3D Motion Planning (Motion Planning Problems)
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Description
Given a set of horizontal (that is, parallel to the xy-plane) non-intersecting, non-touching triangle obstacles in 3-space, and a vertical line segment as a robot, determine whether the robot can be moved, using translations only, from a source to a goal position without colliding with the obstacles.
Related Problems
Related: Planar Motion Planning
Parameters
$n$: number of triangle obstacles
Table of Algorithms
Currently no algorithms in our database for the given problem.
Reductions FROM Problem
| Problem | Implication | Year | Citation | Reduction |
|---|---|---|---|---|
| Triangles Cover Triangle | if: to-time $N^{2-\epsilon}$ for some $\epsilon > {0}$ then: from-time: $N^{2-\epsilon'}$ for some $\epsilon' > {0}$ |
1995 | https://doi-org.ezproxy.canberra.edu.au/10.1016/0925-7721(95)00022-2 | link |