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A well known way of interpolating the gradient field of a scalar field onto faces of a triangular mesh uses the following formula

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(source: https://www.cs.cmu.edu/~kmcrane/Projects/HeatMethod/paperCACM.pdf)

I'm wondering if there is a principled way of either (a) computing gradients on vertices or (b) average the face-based gradients (maybe by say the barycentric area of the vertex).

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