| Resumen |
SUMMARY. A common representation of a 3-D object is a 3-D array of contiguous voxels or elementary cubes –a pile of them, so to speak. The surface of this pile can in turn be rep-resented by 2-D data structures, such as the Hamiltonian graph. In selecting a suitable rep-resentation, one seeks to reduce its size (storage needed), to preserve the shape of the initial object, and to obtain a simple representation, easy to compute. Reconstruction of the origi-nal object is also important, thus a suitable question is whether the selected representation loses information or it allows complete recovery of the original body. If we could in turn represent the surface by lines, further reduction and simplicity may be achieved.
An enclosing tree is a three-dimensional tree formed by 3-D lines totally covering an object (as ivy covers a surface). A simple line in an enclosing tree is a sequence of ele-mentary line segments (in 5 possible spatial directions). A line is a sequence of simple lines and forks, represented just by writing its constituents in sequence. A fork or subtree appears where several lines meet (akin to nodes of a tree), represented by writing its lines in a given order, using parentheses to keep each line distinct. Thus, a tree is just a line with a distin-guished starting point, its root. An enclosing tree is a tree that totally covers (touches, vis-its) each voxel of the surface of the solid.
Enclosing trees have interesting properties. They are invariant under r |
