Michael J de Smith

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VORTAL models

 

 

Steiner problem in the plane, with obstacles

 

VORTAL procedure applied to a triangular region optimisation problem (Steiner problem) with obstacles.

Sample topology shown consists of three paths (coloured) and a single connecting point.

VORTAL stands for Variationally Optimised Rapidly-expanding Random Trees (RRT) Algorithm.

 

VORTAL interactive program (steiner.exe)

 

 

 

Gradient constrained problem in Pentland Hills region, Scotland (pentland.exe)

 

In this example a path is sought across the physical landscape which is of minimum length and satisfies

the gradient constraints imposed (over the step length/path segments selected). In this case the constraint is

that no step can have a gradient of greater than 10%. The red lines are the RRT search routes, the black line is

a feasible solution path and the blue line, a shorter path that is based on the initial solution and still satisfies

the gradient constraints, although its step length may imply a greater degree of cut and fill.

 

The code for this program and notes to be read first are provided below (updated 25 Oct 03):

 

VORTAL model with gradient constraints (pentland.zip)

Notes on pentland.zip (pentland.txt) - read this first!

 

 

Details of RRT can be found at : http://msl.cs.uiuc.edu/rrt/ 

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2002, 2003 Michael J de Smith