I'm not quite sure I understand how the 4 and the 16 come about if, judging by the diagram, n=4. Shouldn't it be (n-3)*p = (4-3)p = p, and dividing by 4?
kalebm
Is there any particular reason that the new edge points take into account the new face points' positions? I feel as though considering the new face points would make the edge points go to odd new places unnecessarily. Also, would making the new edge points first by averaging the endpoints and then making the face points an average of their nearby old vertex points and new edge points work in a similar manner?
adampahlavan
Where do these coefficients come from? Are they based on mathematical proofs or more just what works in practice?
I'm not quite sure I understand how the 4 and the 16 come about if, judging by the diagram, n=4. Shouldn't it be (n-3)*p = (4-3)p = p, and dividing by 4?
Is there any particular reason that the new edge points take into account the new face points' positions? I feel as though considering the new face points would make the edge points go to odd new places unnecessarily. Also, would making the new edge points first by averaging the endpoints and then making the face points an average of their nearby old vertex points and new edge points work in a similar manner?
Where do these coefficients come from? Are they based on mathematical proofs or more just what works in practice?