[vtkusers] TriangleArea() return the not correct value.
Masato Asou
asou at soum.co.jp
Wed Sep 3 01:58:44 EDT 2014
Hi,
Thanks for link, John.
By the way, why vtkTriangle::TriangleArea() doesn't use cross product?
Also cross product requires applying sqrt() only once.
Error of up to 0.0000000000000001 is acceptable in my program. However,
vtkTraiangle::TriangleArea() causes an error of 0.000000001.
--
ASOU Masato
From: "John Platt" <jcplatt at dsl.pipex.com>
Date: Mon, 1 Sep 2014 09:53:16 +0100
> Hi,
>
> It could be worth looking at "Miscalculating Area and Angles of a
> Needle-like Triangle" W. Kahan (24 March 2000)
> http://www.cs.berkeley.edu/~wkahan/Triangle.pdf for implementation of
> Heron's formula.
>
> HTH
>
> John.
>
>
> ----- Original Message -----
> From: "Masato Asou" <asou at soum.co.jp>
> To: <david.gobbi at gmail.com>
> Cc: <vtkusers at vtk.org>
> Sent: Friday, August 29, 2014 7:18 AM
> Subject: Re: [vtkusers] TriangleArea() return the not correct value.
>
>
>>I didn't aware about efficiency.
>>
>> I hope that I can choose whichever efficiency or quality.
>> Thanks.
>> --
>> ASOU Masato
>>
>>> Note that there is a difference in efficiency, because Heron's formula
>>> requires applying sqrt() four times, while VTK's formula requires
>>> applying
>>> sqrt() only once.
>>
>>> It might be worthwhile to use both Heron's formula and the current VTK
>>> formula, with a discriminator to choose which based on the quality of
>>> the
>>> triangle.
>>> - David
>>>
>>>
>>> On Thu, Aug 28, 2014 at 9:10 PM, Cory Quammen
>>> <cory.quammen at kitware.com> wrote:
>>>> Masato,
>>>>
>>>> It looks like you are running into numerical precision problems
>>>> because two of your points are extremely close, almost close enough to
>>>> be indistinguishable by double precision.
>>>>
>>>> The inconsistencies that depend on the order the points are given are
>>>> caused by which sides are considered in the cross product and area
>>>> calculation. Heron's formula, which I wasn't aware of, seems to
>>>> eliminate this inconsistency. We should consider using this in VTK, in
>>>> particular the numerically more stable implementation:
>>>> http://en.wikipedia.org/wiki/Heron's_formula#Numerical_stability
>>>>
>>>> I don't know if my answer helps, but thank you for pointing out
>>>> Heron's formula.
>>>>
>>>> Thanks,
>>>> Cory
>>>>
>>>> On Thu, Aug 28, 2014 at 10:41 PM, Masato Asou <asou at soum.co.jp> wrote:
>>>>> Hi,
>>>>>
>>>>> I have a probrem about vtkTriangle::TriangleArea(). I use VTK-5.10.1.
>>>>>
>>>>> The triangle to be calculated is what one side is very short.
>>>>>
>>>>> I calculate the area of the triangle in vtkTriangle::TriangleArea(),
>>>>> the result are different to that using the Heron's formula and cross
>>>>> products. I also calculate tha area is regarded as a rectanglar
>>>>> triangle,
>>>>> this value is also different vtkTriangle::TriangleArea()
>>>>>
>>>>> In addition, vtkTriangle::TriangleArea() return a different value when
>>>>> change the order of the vertices.
>>>>>
>>>>> This problem be resolved?
>>>>>
>>>>> My system as:
>>>>>
>>>>> $ cat /etc/redhat-release
>>>>> CentOS release 5.6 (Final)
>>>>> $ uname -m -r -s -v
>>>>> Linux 2.6.18-238.19.1.el5 #1 SMP Fri Jul 15 07:31:24 EDT 2011 x86_64
>>>>>
>>>>> My program as below:
>>>>>
>>>>> $ cat triangle.cpp
>>>>> #include <math.h>
>>>>> #include <ostream>
>>>>> using namespace std;
>>>>> #include <vtkTriangle.h>
>>>>>
>>>>> double
>>>>> lineLength(const double p0[3], const double p1[3])
>>>>> {
>>>>> double len2 = 0.0;
>>>>>
>>>>> for(int i = 0; i < 3; i++) {
>>>>> len2 += (p0[i] - p1[i]) * (p0[i] - p1[i]);
>>>>> }
>>>>> return sqrt(len2);
>>>>> }
>>>>>
>>>>> double
>>>>> CrossProduct(double p1[3], double p2[3], double p3[3])
>>>>> {
>>>>> double a[3], b[3], o[3], v[3];
>>>>>
>>>>> // Create the vector a and b.
>>>>> a[0] = p2[0] - p1[0];
>>>>> a[1] = p2[1] - p1[1];
>>>>> a[2] = p2[2] - p1[2];
>>>>> b[0] = p3[0] - p1[0];
>>>>> b[1] = p3[1] - p1[1];
>>>>> b[2] = p3[2] - p1[2];
>>>>>
>>>>> // Calculate the cross product of vector a and b.
