//****************************************************************************80
private static void triangle01_monomial_integral_test()
//****************************************************************************80
//
// Purpose:
//
// TRIANGLE01_MONOMIAL_INTEGRAL_TEST estimates integrals over the unit triangle.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 21 April 2015
//
// Author:
//
// John Burkardt
//
{
int d;
Console.WriteLine("");
Console.WriteLine("TRIANGLE01_MONOMIAL_INTEGRAL_TEST");
Console.WriteLine(" TRIANGLE01_MONOMIAL_INTEGRAL returns the integral Q of");
Console.WriteLine(" a monomial X^I Y^J over the interior of the unit triangle.");
Console.WriteLine("");
Console.WriteLine(" I J Q(I,J)");
for (d = 0; d <= 5; d++)
{
Console.WriteLine("");
int i;
for (i = 0; i <= d; i++)
{
int j = d - i;
double q = Integrals.triangle01_monomial_integral(i, j);
Console.WriteLine(" " + i.ToString(InvariantCulture).PadLeft(2)
+ " " + j.ToString(InvariantCulture).PadLeft(2)
+ " " + q + "");
}
}
}
private static void triangle_poly_integral_test()
//****************************************************************************80
//
// Purpose:
//
// TRIANGLE_POLY_INTEGRAL_TEST estimates integrals over a triangle.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 21 April 2015
//
// Author:
//
// John Burkardt
//
{
int d1 = 1;
int d2 = 2;
int d3 = 2;
int d4 = 2;
double[] p1 =
{
0.0, 1.0, 0.0
}
;
double[] p2 =
{
0.0, 0.0, 0.0, 0.0, 1.0, 0.0
}
;
double[] p3 =
{
2.0, -3.0, 0.0, 0.0, 1.0, 0.0
}
;
double[] p4 =
{
0.0, 0.0, -40.0, 6.0, 0.0, 0.0
}
;
double[] t1 =
{
0.0, 0.0,
1.0, 0.0,
0.0, 1.0
}
;
double[] t2 =
{
0.0, 0.0,
1.0, 0.0,
1.0, 2.0
}
;
double[] t3 =
{
0.0, 0.0,
1.0, 0.0,
1.0, 3.0
}
;
double[] t4 =
{
0.0, 3.0,
1.0, 1.0,
5.0, 3.0
}
;
Console.WriteLine("");
Console.WriteLine("TRIANGLE_POLY_INTEGRAL_TEST");
Console.WriteLine(" TRIANGLE_POLY_INTEGRAL returns the integral Q of");
Console.WriteLine(" a polynomial over the interior of a triangle.");
//
// Test 1:
// Integrate x over reference triangle.
//
Console.WriteLine("");
Console.WriteLine(" Triangle vertices:");
Console.WriteLine(" (" + t1[0 + 0 * 2] + "," + t1[1 + 0 * 2] + ")");
Console.WriteLine(" (" + t1[0 + 1 * 2] + "," + t1[1 + 1 * 2] + ")");
Console.WriteLine(" (" + t1[0 + 2 * 2] + "," + t1[1 + 2 * 2] + ")");
typeMethods.poly_print(d1, ref p1, " Integrand p1(x,y)");
double q = Integrals.triangle_poly_integral(d1, p1, t1);
double q2 = 1.0 / 6.0;
Console.WriteLine(" Computed Q = " + q + "");
Console.WriteLine(" Exact Q = " + q2 + "");
//
// Test 2:
// Integrate xy over a general triangle.
//
Console.WriteLine("");
Console.WriteLine(" Triangle vertices:");
Console.WriteLine(" (" + t2[0 + 0 * 2] + "," + t2[1 + 0 * 2] + ")");
Console.WriteLine(" (" + t2[0 + 1 * 2] + "," + t2[1 + 1 * 2] + ")");
Console.WriteLine(" (" + t2[0 + 2 * 2] + "," + t2[1 + 2 * 2] + ")");
typeMethods.poly_print(d2, ref p2, " Integrand p2(x,y)");
q = Integrals.triangle_poly_integral(d2, p2, t2);
q2 = 0.5;
Console.WriteLine(" Computed Q = " + q + "");
Console.WriteLine(" Exact Q = " + q2 + "");
//
// Test 3:
// Integrate 2-3x+xy over a general triangle.
