We study upward planar straight-line embeddings (UPSE) of directed trees on given point sets. The set S has size at least the number vertices in tree. For special case where tree is a path P we show that: (a) If one-sided convex, UPSE s equals maximal monotone paths P. (b) general position and composed by three paths, middle longer than other two, then it always admits an S. that decision probl...

Registering partial point clouds is crucial in numerous applications the field of robotics, vision, and graphics. For arbitrary configurations, registration problem requires an initial global alignment, which computationally expensive often still refinement. In this paper, we propose a pair-wise method that combines fast convergence made possible by hierarchical surface descriptors with arbitra...