[vtkusers] GenerateValues numerical error bug

[Francois Bertel]

Make sense. Thanks for the report.

On Wed, Oct 29, 2008 at 4:45 PM, Serge Lalonde <serge at infolytica.com> wrote:
> Hello VTK users,
>
> I thought that I'd post this little fix in case others might find it useful.
> The class vtkContourValues (in the Common library) is used to generate a set
> of N linearly spaced values between an upper and lower bound. I discovered
> that its implementation (in 5.2.0 and still in 5.3.0) caused a numerical
> error to be introduced in all but the lower bound value. The effect being
> that values that should be exact would have a very small error introduced.
> For example, instead of 0, 0.1, 0.2, 0.3, ..., 0.8, 0.9, 1 you would get 0,
> 0.1, 0.2, 0.3000000000013, 0.40000000000026, ..., 0.8000000000045,
> 0.99999999999993 (or something very similar).
>
> The problem is that the loop to calculate those values was pre-calculating
> the delta and then incrementing the value before each call to SetValue().
> The more accurate method is to calculate the value from scratch each time so
> that the FPU can properly manage and round-off the errors in the calculation
> caused by the (finite) double-precision arithmetic. With this fix, the
> values are exact.
>
> Here is the corrected version of GenerateValues() in vtkContourValues.cxx.
>
> // Generate numContours equally spaced contour values between specified
> // range. Contour values will include min/max range values.
> // The value is calculated using the lower range values and the loop
> variable
> // at each iteration to avoid accumulating the floating point error that
> // happens when using using an intermediate calculation and/or when
> incrementing.
> void vtkContourValues::GenerateValues(int numContours, double range[2])
> {
>  int i;
>
>  this->SetNumberOfContours(numContours);
>  if (numContours == 1)
>   {
>   this->SetValue(0, range[0]);
>   }
>  else
>   {
>   for (i= 0; i < numContours; ++i)
>     {
>     this->SetValue(i, range[0] + i*(range[1] - range[0])/(numContours - 1));
>     }
>   }
> }
>
> I will submit this change to the bug tracker as well so that it can
> (hopefully) be merged into the development branch.
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-- 
François Bertel, PhD  | Kitware Inc. Suite 204
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