private static void test004()
//****************************************************************************80
//
// Purpose:
//
// TEST004 tests TETRAHEDRON_ORDER10_TO_ORDER4.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 30 July 2009
//
// Author:
//
// John Burkardt
//
{
int node_num = 0;
int tet_num = 0;
const int tet_order = 10;
Console.WriteLine("");
Console.WriteLine("TEST004");
Console.WriteLine(" TET_MESH_NODE_ORDER determines the order of ");
Console.WriteLine(" each node in a tet mesh.");
Console.WriteLine("");
Console.WriteLine(" The order of a node is the number of tetrahedrons");
Console.WriteLine(" that use the node as part of their definition.");
TetMesh.tet_mesh_order10_example_size(ref node_num, ref tet_num);
Console.WriteLine("");
Console.WriteLine(" This mesh has tetrahedron order " + tet_order + "");
Console.WriteLine(" The number of tetrahedrons is " + tet_num + "");
double[] node_xyz = new double[3 * node_num];
int[] tet_node = new int[tet_order * tet_num];
TetMesh.tet_mesh_order10_example_set(node_num, tet_num,
ref node_xyz, ref tet_node);
typeMethods.i4mat_transpose_print(tet_order, tet_num, tet_node,
" The tet mesh:");
int[] node_order = TetMesh.tet_mesh_node_order(tet_order, tet_num, tet_node, node_num);
typeMethods.i4vec_print(node_num, node_order, " Node orders:");
Console.WriteLine("");
Console.WriteLine(" Check that the following are equal:");
Console.WriteLine("");
Console.WriteLine(" Number of tetrahedrons * order = " + tet_num * tet_order + "");
Console.WriteLine(" Sum of node orders = " + typeMethods.i4vec_sum(node_num, node_order) + "");
}
private static void test006()
//****************************************************************************80
//
// Purpose:
//
// TEST006 tests TET_MESH_TET_NEIGHBORS.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 18 August 2009
//
// Author:
//
// John Burkardt
//
{
int node_num = 0;
int tet_num = 0;
const int tet_order = 4;
Console.WriteLine("");
Console.WriteLine("TEST006");
Console.WriteLine(" TET_MESH_TET_NEIGHBORS computes the 4 neighboring");
Console.WriteLine(" tetrahedrons of each tetrahedron in a tet mesh.");
Console.WriteLine(" containing a point.");
//
// Set up the example tetrahedron mesh.
//
TetMesh.tet_mesh_order4_example_size(ref node_num, ref tet_num);
Console.WriteLine("");
Console.WriteLine(" This mesh has tetrahedron order " + tet_order + "");
Console.WriteLine(" The number of tetrahedrons is " + tet_num + "");
double[] node_xyz = new double[3 * node_num];
int[] tet_node = new int[tet_order * tet_num];
TetMesh.tet_mesh_order4_example_set(node_num, tet_num, ref node_xyz, ref tet_node);
//
// Print the tets.
//
typeMethods.i4mat_transpose_print_some(tet_order, tet_num, tet_node,
1, 1, tet_order, 10, " First 10 Tets:");
//
// The TET_NEIGHBOR array is needed by TET_MESH_DELAUNAY_SEARCH.
//
int[] tet_neighbor = TetMesh.tet_mesh_neighbor_tets(tet_order, tet_num, tet_node);
typeMethods.i4mat_transpose_print_some(4, tet_num, tet_neighbor,
1, 1, 4, 10, " First 10 Tet Neighbors:");
}
private static void test007()
//****************************************************************************80
//
// Purpose:
//
// TEST007 tests TET_MESH_SEARCH_NAIVE.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 19 August 2009
//
// Author:
//
// John Burkardt
//
{
int face = 0;
int node_num = 0;
double[] p = new double[3];
int step_num = 0;
int test;
const int test_num = 5;
int tet_num = 0;
const int tet_order = 4;
double[] tet_xyz = new double[3 * 4];
int seed = 123456789;
Console.WriteLine("");
Console.WriteLine("TEST007");
Console.WriteLine(" TET_MESH_SEARCH_NAIVE uses a naive algorithm");
Console.WriteLine(" to search a tetrahedral mesh for the tetrahedron");
Console.WriteLine(" containing a point.");
//
// Set up the example tetrahedron mesh.
