# [Paraview] Question about Integrate Variables Filter

Yuanxin Liu leo.liu at kitware.com
Sun Jun 10 20:36:51 EDT 2012

```Hi, Sam,
Would you mind reposting this?  The pdf file seems corrupt.
thanks,
Leo

On Sun, Jun 10, 2012 at 7:38 PM, Samuel Key <samuelkey at bresnan.net> wrote:

>  Hi Leo,
>
> Though likely more arithmetically intense than you would like, I have
> attached a 3-page write-up on how to do an exact integration over the
> surface of a bi-linear isoparametric coordinate based quadrilateral in
> three-space. It is easily adapted to a flux integration as well.
>
> If it helps, please free to incorporate it into ParaView.
>
> Sam Key.
>
>
>
>
> On 6/10/2012 12:55 PM, Yuanxin Liu wrote:
>
> Hi,
>    This is not really a bug, but just what the linear precision
> integration does.  As you can see in vtkIntegrateAttributes.cxx:215, the
> quad cell is basically cut into two triangles along a diagonal, integration
> is done for each triangle and the results are added up.   So, depending
> where your "1" falls on a diagonal vertex, you will get different results.
>
>  Leo
>
>
> On Sat, Jun 9, 2012 at 8:57 AM, Magician <f_magician at mac.com> wrote:
>
>> Hi all,
>>
>>
>> Now I found a bug of the filter.
>>
>> My ParaView's version is 3.14.1.
>> I define node names as below:
>> > c--d
>> > |  |
>> > a--b
>>
>> Case 1: a=1.0, b=0.0, c=0.0, d=0.0
>> Integration Value = 0.33333
>>
>> Case 2: a=0.0, b=1.0, c=0.0, d=0.0
>> Integration Value = 0.16666
>>
>> Case 3: a=0.0, b=0.0, c=1.0, d=0.0
>> Integration Value = 0.16666
>>
>> Case 4: a=0.0, b=0.0, c=0.0, d=1.0
>> Integration Value = 0.33333
>>
>> So Integration Values are calculated as (2*a+b+c+2*d)/6.
>> I think it's not a good result.
>>
>>
>> Magician
>>
>>
>> On 2012/06/08, at 12:54, Magician wrote:
>>
>> > Hi all,
>> >
>> >
>> > I'm now comparing integration results of each postprocessors.
>> >> # vtk DataFile Version 2.0
>> >
>> >> ASCII
>> >> DATASET UNSTRUCTURED_GRID
>> >> POINTS 4 FLOAT
>> >> 0 0 0
>> >> 1 0 0
>> >> 0 1 0
>> >> 1 1 0
>> >> CELLS 1 5
>> >> 4 0 1 3 2
>> >> CELL_TYPES 1
>> >> 9
>> >> POINT_DATA 4
>> >> SCALARS scalar FLOAT 1
>> >> LOOKUP_TABLE DEFAULT
>> >> 0.0
>> >> 1.0
>> >> 2.0
>> >> 4.0
>> >
>> > When I apply Point Data to Cell Data filter,
>> > scalar values are interpolated as 1.75.
>> > It may be calculated as (0.0+1.0+2.0+4.0)/4.0.
>> >
>> > But when I apply Integrate Variables filter,
>> > scalar value is integrated as 1.833....
>> > The area value of quadratic cell is 1.0, so I thought
>> > integrated values should be equal to cell data.
>> >
>> > How the integrated value is calculated?
>> >
>> >
>> > Magician
>>
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>>
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>
>
>
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>
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>
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>