>>>>> o[0] = 0.0;
>>>>> o[1] = 0.0;
>>>>> o[2] = 0.0;
>>>>> v[0] = (a[1] * b[2]) - (a[2] * b[1]);
>>>>> v[1] = (a[2] * b[0]) - (a[0] * b[2]);
>>>>> v[2] = (a[0] * b[1]) - (a[1] * b[0]);
>>>>> return fabs(lineLength(o, v)) / 2;
>>>>> }
>>>>>
>>>>> double
>>>>> HeronsFormula(double p1[3], double p2[3], double p3[3])
>>>>> {
>>>>> double a = lineLength(p1, p2);
>>>>> double b = lineLength(p2, p3);
>>>>> double c = lineLength(p3, p1);
>>>>>
>>>>> return sqrt((a+b+c) * (-a+b+c) * (a-b+c) * (a+b-c)) * 0.25;
>>>>> }
>>>>>
>>>>> int
>>>>> main(void)
>>>>> {
>>>>> double A[3] = {-3.58117425311239667707, -3.58117425311239667707,
>>>>> 1.0};
>>>>> double B[3] = {-3.04058712655619833853, -3.04058712655619833853,
>>>>> 0.95};
>>>>> double C[3] = {-3.04058712655619833853, -3.04058712655619789444,
>>>>> 0.95};
>>>>> double a = lineLength(A, B);
>>>>> double b = lineLength(B, C);
>>>>> double c = lineLength(C, A);
>>>>>
>>>>> cout << fixed << setprecision(20);
>>>>> cout << "TriangleArea(A, B, C): " << vtkTriangle::TriangleArea(A, B,
>>>>> C) << endl;
>>>>> cout << "TriangleArea(B, C, A): " << vtkTriangle::TriangleArea(B, C,
>>>>> A) << endl;
>>>>> cout << "CrossProduct(A, B, C): " << CrossProduct(A, B, C) << endl;
>>>>> cout << "CrossProduct(B, C, A): " << CrossProduct(B, C, A) << endl;
>>>>> cout << "HeronsFormula(A, B, C): " << HeronsFormula(A, B, C) << endl;
>>>>> cout << "HeronsFormula(B, C, A): " << HeronsFormula(B, C, A) << endl;
>>>>> cout << "RectangularTriangle: " << (a * b / 2) << endl;
>>>>> cout << "line length: a: " << a << ", b: " << b << ", c: " << c <<
>>>>> endl;
>>>>>
>>>>> return 0;
>>>>> }
>>>>> $ g++ -g -I../../src -I/home/asou/freesw/vtk-5.10.1/include/vtk-5.10
>>>>> triangle.cpp -Xlinker -rpath -Xlinker ../../src
>>>>> -L/home/asou/freesw/vtk-5.10.1/lib/vtk-5.10 -lvtkCommon -lvtkWidgets
>>>>> -Xlinker -rpath -Xlinker /home/asou/freesw/vtk-5.10.1/lib/vtk-5.10
>>>>> In file included from
>>>>> /usr/lib/gcc/x86_64-redhat-linux/4.1.2/../../../../include/c++/4.1.2/backward/strstream:51,
>>>>> from
>>>>> /home/asou/freesw/vtk-5.10.1/include/vtk-5.10/vtkIOStream.h:108,
>>>>> from
>>>>> /home/asou/freesw/vtk-5.10.1/include/vtk-5.10/vtkSystemIncludes.h:40,
>>>>> from
>>>>> /home/asou/freesw/vtk-5.10.1/include/vtk-5.10/vtkIndent.h:24,
>>>>> from
>>>>> /home/asou/freesw/vtk-5.10.1/include/vtk-5.10/vtkObjectBase.h:43,
>>>>> from
>>>>> /home/asou/freesw/vtk-5.10.1/include/vtk-5.10/vtkObject.h:41,
>>>>> from
>>>>> /home/asou/freesw/vtk-5.10.1/include/vtk-5.10/vtkCell.h:40,
>>>>> from
>>>>> /home/asou/freesw/vtk-5.10.1/include/vtk-5.10/vtkTriangle.h:23,
>>>>> from triangle.cpp:4:
>>>>> /usr/lib/gcc/x86_64-redhat-linux/4.1.2/../../../../include/c++/4.1.2/backward/backward_warning.h:32:2:
>>>>> warning: #warning This file includes at least one deprecated or
>>>>> antiquated header. Please consider using one of the 32 headers found
>>>>> in section 17.4.1.2 of the C++ standard. Examples include substituting
>>>>> the <X> header for the <X.h> header for C++ includes, or <iostream>
>>>>> instead of the deprecated header <iostream.h>. To disable this warning
>>>>> use -Wno-deprecated.
>>>>> $ ./a.out
>>>>> TriangleArea(A, B, C): 0.00000000526835606386
>>>>> TriangleArea(B, C, A): 0.00000000000000009839
>>>>> CrossProduct(A, B, C): 0.00000000000000011168
>>>>> CrossProduct(B, C, A): 0.00000000000000012055
>>>>> HeronsFormula(A, B, C): 0.00000000000000011252
>>>>> HeronsFormula(B, C, A): 0.00000000000000011252
>>>>> RectangularTriangle: 0.00000000000000017012
>>>>> line length: a: 0.76613894483740641039, b: 0.00000000000000044409, c:
>>>>> 0.76613894483740674346
>>>>> $
>>>>>
>>>>> Thanks in advance any help or suggestions.
>>>>> --
>>>>> ASOU Masato
>>>>> _______________________________________________
>>>>> Powered by www.kitware.com
>>>>>
>>>>> Visit other Kitware open-source projects at
>>>>> http://www.kitware.com/opensource/opensource.html
>>>>>
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