//
Console.WriteLine("");
Console.WriteLine(" Triangle vertices:");
Console.WriteLine(" (" + t3[0 + 0 * 2] + "," + t3[1 + 0 * 2] + ")");
Console.WriteLine(" (" + t3[0 + 1 * 2] + "," + t3[1 + 1 * 2] + ")");
Console.WriteLine(" (" + t3[0 + 2 * 2] + "," + t3[1 + 2 * 2] + ")");
typeMethods.poly_print(d3, ref p3, " Integrand p3(x,y)");
q = Integrals.triangle_poly_integral(d3, p3, t3);
q2 = 9.0 / 8.0;
Console.WriteLine(" Computed Q = " + q + "");
Console.WriteLine(" Exact Q = " + q2 + "");
//
// Test 4:
// Integrate -40y + 6x^2 over a general triangle.
//
Console.WriteLine("");
Console.WriteLine(" Triangle vertices:");
Console.WriteLine(" (" + t4[0 + 0 * 2] + "," + t4[1 + 0 * 2] + ")");
Console.WriteLine(" (" + t4[0 + 1 * 2] + "," + t4[1 + 1 * 2] + ")");
Console.WriteLine(" (" + t4[0 + 2 * 2] + "," + t4[1 + 2 * 2] + ")");
typeMethods.poly_print(d4, ref p4, " Integrand p4(x,y)");
q = Integrals.triangle_poly_integral(d4, p4, t4);
q2 = -935.0 / 3.0;
Console.WriteLine(" Computed Q = " + q + "");
Console.WriteLine(" Exact Q = " + q2 + "");
}
private static void triangle_monomial_integral_test()
//****************************************************************************80
//
// Purpose:
//
// TRIANGLE_MONOMIAL_INTEGRAL_TEST estimates integrals over a triangle.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 21 April 2015
//
// Author:
//
// John Burkardt
//
{
double[] t1 =
{
0.0, 0.0,
1.0, 0.0,
0.0, 1.0
}
;
double[] t2 =
{
0.0, 0.0,
1.0, 0.0,
1.0, 2.0
}
;
double[] t3 =
{
-3.0, 0.0,
6.0, 0.0,
0.0, 3.0
}
;
double[] t4 =
{
0.0, 0.0,
4.0, 0.0,
0.0, 1.0
}
;
Console.WriteLine("");
Console.WriteLine("TRIANGLE_MONOMIAL_INTEGRAL_TEST");
Console.WriteLine(" TRIANGLE_MONOMIAL_INTEGRAL returns the integral Q of");
Console.WriteLine(" a monomial X^I Y^J over the interior of a triangle.");
//
// Test 1:
//
int i = 1;
int j = 0;
Console.WriteLine("");
Console.WriteLine(" Triangle vertices:");
Console.WriteLine(" (" + t1[0 + 0 * 2] + "," + t1[1 + 0 * 2] + ")");
Console.WriteLine(" (" + t1[0 + 1 * 2] + "," + t1[1 + 1 * 2] + ")");
Console.WriteLine(" (" + t1[0 + 2 * 2] + "," + t1[1 + 2 * 2] + ")");
Console.WriteLine(" Integrand = x^" + i + " * y^" + j + "");
double q = Integrals.triangle_monomial_integral(i, j, t1);
double q2 = 1.0 / 6.0;
Console.WriteLine(" Computed Q = " + q + "");
Console.WriteLine(" Exact Q = " + q2 + "");
//
// Test 2:
//
i = 1;
j = 1;
Console.WriteLine("");
Console.WriteLine(" Triangle vertices:");
Console.WriteLine(" (" + t2[0 + 0 * 2] + "," + t2[1 + 0 * 2] + ")");
Console.WriteLine(" (" + t2[0 + 1 * 2] + "," + t2[1 + 1 * 2] + ")");
Console.WriteLine(" (" + t2[0 + 2 * 2] + "," + t2[1 + 2 * 2] + ")");
Console.WriteLine(" Integrand = x^" + i + " * y^" + j + "");
q = Integrals.triangle_monomial_integral(i, j, t2);
q2 = 0.5;
Console.WriteLine(" Computed Q = " + q + "");
Console.WriteLine(" Exact Q = " + q2 + "");
//
// Test 3:
//
i = 1;
j = 0;
