[vtk-developers] Triangular patch interpolation

[Lin M]

Hi Dr. Thompson,

I have merged the branch to spline/VTK. How can I make the Cdash test work
then?

On Fri, Aug 21, 2015 at 12:58 PM, Lin M <majcjc at gmail.com> wrote:

> Hi Dr. Thompson,
>
> I have finished supplementary documentation for the vtkFiltersBezier
> module. I think it's ready to be tested now.
>
> On Thu, Aug 20, 2015 at 11:56 PM, Lin M <majcjc at gmail.com> wrote:
>
>> Hi Dr. Thompson,
>>
>> I have added image based tests for almost all vtkFiltersBezier related
>> class including BREP file reader, patch(simplicial) interpolation and point
>> projection for both curve and surface example.
>>
>> I will complete required documents soon.
>>
>> Best,
>> Lin
>>
>> On Tue, Aug 18, 2015 at 8:23 PM, David Thompson <
>> david.thompson at kitware.com> wrote:
>>
>>> Hi Lin,
>>>
>>> It has been a while since we talked about that, and I am not sure from
>>> looking at the method whether Pt is supposed to be the input or output. If
>>> the input, then it should be named something like coord instead of Pt. If
>>> the output, then you are correct, it should be a "double*" and the
>>> documentation should spell out how much memory it must point to. (Since in
>>> general the n-th derivative is a symmetric tensor of rank n, there are
>>> (n+1)(n+2)...(n+k-1)/(k-1) partial derivatives. This is related to Pascal's
>>> simplex. See
>>> https://en.wikipedia.org/wiki/Pascal%27s_pyramid#Parallels_to_Pascal.27s_triangle_and_Multinomial_Coefficients
>>>  and
>>> https://en.wikipedia.org/wiki/Differential_of_a_function#Higher-order_differentials
>>>  .)
>>>
>>> It is fine to have different methods for curves, surfaces, and volumes
>>> for now. As you can see in the links above, the general pattern is that the
>>> n-th total derivative is a tensor of all possible combinations of partial
>>> derivatives with respect to the 1, 2, or 3 parametric coordinates. Call the
>>> parametric coordinates r_i for i in {1, 2, 3} and say we are taking the
>>> n-th derivative of f. Then Python code to compute one possible ordering of
>>> the partial differentials in the output array would be
>>>
>>> def pdiff(i,n):
>>>     r=[]
>>>     if i == 1:
>>>         return [[n,],]
>>>     for x in range(n+1):
>>>         for y in pdiff(i-1,n-x):
>>>             r.append(y+[x,])
>>>     return r
>>>
>>> which returns a list of i-tuples that all sum to n. For example
>>>
>>> pdiff(2,1) returns [[1, 0], [0, 1]]
>>> pdiff(2,2) returns [[2, 0], [1, 1], [0, 2]]
>>>
>>> pdiff(3,1) returns [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
>>> pdiff(3,2) returns [[2, 0, 0], [1, 1, 0], [0, 2, 0], [1, 0, 1], [0, 1,
>>> 1], [0, 0, 2]]
>>>
>>> However, really only the first (Jacobian, a vector) and second (Hessian,
>>> a symmetric 3x3 matrix with 6 unique entries) derivatives are used very
>>> much because (a) the number of terms grows very fast with increasing
>>> derivative and (b) the first 2 derivatives are used widely for root-finding
>>> and curvature computation but further derivatives are not.
>>>
>>>     David
>>>
>>> On Aug 17, 2015, at 22:40, Lin M <majcjc at gmail.com> wrote:
>>>
>>> Hi Dr. Thompson,
>>>
>>> I found you left an interface for
>>> vtkBezierPatchAdaptro::EvaluateDeriv(double Pt[3], double* Paras, int d).
>>> For 1-d curve, the derivative is always a 3*1 vector, but with the
>>> parametric dimension increasing, higher order derivatives will contain
>>> many points (it becomes matrix-by-vector differential). I can't figure out
>>> a generalized way to interpret this. That's why I declared functions to
>>> compute derivative for curve, surface and volume separately. Do you have
>>> any suggestions for that? Thanks!
>>>
>>> Best,
>>> Lin
>>>
>>> On Tue, Aug 18, 2015 at 1:04 AM, David Thompson <
>>> david.thompson at kitware.com> wrote:
>>>
>>>> Hi Lin,
>>>>
>>>> > I have some questions about the test.
>>>> > 1. About simplicial interpolation. Should I test some simple cases
>>>> (hard coded simple shape) or some shapes like the motorcycle?
>>>>
>>>> Those are 2 different types of tests. (There are many; see
>>>> http://stackoverflow.com/questions/437897/what-are-unit-testing-and-integration-testing-and-what-other-types-of-testing-s
>>>> for some lists of test types). The first test (simple hard-coded shape) is
>>>> a unit test and the second (test of both the reader, spline-to-patch class,
>>>> and patch interpolation) is an integration test.
>>>>
>>>> Both are important, but since you already have an integration test for
>>>> the motorcycle, I think a good set of unit tests for simplicial
>>>> interpolation would be enough.
>>>>
>>>> > If it is the latter one, how to convert the rectangular patch to
>>>> simpicial patch?
>>>> >
>>>> > 2. About point inversion. How to test it for the simpicial patch? I
>>>> only implemented the point inversion for NURBS patch.
>>>>
>>>> If you didn't implement it, you can't test it. :-) However, if you know
>>>> what you want the test to look like, you can write the test before you
>>>> implement inversion and just leave it commented out with a note. Many
>>>> people think this is how development should be done in the first place,
>>>> since it forces you to consider how people will use what you write.
>>>>
>>>> > 3. About derivative computation. Should I just test them numerically?
>>>> For example, given a shape and a parametric coordinate, test the result of
>>>> our implementation with ground truth.
>>>>
>>>> Again, since you are using the derivatives in code that is part of an
>>>> integration, I think unit testing (as you suggest) is enough.
>>>>
>>>>         David
>>>
>>>
>>>
>>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://public.kitware.com/pipermail/vtk-developers/attachments/20150821/84a9b765/attachment-0001.html>