//
TetMesh.tet_mesh_order4_example_size(ref node_num, ref tet_num);
Console.WriteLine("");
Console.WriteLine(" This mesh has tetrahedron order " + tet_order + "");
Console.WriteLine(" The number of tetrahedrons is " + tet_num + "");
double[] node_xyz = new double[3 * node_num];
int[] tet_node = new int[tet_order * tet_num];
TetMesh.tet_mesh_order4_example_set(node_num, tet_num, ref node_xyz, ref tet_node);
//
// The TET_NEIGHBOR array is needed for the Delaunay search.
//
int[] tet_neighbor = TetMesh.tet_mesh_neighbor_tets(tet_order, tet_num, tet_node);
for (test = 1; test <= test_num; test++)
{
//
// Choose a tetrahedron at random.
//
int tet1 = UniformRNG.i4_uniform_ab(0, tet_num - 1, ref seed);
Console.WriteLine("");
Console.WriteLine(" Point was chosen from tetrahedron " + tet1.ToString(CultureInfo.InvariantCulture).PadLeft(8) + "");
int j;
for (j = 0; j < 4; j++)
{
int k = tet_node[j + tet1 * 4];
int i;
for (i = 0; i < 3; i++)
{
tet_xyz[i + j * 3] = node_xyz[i + k * 3];
}
}
//
// Choose a point in the tetrahedron at random.
//
Tetrahedron.tetrahedron_sample(tet_xyz, 1, ref seed, ref p);
//
// Naive search.
//
int tet2 = TetMesh.tet_mesh_search_naive(node_num, node_xyz, tet_order, tet_num,
tet_node, p, ref step_num);
Console.WriteLine(" Naive search ended in tetrahedron " + tet2.ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ ", number of steps = " + step_num + "");
//
// Delaunay search.
//
int tet3 = TetMesh.tet_mesh_search_delaunay(node_num, node_xyz, tet_order,
tet_num, tet_node, tet_neighbor, p, ref face, ref step_num);
Console.WriteLine(" Delaunay search ended in tetrahedron " + tet3.ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ ", number of steps = " + step_num + "");
}
}
private static void test003()
//****************************************************************************80
//
// Purpose:
//
// TEST003 tests TETRAHEDRON_ORDER10_TO_ORDER4.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 22 January 2007
//
// Author:
//
// John Burkardt
//
{
int node_num1 = 0;
int node_num2 = 0;
int tet_num1 = 0;
int tet_num2 = 0;
const int tet_order1 = 10;
const int tet_order2 = 4;
Console.WriteLine("");
Console.WriteLine("TEST003");
Console.WriteLine(" For an order 10 tet mesh,");
Console.WriteLine(" TETRAHEDRON_ORDER10_TO_ORDER4");
Console.WriteLine(" makes a linear (order 4) tet mesh by using");
Console.WriteLine(" the existing nodes, and replacing each");
Console.WriteLine(" quadratic tetrahedron by 8 linear tetrahedrons.");
TetMesh.tet_mesh_order10_example_size(ref node_num1, ref tet_num1);
double[] node_xyz = new double[3 * node_num1];
int[] tet_node1 = new int[tet_order1 * tet_num1];
TetMesh.tet_mesh_order10_example_set(node_num1, tet_num1,
ref node_xyz, ref tet_node1);
typeMethods.i4mat_transpose_print_some(tet_order1, tet_num1, tet_node1,
1, 1, tet_order1, 5, " First 5 quadratic tetrahedrons:");
TetMesh.tet_mesh_order10_to_order4_size(node_num1, tet_num1,
ref node_num2, ref tet_num2);
Console.WriteLine("");
Console.WriteLine(" Quadratic mesh size is " + tet_num1 + "");
Console.WriteLine(" Linearized mesh size will be " + tet_num2 + "");
int[] tet_node2 = new int[tet_order2 * tet_num2];
TetMesh.tet_mesh_order10_to_order4_compute(tet_num1, tet_node1,
tet_num2, ref tet_node2);
typeMethods.i4mat_transpose_print_some(tet_order2, tet_num2, tet_node2,
1, 1, tet_order2, 5, " First 5 linear tetrahedrons:");
}
private static void Main(string[] args)
//****************************************************************************80
//
// Purpose:
//
// MAIN is the main program for TET_MESH_REFINE.
