THE EULER NUMBER FROM THE DISTANCE FUNCTION
DOI:
https://doi.org/10.5566/ias.v32.p175-181Keywords:
critical points, distance function, Euler number, stereology, tangent countsAbstract
We present a new method to obtain the Euler number of a domain based on the tangent counts of concentric spheres in ℝ³ (or circles in ℝ², with respect to the center O, that sweeps the domain. This method is derived from the Poincaré-Hopf Theorem, when the index of critical points of the square of the distance function with respect to the origin O are considered.References
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