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All non self-intersecting paths are those paths that do not contain loops (self-intersections).
The region library (C version) was re-written in CIAO 4.8, so that some routines may give different answers, in particular when handling self-intersecting (non-simple) polygons.
Fig. 4 Example of a non-continuous trajectory on the 2-simplex Fig. 5 Example of a self-intersecting (and continuous) trajectory on the 2-simplex.
It allowed automatic changes in the topology when implemented using the level-sets-based numerical algorithm [14] and also naturally prevented self-intersecting, which is a costly procedure in parametric deformable models.
BiNoM analysis functions also include classical path analysis algorithms, such as finding the shortest paths, the suboptimal shortest paths or all non self-intersecting paths (Table 3).
In BiNoM, we propose three solutions to search for paths between the annotated and target nodes (shortest paths, suboptimal shortest paths and all non self-intersecting paths, see previous paragraph).
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Moving surfaces that self-intersect arise naturally in the geometric optics model of wavefront motion.
This formulation allows fronts to self-intersect, develop singularities, and change topology.
The polygon should not self-intersect nor intersect any other patterning shapes, but may contain or be contained within other shapes.
Whereas traditional low-order methods use planar-faced elements, high-order methods introduce curvature into elements that may, if added naively, cause the element to self-intersect.
Note, however, that, if the constant curvature is bigger than 1/2, (h(partial D)) can self-intersect.
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