//
// Discussion:
//
// TET_MESH_REFINE refines a tetrahedral mesh of order 4 (linear).
//
// Usage:
//
// tet_mesh_refine prefix
//
// where prefix is the common file prefix:
//
// * prefix_nodes.txt, the node coordinates;
// * prefix_elements.txt, the element definitions.
// * prefix_ref_nodes.txt, the new node coordinates;
// * prefix_ref_elements.txt, the new element definitions.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 18 August 2009
//
// Author:
//
// John Burkardt
//
{
int[] element_node2 = new int[1];
int element_num2 = 0;
int node_num2 = 0;
double[] node_xyz2 = new double[1];
string prefix;
Console.WriteLine("");
Console.WriteLine("TET_MESH_REFINE");
Console.WriteLine(" READ a tet mesh, REFINE it, and WRITE the new data.");
Console.WriteLine("");
Console.WriteLine(" READ:");
Console.WriteLine(" a node dataset of NODE_NUM1 points in 3 dimensions.");
Console.WriteLine(" a tet mesh of TETRA_NUM1 tets of order TET_ORDER.");
Console.WriteLine("");
Console.WriteLine(" REFINE:");
Console.WriteLine(" compute a new set of nodes and tets, which is an");
Console.WriteLine(" eightfold refinement of the input mesh.");
Console.WriteLine("");
Console.WriteLine(" WRITE:");
Console.WriteLine(" a node dataset of NODE_NUM2 points in 3 dimensions.");
Console.WriteLine(" a tet mesh of 8*TETRA_NUM1 tets of order TET_ORDER.");
Console.WriteLine("");
Console.WriteLine(" At the moment, this program only works for a linear");
Console.WriteLine(" mesh (TET_ORDER=4).");
Console.WriteLine("");
//
// Get the filename prefix.
//
try
{
prefix = args[0];
}
catch
{
Console.WriteLine("");
Console.WriteLine("TET_MESH_REFINE:");
Console.WriteLine(" Please enter the filename prefix.");
prefix = Console.ReadLine();
}
//
// Create the filenames.
//
string input_node_filename = prefix + "_nodes.txt";
string input_element_filename = prefix + "_elements.txt";
string output_node_filename = prefix + "_ref_nodes.txt";
string output_element_filename = prefix + "_ref_elements.txt";
//
// Read the node data.
//
TableHeader h = typeMethods.r8mat_header_read(input_node_filename);
int dim_num = h.m;
int node_num1 = h.n;
if (dim_num != 3)
{
Console.WriteLine("");
Console.WriteLine("TET_MESH_REFINE - Fatal error!");
Console.WriteLine(" The spatial dimension must be 3.");
return;
}
Console.WriteLine("");
Console.WriteLine(" Read the header of \"" + input_node_filename + "\".");
Console.WriteLine("");
Console.WriteLine(" Spatial dimension = " + dim_num + "");
Console.WriteLine(" Number of nodes = " + node_num1 + "");
double[] node_xyz1 = typeMethods.r8mat_data_read(input_node_filename, dim_num,
node_num1);
Console.WriteLine("");
Console.WriteLine(" Read the data in \"" + input_node_filename + "\".");
typeMethods.r8mat_transpose_print_some(dim_num, node_num1,
node_xyz1, 1, 1, dim_num, 5, " First 5 input nodes:");
//
// Read the tet mesh data.
//
h = typeMethods.i4mat_header_read(input_element_filename);
int element_order = h.m;
int element_num1 = h.n;
switch (element_order)
{
case 4:
break;
case 10:
Console.WriteLine("");
Console.WriteLine("TET_MESH_REFINE - Fatal error!");
Console.WriteLine(" The program cannot yet handel the 10-node case.");
Console.WriteLine(" Try using the sequence:");
Console.WriteLine(" TET_MESH_Q2L --> TET_MESH_REFINE --> TET_MESH_L2Q.");
return;
default:
Console.WriteLine("");
Console.WriteLine("TET_MESH_REFINE - Fatal error!");
Console.WriteLine(" The tet mesh must have order 4 or order 10.");
return;
}
Console.WriteLine("");
Console.WriteLine(" Read the header of \"" + input_element_filename + "\".");
Console.WriteLine("");
Console.WriteLine(" Tetrahedron order = " + element_order + "");
Console.WriteLine(" Number of tetras = " + element_num1 + "");
int[] element_node1 = typeMethods.i4mat_data_read(input_element_filename, element_order,
element_num1);
Console.WriteLine("");
Console.WriteLine(" Read the data in \"" + input_element_filename + "\".");
typeMethods.i4mat_transpose_print_some(element_order, element_num1,
element_node1, 1, 1, element_order, 5, " First 5 input tetrahedrons:");
//
// Check for 1-based node-indexing, and convert it to 0-based.
