# Constrained Optimal Routes in 3D Space

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Given a set of constraints, what is an optimal travel route between given points? Such problems are usually posed in 2D or on a surface; for example, finding the shortest path through a set of points on the surface of Earth. This Demonstration highlights a subset of such optimization problems in 3D, as might be needed in outer space or under water.

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Contributed by: Vitaliy Kaurov (July 2015)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Controls

“range” sets how far the spaceship can travel without refueling. Hence it defines which planets can be reached from a given one.

“new” generates a new random set of planets.

“number” defines how many planets are on the route.

“constrained” shows the shortest tour on the percolation network. If there is no route shown even with the control checked, then it does not exist.

“optimal” shows the traveling salesman route.

“network” shows the percolation network or distances between nearest-neighbor planets that you can travel to without refueling.

“nodes” shows the nodes of the network, in this case planets.

## Permanent Citation

"Constrained Optimal Routes in 3D Space"

http://demonstrations.wolfram.com/ConstrainedOptimalRoutesIn3DSpace/

Wolfram Demonstrations Project

Published: July 17 2015