Question

Which formula is suitable for finding the geometric centre of a polygonal face?

(a) \(\frac{1}{No.of points}\sum_{i=1}^{No.of points}\) Point defining the polygoni

(b) \(\sum_{i=1}^{No.of\, points}\) Point defining the polygoni

(c) \(\frac{1}{Point\, defining\, the\, polygon}\sum_{i=1}^{No.of\, points}\) Point defining the polygoni

(d) \(\frac{1}{No.of\, points}\sum_{i=1}^{No.of\, points}\)Centroidi

This question was addressed to me in homework.

This interesting question is from The Geometry of FVM Elements topic in division Finite Volume Methods of Computational Fluid Dynamics

Answer 1

Right choice is (a) \(\frac{1}{No.of points}\sum_{i=1}^{No.of points}\) Point defining the polygoni

Easiest explanation: The average of all the points that define the polygon is the geometric centre of the polygon. Therefore,

Geometric centre=\(\frac{1}{No.of points}\sum_{i=1}^{No.of points}\) Point defining the polygoni