Karlsruhe metric

In metric geometry, the Karlsruhe metric (the name alludes to the layout of the city of Karlsruhe), also called Moscow metric, is a measure of distance that assumes travel is only possible along radial streets and along circular avenues around the center.^[1]

The Karlsruhe distance between two points $d_k(p_1,p_2)$ is given as

$d_k(p_1,p_2)= \begin{cases} \min(r_1,r_2) \cdot \delta(p_1,p_2) +|r_1-r_2|,&\text{if } 0\leq \delta(p_1,p_2)\leq 2\\ r_1+r_2,&\text{otherwise} \end{cases}$

where $(r_i,\varphi_i)$ are the polar coordinates of $p_i$ and $\delta(p_1,p_2)=\min(|\varphi_1-\varphi_2|,2\pi-|\varphi_1-\varphi_2|)$ is the angular distance between the two points.

See also

• Metric (mathematics)
• Manhattan distance
• Hamming distance

Notes

1. Karlsruhe-Metric Voronoi Diagram

External links

• Karlsruhe-metric Voronoi diagram, by Takashi Ohyama
• Karlsruhe-Metric Voronoi Diagram, by Rashid Bin Muhammad