CGAL users discussion list

[Sebastien Loriot <>]

IIRC, it's because edges are seen per incident triangles so for the 
vertex vi, you will consider edges (vi,vj) and (vj,vi) from vi and vj 
and only one time vivj from vn and vivi from vm. Then in the partial 
derivative, you have 6 terms to consider giving you what you have in 
equation (10).

HTH

Sebastien.


On 12/29/20 2:28 PM, Maximilian Weiherer ( via 
cgal-discuss Mailing List) wrote:
> Dear cgal-community,
> I have a rather theoretical question concerning the spokes-and-rims 
> as-rigid-as-possible (ARAP) surface mesh deformation, see 
> https://doc.cgal.org/latest/Surface_mesh_deformation/index.html, 
> chapter 5 "Deformation Techniques, Energies and Weighting Schemes", 
> section 5.3 "Spokes and Rims Version".
> I am trying to re-calculate the partial derivative w.r.t. new 
> positions p'_i as stated in equation 10. However, I want to use 
> symmetric cotangent weights, thus w_ij = w_ji. Taking partial 
> derivative of equation 8 w.r.t. p'_i, only the vertices i, j, m, and n 
> remain since they are directly connected to p'_i (see Fig. 69.9). All 
> the other derivatives vanish. Thus, I would expect the rhs of equation 
> 10 to be something like: sum_j [w_ij * ((R_i + R_j + R_m + R_n) / 4) * 
> (p_i - p_j)]. However, using the fact that w_ij = w_ji equation 10 
> becomes clearly not the same as what I obtained: sum_j [w_ij * ((2R_i 
> + 2R_j + R_m + R_n) / 6) * (p_i - p_j)]. I do not understand why R_i 
> and R_j have double influcence.
> Any hints are greatly appreciated.
> Max
>
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