On the Piano Movers Problem Iii Coordinating the Motion of Several Independen
On the Piano Movers Problem Iii Coordinating the Motion of Several Independen
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It is also easy to check that the initial (resp. Final) configuration of the two circles (shown in Fig. 2. 3) belongs to the cell of FP represented by the node n3 (resp. N l3) of CG. Since CG is connected, there exists a continuous motion of the two circles between the initial and the final configurations. In fact, CG contains just two paths between n3 and n 13, corresponding to motions of the circles in which the line -41- Fig. 2. 5. The Connectivity Graph of our Example, connecting their cent...ers rotates in a clockwise or counterclockwise direction. The actual motion of the two circles can be reconstructed from these paths in the manner described in Theorem 1. 1. One of these motions is easily seen to coincide with the motion described above, and the other is simply a 'mirror image' of this motion.
-42- 3. Coordinating the motion of 3 independent circular bodies Having now treated the case of 2 independent circles, we go on to study motion-planning algorithms for 3 independent circles.
What to read after On the Piano Movers Problem Iii Coordinating the Motion of Several Independen?
You can find similar books in the "Read Also" column, or choose other free books by Jacob T Schwartz to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
It is also easy to check that the initial (resp. Final) configuration of the two circles (shown in Fig. 2. 3) belongs to the cell of FP represented by the node n3 (resp. N l3) of CG. Since CG is connected, there exists a continuous motion of the two circles between the initial and the final configurations. In fact, CG contains just two paths between n3 and n 13, corresponding to motions of the circles in which the line -41- Fig. 2. 5. The Connectivity Graph of our Example, connecting their cent...ers rotates in a clockwise or counterclockwise direction. The actual motion of the two circles can be reconstructed from these paths in the manner described in Theorem 1. 1. One of these motions is easily seen to coincide with the motion described above, and the other is simply a 'mirror image' of this motion.
-42- 3. Coordinating the motion of 3 independent circular bodies Having now treated the case of 2 independent circles, we go on to study motion-planning algorithms for 3 independent circles.
What to read after On the Piano Movers Problem Iii Coordinating the Motion of Several Independen?
You can find similar books in the "Read Also" column, or choose other free books by Jacob T Schwartz to read onlineMoreLess
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