Console.WriteLine("");
Console.WriteLine(" Triangle vertices:");
Console.WriteLine(" (" + t3[0 + 0 * 2] + "," + t3[1 + 0 * 2] + ")");
Console.WriteLine(" (" + t3[0 + 1 * 2] + "," + t3[1 + 1 * 2] + ")");
Console.WriteLine(" (" + t3[0 + 2 * 2] + "," + t3[1 + 2 * 2] + ")");
Console.WriteLine(" Integrand = x^" + i + " * y^" + j + "");
q = Integrals.triangle_monomial_integral(i, j, t3);
q2 = 13.5;
Console.WriteLine(" Computed Q = " + q + "");
Console.WriteLine(" Exact Q = " + q2 + "");
//
// Test 4:
//
i = 1;
j = 1;
Console.WriteLine("");
Console.WriteLine(" Triangle vertices:");
Console.WriteLine(" (" + t4[0 + 0 * 2] + "," + t4[1 + 0 * 2] + ")");
Console.WriteLine(" (" + t4[0 + 1 * 2] + "," + t4[1 + 1 * 2] + ")");
Console.WriteLine(" (" + t4[0 + 2 * 2] + "," + t4[1 + 2 * 2] + ")");
Console.WriteLine(" Integrand = x^" + i + " * y^" + j + "");
q = Integrals.triangle_monomial_integral(i, j, t4);
q2 = 2.0 / 3.0;
Console.WriteLine(" Computed Q = " + q + "");
Console.WriteLine(" Exact Q = " + q2 + "");
}
private static void triangle_area_test()
//****************************************************************************80
//
// Purpose:
//
// TRIANGLE_AREA_TEST tests TRIANGLE_AREA_MAP.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 21 April 2015
//
// Author:
//
// John Burkardt
//
{
int i;
const double r8_pi = 3.141592653589793;
double[] t =
{
0.0, 0.0,
2.0, 0.0,
0.0, 1.0
}
;
Console.WriteLine("");
Console.WriteLine("TRIANGLE_AREA_TEST:");
Console.WriteLine(" TRIANGLE_AREA determines the (signed) area of a triangle.");
Console.WriteLine("");
Console.WriteLine(" Triangle vertices are:");
Console.WriteLine(" (X1,Y1) = (0,0)");
Console.WriteLine(" (X2,Y2) = 2*(cos(angle),sin(angle))");
Console.WriteLine(" (X3,Y3) = (0,1)");
Console.WriteLine(" where angle will sweep from 0 to 360 degrees.");
double r = 2.0;
Console.WriteLine("");
Console.WriteLine(" I Angle X2 Y2 Area");
Console.WriteLine(" (degrees)");
Console.WriteLine("");
for (i = 0; i <= 24; i++)
{
double angled = i * 180.0 / 12.0;
double angler = i * r8_pi / 12.0;
t[0 + 1 * 2] = r * Math.Cos(angler);
t[1 + 1 * 2] = r * Math.Sin(angler);
double area = Integrals.triangle_area(t);
Console.WriteLine(" " + i.ToString(InvariantCulture).PadLeft(2)
+ " " + angled.ToString(InvariantCulture).PadLeft(10)
+ " " + t[0 + 1 * 2].ToString(InvariantCulture).PadLeft(10)
+ " " + t[1 + 1 * 2].ToString(InvariantCulture).PadLeft(10)
+ " " + area.ToString(InvariantCulture).PadLeft(10) + "");
}
}
private static void triangle_xy_integral_test()
//****************************************************************************80
//
// Purpose:
//
// TRIANGLE_XY_INTEGRAL_TEST tests TRIANGLE_XY_INTEGRAL.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 21 April 2015
//
// Author:
//
// John Burkardt
//
{
Console.WriteLine("");
Console.WriteLine("TRIANGLE_XY_INTEGRAL_TEST");
Console.WriteLine(" TRIANGLE_XY_INTEGRAL determines Q, the integral of the");
