projected_dij.cpp File Reference

Compute $\sum_{i \neq j} d_{i,j}$ and $\sum_{i \neq j} d_{i,j}^{-1}$ of a given projection. More...

Detailed Description

Compute $\sum_{i \neq j} d_{i,j}$ and $\sum_{i \neq j} d_{i,j}^{-1}$ of a given projection.

This tool aligns the pkf curve along an axis given as an input to the program. The pkf filename is expected to be the last argument on the command line. Then the reoriented curve is projected onto the XY-plane and resampled, such that the curve has a uniform distribution in the sense of arc-length. Then the following quantity is computed :

$\frac{1}{N\cdot(N-1)} \sum_{i \neq j} d_{i,j} and \frac{1}{N\cdot(N-1)} \sum_{i \neq j} \frac{1}{d_{i,j}},$ where $N$ is the number of points on the curve.

The values are written to the standart output. There is a result with the sum of the distances and a result for the sum of the inverse of each distance.

Points that are closer than some tolerance are rejected and do not contribute to the sum.