UVicSpace

# Random Distances Associated with Arbitrary Triangles: A Recursive Approach with an Arbitrary Reference Point

 dc.contributor.author Ahmadi, Maryam dc.contributor.author Pan, Jianping dc.date.accessioned 2014-01-06T21:00:26Z dc.date.available 2014-01-06T21:00:26Z dc.date.copyright 2013 en_US dc.date.issued 2014-01-06 dc.identifier.uri http://hdl.handle.net/1828/5134 dc.description.abstract In this work, we propose a decomposition and recursion approach in order to obtain the distance distributions associated with arbitrary triangles. The focus of this work is to derive the distance dis- tributions from an arbitrary reference point to a random point within the triangle, where the reference point can be inside or outside of the triangle. Our approach is based on the distance distributions from a vertex of an arbitrary triangle to a random point inside. By decomposing the original triangle, using the probabilistic sum, and using the distance distributions from the vertex of the decomposed triangles, we obtain the desired distance distributions. We compare our analytical results with those of simulation, where a close match can be seen between them. Since any polygon can be decomposed into triangles, this approach also applies to the random distances from an arbitrary reference point to an arbitrary polygon, regardless convex or concave. en_US dc.language.iso en en_US dc.relation.ispartofseries UVic-PanLab-TR-14-01 en_US dc.subject Random distances with a reference point en_US dc.subject Distance distribution functions en_US dc.subject Arbitrary triangles en_US dc.subject Arbitrary polygons en_US dc.title Random Distances Associated with Arbitrary Triangles: A Recursive Approach with an Arbitrary Reference Point en_US dc.type Technical Report en_US dc.description.scholarlevel Faculty en_US dc.description.reviewstatus Unreviewed en_US
﻿