The need to visualize and interpret human body movement data from experiments and simulations has... more The need to visualize and interpret human body movement data from experiments and simulations has led to the development of a new, computerized, three-dimensional representation for the human body. Based on a skeleton of joints and segments, the model is manipulated by specifying joint positions with respect to arbitrary frames of reference. The external form is modelled as the union of overlapping spheres which define the surface of each segment. The properties of the segment and sphere model include: an ability to utilize any connected portion of the body in order to examine selected movements without computing movements of undesired parts , a naming mechanism for describing parts within a segment, and a collision detection algorithm for finding contacts or illegal intersections of the body with itself or other objects. One of the most attractive features of this model is the simple hidden surface removal algorithm. Since spheres always project onto a plane as disks, a solid, shad...
International Journal of Computational Geometry & Applications, 2012
We show that the Yao graph Y4 in the L2 metric is a spanner with stretch factor [Formula: see tex... more We show that the Yao graph Y4 in the L2 metric is a spanner with stretch factor [Formula: see text]. Enroute to this, we also show that the Yao graph [Formula: see text] in the L∞ metric is a plane spanner with stretch factor 8.
We prove that a particular pushing-blocks puzzle is intractable in 3D. The puzzle, inspired by th... more We prove that a particular pushing-blocks puzzle is intractable in 3D. The puzzle, inspired by the game PushPush, consists of unit square blocks on an integer lattice. An agent may push blocks (but never pull them) in attempting to move between given start and goal positions. In the PushPush version, the agent can only push one block at a time, and moreover, each block, when pushed, slides the maximal extent of its free range. We prove this version is NP-hard in 3D by reduction from SAT. The corresponding problem in 2D remains open.
The need to visualize and interpret human body movement data from experiments and simulations has... more The need to visualize and interpret human body movement data from experiments and simulations has led to the development of a new, computerized, three-dimensional representation for the human body. Based on a skeleton of joints and segments, the model is manipulated by specifying joint positions with respect to arbitrary frames of reference. The external form is modelled as the union of overlapping spheres which define the surface of each segment. The properties of the segment and sphere model include: an ability to utilize any connected portion of the body in order to examine selected movements without computing movements of undesired parts , a naming mechanism for describing parts within a segment, and a collision detection algorithm for finding contacts or illegal intersections of the body with itself or other objects. One of the most attractive features of this model is the simple hidden surface removal algorithm. Since spheres always project onto a plane as disks, a solid, shad...
International Journal of Computational Geometry & Applications, 2012
We show that the Yao graph Y4 in the L2 metric is a spanner with stretch factor [Formula: see tex... more We show that the Yao graph Y4 in the L2 metric is a spanner with stretch factor [Formula: see text]. Enroute to this, we also show that the Yao graph [Formula: see text] in the L∞ metric is a plane spanner with stretch factor 8.
We prove that a particular pushing-blocks puzzle is intractable in 3D. The puzzle, inspired by th... more We prove that a particular pushing-blocks puzzle is intractable in 3D. The puzzle, inspired by the game PushPush, consists of unit square blocks on an integer lattice. An agent may push blocks (but never pull them) in attempting to move between given start and goal positions. In the PushPush version, the agent can only push one block at a time, and moreover, each block, when pushed, slides the maximal extent of its free range. We prove this version is NP-hard in 3D by reduction from SAT. The corresponding problem in 2D remains open.
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Papers by Joseph O'Rourke