private static void test03()
//****************************************************************************80
//
// Purpose:
//
// TEST03 checks that the two functions are inverses.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 11 November 2010
//
// Author:
//
// John Burkardt
//
{
int i;
int j;
typeMethods.r8vecNormalData data = new();
Console.WriteLine("");
Console.WriteLine("TEST03");
Console.WriteLine(" SPHERE_STEREOGRAPH2 maps from sphere to plane.");
Console.WriteLine(" SPHERE_STEREOGRAPH2_INVERSE is the inverse map.");
Console.WriteLine(" Check that these two functions are inverses.");
const int m = 3;
const int n = 100;
int seed = 123456789;
double[] focus = UniformRNG.r8vec_uniform_01_new(m, ref seed);
double[] center = UniformRNG.r8vec_uniform_01_new(m, ref seed);
double r = typeMethods.r8vec_norm_affine(m, focus, center);
Console.WriteLine("");
Console.WriteLine(" Using radius = " + r + "");
typeMethods.r8vec_transpose_print(m, center, " Center:");
typeMethods.r8vec_transpose_print(m, focus, " Focus:");
//
// Check #1.
//
double[] p1 = Burkardt.Uniform.Sphere.uniform_on_sphere01_map(m, n, ref data, ref seed);
for (j = 0; j < n; j++)
{
for (i = 0; i < m; i++)
{
p1[i + j * m] = center[i] + r * p1[i + j * m];
}
}
double[] q = Stereograph.sphere_stereograph2(m, n, p1, focus, center);
double[] p2 = Stereograph.sphere_stereograph2_inverse(m, n, q, focus, center);
double dif = 0.0;
for (j = 0; j < n; j++)
{
for (i = 0; i < m; i++)
{
dif += Math.Pow(p1[i + j * m] - p2[i + j * m], 2);
}
}
dif = Math.Sqrt(dif) / n;
Console.WriteLine("");
Console.WriteLine(" Map points from sphere to plane to sphere.");
Console.WriteLine(" RMS difference for " + n + " points was " + dif + "");
//
// Check #2.
// We have to work hard to get random points on the plane, since
// all we know to begin with is the point of tangency and the normal.
//
double[] tang = new double[m];
for (i = 0; i < m; i++)
{
tang[i] = 2.0 * center[i] - focus[i];
}
double[] normal = new double[m];
for (i = 0; i < m; i++)
{
normal[i] = center[i] - focus[i];
}
double[] pr = new double[m];
double[] pq = new double[m];
Plane.plane_normal_basis_3d(tang, ref normal, ref pr, ref pq);
double[] q1 = new double[m * n];
double[] alpha = UniformRNG.r8vec_uniform_01_new(n, ref seed);
double[] beta = UniformRNG.r8vec_uniform_01_new(n, ref seed);
for (j = 0; j < n; j++)
{
for (i = 0; i < m; i++)
{
q1[i + j * m] = tang[i] + pr[i] * alpha[j] + pq[i] * beta[j];
}
}
double[] p = Stereograph.sphere_stereograph2_inverse(m, n, q1, focus, center);
double[] q2 = Stereograph.sphere_stereograph2(m, n, p, focus, center);
dif = 0.0;
for (j = 0; j < n; j++)
{
for (i = 0; i < m; i++)
{
dif += Math.Pow(q1[i + j * m] - q2[i + j * m], 2);
}
}
dif = Math.Sqrt(dif) / n;
Console.WriteLine("");
Console.WriteLine(" Map points from plane to sphere to plane.");
Console.WriteLine(" RMS difference for " + n + " points was " + dif + "");
}
private static void test01()
//****************************************************************************80
//
// Purpose:
//
// TEST01 checks that the two functions are inverses.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 10 November 2010
//
// Author:
//
// John Burkardt
//
{
int i;
int j;
typeMethods.r8vecNormalData data = new();
Console.WriteLine("");
Console.WriteLine("TEST01");
Console.WriteLine(" SPHERE_STEREOGRAPH maps from sphere to plane.");
Console.WriteLine(" SPHERE_STEREOGRAPH_INVERSE is the inverse map.");
Console.WriteLine(" Check that these two functions are inverses.");
const int m = 3;
const int n = 100;
//
// Check #1.
