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Question about the B-spline function #49

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antibes0415 opened this issue Mar 5, 2018 · 9 comments
Closed

Question about the B-spline function #49

antibes0415 opened this issue Mar 5, 2018 · 9 comments

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@antibes0415
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Hi. I have two questions.

  1. In Poisson Surface Reconstruction (2006), the value of the base function is sacled by (1 / o.w^3).
    2018-03-05 15_27_23-2006 2117 poisson surface reconstruction pdf _ -
    Do you implement this feature in screened Poisson, i.e. is the B-spline function scaled by (1 / o.w^3) in 3D or (1 / o.w) in 1D whenever it is called ?
  2. Is the implicit function value of an arbitary point computed as the linear combination of the solution of related nodes ( x(p) = sum(xiBi(p) ) ? Except for B-spline function, there is no other scaling factor to adjust the weight of solution value of different depth nodes, right ?
@mkazhdan
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mkazhdan commented Mar 5, 2018 via email

@mkazhdan
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mkazhdan commented Mar 5, 2018 via email

@antibes0415
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antibes0415 commented Mar 7, 2018

Thanks. I've implemented unscreened Poisson by myself. Maybe due to different ways of implementation, I have to use an extra factor to adjust the weight among different levels ( x(p) = sum(factor * xi * Bi(p) ). Right now I try to implement the screened Poisson, however the adaptive weight of the screen term ( 2^d ) described in your paper just doesn't work for my code. Anyway I will be trying. Thanks.

@antibes0415
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Hi. Where can I find the standard B-spline prolongation stencil ? Could you give me some help ?

@mkazhdan
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mkazhdan commented Mar 8, 2018 via email

@antibes0415
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antibes0415 commented Mar 9, 2018

Much thanks. I've found this 1D stencil described in your V4 Poisson code comments. But I was not so sure.

@antibes0415
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antibes0415 commented Mar 12, 2018

Hi, I have another question about the prolongation. I use the 2 degree B-spline and the prolongation stencil is {1/4, 3/4, 3/4, 1/4}. For example, in 1D, if the solution of a node T in depth D-1 is b(T), and the B-spline range of the node is [-1.5w, 1.5w], then the prolonged solutions of related 6 nodes in depth D are {0,1/4, 3/4, 3/4, 1/4,0} * b(T) ? To my understanding, it's like this:

node T in depth D - 1:
              |-------------|
                     b(T)
nodes in depth D covered by node T:
|------|------|------|------|------|------|
  0            0.75b(T)      0.25b(T)
       0.25b(T)      0.75b(T)         0

But when there are some neighbor nodes T1,T2,... in depth D-1, how to compute the prolonged solution in overlap nodes in depth D ?

@antibes0415
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Hi. I just accumulate those prolonged solutions of depth D - 1 nodes for overlapped depth D nodes. It works. Much thanks. Finally I get the same quality and accuracy mesh compared with mesh generated by your codes.

@mkazhdan
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mkazhdan commented Mar 15, 2018 via email

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