private static void test06()
//****************************************************************************80
//
// Purpose:
//
// TEST06 tests SPHERE01_TRIANGLE_QUAD_ICOS2V.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 29 September 2010
//
// Author:
//
// John Burkardt
//
{
int[] e = new int[3];
int i;
int node_num = 0;
int seed = 123456789;
Console.WriteLine("");
Console.WriteLine("TEST06");
Console.WriteLine(" Approximate the integral of a function on a random spherical triangle.");
Console.WriteLine("");
Console.WriteLine(" SPHERE01_TRIANGLE_QUAD_ICOS2V approximates the");
Console.WriteLine(" integral of a function over a spherical triangle on");
Console.WriteLine(" the surface of the unit sphere using a vertex rule.");
Console.WriteLine("");
Console.WriteLine(" We do not have an exact result, so we compare each");
Console.WriteLine(" estimate to the final one.");
//
// Choose three points at random to define a spherical triangle.
//
double[] v1 = MonteCarlo.sphere01_sample(1, ref seed);
double[] v2 = MonteCarlo.sphere01_sample(1, ref seed);
double[] v3 = MonteCarlo.sphere01_sample(1, ref seed);
Console.WriteLine("");
Console.WriteLine(" Vertices of random spherical triangle:");
Console.WriteLine("");
typeMethods.r8vec_transpose_print(3, v1, " V1:");
typeMethods.r8vec_transpose_print(3, v2, " V2:");
typeMethods.r8vec_transpose_print(3, v3, " V3:");
Console.WriteLine("");
Console.WriteLine("FACTOR N RESULT");
for (i = 1; i <= 17; i++)
{
switch (i)
{
case 1:
e[0] = 0;
e[1] = 0;
e[2] = 0;
break;
case 2:
e[0] = 1;
e[1] = 0;
e[2] = 0;
break;
case 3:
e[0] = 0;
e[1] = 1;
e[2] = 0;
break;
case 4:
e[0] = 0;
e[1] = 0;
e[2] = 1;
break;
case 5:
e[0] = 2;
e[1] = 0;
e[2] = 0;
break;
case 6:
e[0] = 0;
e[1] = 2;
e[2] = 2;
break;
case 7:
e[0] = 2;
e[1] = 2;
e[2] = 2;
break;
case 8:
e[0] = 0;
e[1] = 2;
e[2] = 4;
break;
case 9:
e[0] = 0;
e[1] = 0;
e[2] = 6;
break;
case 10:
e[0] = 1;
e[1] = 2;
e[2] = 4;
break;
case 11:
e[0] = 2;
e[1] = 4;
e[2] = 2;
break;
case 12:
e[0] = 6;
e[1] = 2;
e[2] = 0;
break;
case 13:
e[0] = 0;
e[1] = 0;
e[2] = 8;
break;
case 14:
e[0] = 6;
e[1] = 0;
e[2] = 4;
break;
case 15:
e[0] = 4;
e[1] = 6;
e[2] = 2;
break;
case 16:
e[0] = 2;
e[1] = 4;
e[2] = 8;
break;
case 17:
e[0] = 16;
e[1] = 0;
e[2] = 0;
break;
}
polyterm_exponent("SET", e);
polyterm_exponent("PRINT", e);
int factor = (int)Math.Pow(2, 9);
double best = TriangleQuad.sphere01_triangle_quad_icos2v(v1, v2, v3, factor,
polyterm_value_3d, ref node_num);
factor = 1;
int factor_log;
for (factor_log = 0; factor_log <= 9; factor_log++)
{
double result = TriangleQuad.sphere01_triangle_quad_icos2v(v1, v2, v3, factor,
polyterm_value_3d, ref node_num);
double error = Math.Abs(result - best);
Console.WriteLine(" " + factor.ToString().PadLeft(4)
+ " " + node_num.ToString().PadLeft(8)
+ " " + result.ToString(CultureInfo.InvariantCulture).PadLeft(16)
+ " " + error.ToString(CultureInfo.InvariantCulture).PadLeft(10) + "");
factor *= 2;
}
}
}
private static void test01()
//****************************************************************************80
//
// Purpose:
//
// TEST01 tests SPHERE01_TRIANGLE_QUAD_01, 02, 03.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 28 September 2010
//
// Author:
//
// John Burkardt
//
{
int[] e = new int[3];
int i;
int seed = 123456789;
Console.WriteLine("");
Console.WriteLine("TEST01");
Console.WriteLine(" Approximate the integral of a function on a random spherical triangle.");
Console.WriteLine("");
Console.WriteLine(" QUAD_01 uses centroids of spherical triangles.");
Console.WriteLine(" QUAD_02 uses vertices of spherical triangles.");
Console.WriteLine(" QUAD_03 uses midsides of spherical triangles.");
//
// Choose three points at random to define a spherical triangle.
//
double[] v1 = MonteCarlo.sphere01_sample(1, ref seed);
double[] v2 = MonteCarlo.sphere01_sample(1, ref seed);
double[] v3 = MonteCarlo.sphere01_sample(1, ref seed);
Console.WriteLine("");
Console.WriteLine(" Vertices of random spherical triangle:");
Console.WriteLine("");
typeMethods.r8vec_transpose_print(3, v1, " V1:");
typeMethods.r8vec_transpose_print(3, v2, " V2:");
typeMethods.r8vec_transpose_print(3, v3, " V3:");
Console.WriteLine("");
Console.WriteLine("QUAD_01 QUAD_02 QUAD_03");
for (i = 1; i <= 17; i++)
{
switch (i)
{
case 1:
e[0] = 0;
e[1] = 0;
e[2] = 0;
break;
case 2:
e[0] = 1;
e[1] = 0;
e[2] = 0;
break;
case 3:
e[0] = 0;
e[1] = 1;
e[2] = 0;
break;
case 4:
e[0] = 0;
e[1] = 0;
e[2] = 1;
break;
case 5:
e[0] = 2;
e[1] = 0;
e[2] = 0;
break;
case 6:
e[0] = 0;
e[1] = 2;
e[2] = 2;
break;
case 7:
e[0] = 2;
e[1] = 2;
e[2] = 2;
break;
case 8:
e[0] = 0;
e[1] = 2;
e[2] = 4;
break;
case 9:
e[0] = 0;
e[1] = 0;
e[2] = 6;
break;
case 10:
e[0] = 1;
e[1] = 2;
e[2] = 4;
break;
case 11:
e[0] = 2;
e[1] = 4;
e[2] = 2;
break;
case 12:
e[0] = 6;
e[1] = 2;
e[2] = 0;
break;
case 13:
e[0] = 0;
e[1] = 0;
e[2] = 8;
break;
case 14:
e[0] = 6;
e[1] = 0;
e[2] = 4;
break;
case 15:
e[0] = 4;
e[1] = 6;
e[2] = 2;
break;
case 16:
e[0] = 2;
e[1] = 4;
e[2] = 8;
break;
case 17:
e[0] = 16;
e[1] = 0;
e[2] = 0;
break;
}
polyterm_exponent("SET", e);
polyterm_exponent("PRINT", e);
double result_01 = TriangleQuad.sphere01_triangle_quad_01(v1, v2, v3, polyterm_value_3d);
double result_02 = TriangleQuad.sphere01_triangle_quad_02(v1, v2, v3, polyterm_value_3d);
double result_03 = TriangleQuad.sphere01_triangle_quad_03(v1, v2, v3, polyterm_value_3d);
Console.WriteLine(" " + result_01.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + result_02.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + result_03.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
}
