Study-of-the-V-HACD-algorithm/Quality-Measurement.md

@@ -4,5 +4,11 @@ We can think that the best decomposition is the one whose decomposed model is th
 
 In general terms, the Hausdorff Distance is the maximum distance of a set to the nearest point in the other set. As we have two sets (two meshes) the Hausdorff distance is the maximum of the two distances (A to B and B to A). These two distances are not symmetric (quite often we say that the Hausdorff distance is oriented) so both of them need to be calculated.
 
+```math
+H(A,B) = max\{h (A, B), h (B, A)\} \\[2mm]
+with: \\[2mm]
+h (A, B) = \max_{a \in A} \{ \min_{b \in B} \{ d(a,b)\} \} \\[2mm]
+```
+
 Meshlab provides a Hausdorff distance calculation (a filter) so we decided to use it to calculate our quality parameter. For simplicity we used the python library Pymeshlab to automatize the quality calculation.