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[Maximilian Weiherer <>]

Hi Sebastien,

 

thank you for your reply. You helped me a lot.

I was missing the information that edges are seen per incident triangles. I finally obtained the desired result.

Max

 

Gesendet: Montag, 04. Januar 2021 um 18:45 Uhr
Von: "Sebastien Loriot ( via cgal-discuss Mailing List)" <>
An: 
Betreff: Re: [cgal-discuss] ARAP spokes-and-rims partial derivative

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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