//
int seed = 123456789;
double[] p1 = Burkardt.Uniform.Sphere.uniform_on_sphere01_map(m, n, ref data, ref seed);
double[] q = Stereograph.sphere_stereograph(m, n, p1);
double[] p2 = Stereograph.sphere_stereograph_inverse(m, n, q);
double dif = 0.0;
for (j = 0; j < n; j++)
{
for (i = 0; i < m; i++)
{
dif += Math.Pow(p1[i + j * m] - p2[i + j * m], 2);
}
}
dif = Math.Sqrt(dif) / n;
Console.WriteLine("");
Console.WriteLine(" Map points from sphere to plane to sphere.");
Console.WriteLine(" RMS difference for " + n + " points was " + dif + "");
//
// Check #2.
//
double[] q1 = UniformRNG.r8mat_uniform_01_new(m, n, ref seed);
for (j = 0; j < n; j++)
{
q1[m - 1 + j * m] = 1.0;
}
double[] p = Stereograph.sphere_stereograph_inverse(m, n, q1);
double[] q2 = Stereograph.sphere_stereograph(m, n, p);
dif = 0.0;
for (j = 0; j < n; j++)
{
for (i = 0; i < m; i++)
{
dif += Math.Pow(q1[i + j * m] - q2[i + j * m], 2);
}
}
dif = Math.Sqrt(dif) / n;
Console.WriteLine("");
Console.WriteLine(" Map points from plane to sphere to plane.");
Console.WriteLine(" RMS difference for " + n + " points was " + dif + "");
}
private static void test02()
//****************************************************************************80
//
// Purpose:
//
// TEST02 checks the generalized mapping.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 11 November 2010
//
// Author:
//
// John Burkardt
//
{
int i;
int j;
typeMethods.r8vecNormalData data = new();
Console.WriteLine("");
Console.WriteLine("TEST02");
Console.WriteLine(" SPHERE_STEREOGRAPH standard mapping from sphere to plane.");
Console.WriteLine(" SPHERE_STEREOGRAPH2 generalized mapping:");
Console.WriteLine(" (focus and center are arbitrary)");
Console.WriteLine(" Check that these two functions can agree.");
const int m = 3;
const int n = 100;
double[] focus = new double[m];
for (i = 0; i < m - 1; i++)
{
focus[i] = 0.0;
}
focus[m - 1] = -1.0;
double[] center = new double[m];
for (i = 0; i < m; i++)
{
center[i] = 0.0;
}
//
// Check #1.
//
int seed = 123456789;
double[] p1 = Burkardt.Uniform.Sphere.uniform_on_sphere01_map(m, n, ref data, ref seed);
double[] q1 = Stereograph.sphere_stereograph(m, n, p1);
double[] q2 = Stereograph.sphere_stereograph2(m, n, p1, focus, center);
double dif = 0.0;
for (j = 0; j < n; j++)
{
for (i = 0; i < m; i++)
{
dif += Math.Pow(q1[i + j * m] - q2[i + j * m], 2);
}
}
dif = Math.Sqrt(dif) / n;
Console.WriteLine("");
Console.WriteLine(" Map points from sphere to plane.");
Console.WriteLine(" RMS difference for " + n + " points was " + dif + "");
//
// Check #2.
//
q1 = UniformRNG.r8mat_uniform_01_new(m, n, ref seed);
for (j = 0; j < n; j++)
{
q1[m - 1 + j * m] = 1.0;
}
p1 = Stereograph.sphere_stereograph_inverse(m, n, q1);
double[] p2 = Stereograph.sphere_stereograph2_inverse(m, n, q1, focus, center);
dif = 0.0;
for (j = 0; j < n; j++)
{
for (i = 0; i < m; i++)
{
dif += Math.Pow(p1[i + j * m] - p2[i + j * m], 2);
}
}
dif = Math.Sqrt(dif) / n;
Console.WriteLine("");
Console.WriteLine(" Map points from plane to sphere.");
Console.WriteLine(" RMS difference for " + n + " points was " + dif + "");
}