1 for a review and summary of other related data structures such as the Quad-edge structure [6 for 2D models and the Facet-edge pair structure [4, 5] for 3-D models Figures 19.8 and 19.9 present 2D and 3D examples. This data structure can be mapped into a relational database or a graph structure 1119.4 Cell decompositions 19.4.1 Motivation The motivation for cell decomposition methods is: • Use of elements other than cubes, see Figure 19.7 for an example. • Applications such as design of inhomogeneous (eg. composites) and functionally graded materials, finite element analysis methods, scientific visualization of scalar and vector fields. • Cells are parametrized instances of a generic cell type, eg. a cell bounded by quadratic curves and surfaces. • Cells are homeomorphic to spheres. • Cells meet at a vertex, edge, face otherwise the representation is invalid. • Cells are disjoint and non-overlapping. • Cells may belong to different cell types, eg. box-like, tetrahedra-like, etc. Figure 19.7: A cell decomposition (finite element mesh). 19.4.2 Cell tuple data structure A cell decomposition can be represented using the cell-tuple data structure [2] which applies for n-D models, see also [1] for a review and summary of other related data structures such as the Quad-edge structure [6] for 2D models and the Facet-edge pair structure [4, 5] for 3-D models. Figures 19.8 and 19.9 present 2D and 3D examples. This data structure can be mapped into a relational database or a graph structure. 11