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[Tapadi <>]

Hi again,

Yang, what you propose is actually an other way to discretize the polygon :
small squares instead of small triangles. But you have to add a
normalization term in order to make your formula homogeneous. Look at the
previous formula:

[A]  "value of the function at center of the triangle" x "area of the
triangle"

This has the dimension of an integral : function value x area. If you just
sum values of the function over the grid you propose, you'll only get a sum
of values. You have to multiply those values by the areas of each grid cell
to make up an integral value. A hint is that such areas should be small. The
formula becomes:

[B]  "value of the function at center of the grid cell" x "area of the cell"

... And you just have to sum this result for all cells in your grid.

Best regards,
Hugo Loi
PhD student at Inria - Maverick team




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