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Differential
D1422
Diff 4712
source/blender/modifiers/intern/MOD_laplaciansmooth.c
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On IRC you reported that the results with this patch were different from 2.75a.
This would definitely be one reason why, since its adding the weight of a tessellated corner.
I think its worth to investigate supporting ngon's for this code, where each corner is calculated and evaluated based on the 2 adjacent verts of the loop. And the area is calculated on the polygon.