[vtkusers] TriangleArea() return the not correct value.

[Masato Asou]

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