Console.WriteLine(" monomial X*Y over a triangle (X1,Y1), (X2,Y2), (X3,Y3).");
double x1 = 0.0;
double y1 = 0.0;
double x2 = 1.0;
double y2 = 0.0;
double x3 = 1.0;
double y3 = 2.0;
double q = Integrals.triangle_xy_integral(x1, y1, x2, y2, x3, y3);
Console.WriteLine("");
Console.WriteLine(" (X1,Y1) = (" + x1 + "," + y1 + ")");
Console.WriteLine(" (X2,Y2) = (" + x2 + "," + y2 + ")");
Console.WriteLine(" (X3,Y3) = (" + x3 + "," + y3 + ")");
Console.WriteLine(" Q = " + q + "");
Console.WriteLine(" (Expecting answer 1/2.");
x1 = 0.0;
y1 = 0.0;
x2 = 4.0;
y2 = 0.0;
x3 = 0.0;
y3 = 1.0;
q = Integrals.triangle_xy_integral(x1, y1, x2, y2, x3, y3);
Console.WriteLine("");
Console.WriteLine(" (X1,Y1) = (" + x1 + "," + y1 + ")");
Console.WriteLine(" (X2,Y2) = (" + x2 + "," + y2 + ")");
Console.WriteLine(" (X3,Y3) = (" + x3 + "," + y3 + ")");
Console.WriteLine(" Q = " + q + "");
Console.WriteLine(" (Expecting answer 2/3.");
}
private static void triangle01_poly_integral_test()
//****************************************************************************80
//
// Purpose:
//
// TRIANGLE01_POLY_INTEGRAL_TEST: polynomial integrals over the unit triangle.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 21 April 2015
//
// Author:
//
// John Burkardt
//
{
int d_max = 6;
int d1 = 1;
int d2 = 2;
int d3 = 2;
int i = 0;
int j = 0;
int k;
int m_max = (d_max + 1) * (d_max + 2) / 2;
int m1 = (d1 + 1) * (d1 + 2) / 2;
int m2 = (d2 + 1) * (d2 + 2) / 2;
int m3 = (d3 + 1) * (d3 + 2) / 2;
double[] p1 =
{
1.0, 2.0, 3.0
}
;
double[] p2 =
{
0.0, 0.0, 0.0, 0.0, 1.0, 0.0
}
;
double[] p3 =
{
1.0, -2.0, 3.0, -4.0, 5.0, -6.0
}
;
double[] qm = new double[28];
for (k = 1; k <= m_max; k++)
{
typeMethods.i4_to_pascal(k, ref i, ref j);
int km1 = k - 1;
qm[km1] = Integrals.triangle01_monomial_integral(i, j);
}
Console.WriteLine("");
Console.WriteLine("TRIANGLE01_POLY_INTEGRAL_TEST");
Console.WriteLine(" TRIANGLE01_POLY_INTEGRAL returns the integral Q of");
Console.WriteLine(" a polynomial P(X,Y) over the interior of the unit triangle.");
Console.WriteLine("");
typeMethods.poly_print(d1, ref p1, " p(x,y)");
double q = Integrals.triangle01_poly_integral(d1, p1);
Console.WriteLine("");
Console.WriteLine(" Q = " + q + "");
double q2 = typeMethods.r8vec_dot_product(m1, p1, qm);
Console.WriteLine(" Q (exact) = " + q2 + "");
Console.WriteLine("");
typeMethods.poly_print(d2, ref p2, " p(x,y)");
q = Integrals.triangle01_poly_integral(d2, p2);
Console.WriteLine("");
Console.WriteLine(" Q = " + q + "");
q2 = typeMethods.r8vec_dot_product(m2, p2, qm);
Console.WriteLine(" Q (exact) = " + q2 + "");
Console.WriteLine("");
typeMethods.poly_print(d3, ref p3, " p(x,y)");
q = Integrals.triangle01_poly_integral(d3, p3);
Console.WriteLine("");
Console.WriteLine(" Q = " + q + "");
q2 = typeMethods.r8vec_dot_product(m3, p3, qm);
Console.WriteLine(" Q (exact) = " + q2 + "");
}