//
TetMesh.tet_mesh_base_zero(node_num1, element_order, element_num1, ref element_node1);
switch (element_order)
{
//
// Compute the refined mesh.
//
case 4:
int[] edge_data = new int[5 * 6 * element_num1];
TetMesh_Refine.tet_mesh_order4_refine_size(node_num1, element_num1, element_node1,
ref node_num2, ref element_num2, ref edge_data);
Console.WriteLine(" Number of refined nodes = " + node_num2 + "");
Console.WriteLine(" Number of refined tetras = " + element_num2 + "");
node_xyz2 = new double[dim_num * node_num2];
element_node2 = new int[element_order * element_num2];
TetMesh_Refine.tet_mesh_order4_refine_compute(node_num1, element_num1, node_xyz1,
element_node1, node_num2, element_num2, edge_data, ref node_xyz2, ref element_node2);
break;
case 10:
{
break;
}
}
//
// Print a small amount of the refined data.
//
typeMethods.r8mat_transpose_print_some(dim_num, node_num2, node_xyz2,
1, 1, dim_num, 5, " First 5 output nodes:");
typeMethods.i4mat_transpose_print_some(element_order, element_num2, element_node2,
1, 1, element_order, 5, " First 5 output tetras");
//
// Write out the node and tetra data for the refined mesh
//
typeMethods.r8mat_write(output_node_filename, dim_num, node_num2, node_xyz2);
Console.WriteLine("");
Console.WriteLine(" Wrote the file \"" + output_node_filename + "\".");
typeMethods.i4mat_write(output_element_filename, element_order, element_num2, element_node2);
Console.WriteLine(" Wrote the file \"" + output_element_filename + "\".");
Console.WriteLine("");
Console.WriteLine("TET_MESH_REFINE:");
Console.WriteLine(" Normal end of execution.");
Console.WriteLine("");
}
public static double[] fem3d_evaluate(int fem_node_num, double[] fem_node_xyz,
int fem_element_order, int fem_element_num, int[] fem_element_node,
int[] fem_element_neighbor, int fem_value_dim, double[] fem_value,
int sample_node_num, double[] sample_node_xyz)
//****************************************************************************80
//
// Purpose:
//
// FEM3D_EVALUATE samples an FEM function on a T4 tet mesh.
//
// Discussion:
//
// Note that the sample values returned are true values of the underlying
// finite element function. They are NOT produced by constructing some
// other function that interpolates the data at the finite element nodes
// (something which MATLAB's griddata function can easily do.) Instead,
// each sampling node is located within one of the associated finite
// element tetrahedrons, and the finite element function is developed and
// evaluated there.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 08 August 2009
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int FEM_NODE_NUM, the number of nodes.
//
// Input, double FEM_NODE_XYZ[3*FEM_NODE_NUM], the coordinates
// of the nodes.
//
// Input, int FEM_ELEMENT_ORDER, the order of the elements,
// which should be 4.
//
// Input, int FEM_ELEMENT_NUM, the number of elements.
//
// Input, int FEM_ELEMENT_NODE[FEM_ELEMENT_ORDER*FEM_ELEMENT_NUM], the
// nodes that make up each element.
//
// Input, int FEM_ELEMENT_NEIGHBOR[4*FEM_ELEMENT_NUM], the
// index of the neighboring element on each side, or -1 if no neighbor there.
//
// Input, int FEM_VALUE_DIM, the "dimension" of the values.
//
// Input, double FEM_VALUE[FEM_VALUE_DIM*FEM_NODE_NUM], the
// finite element coefficient values at each node.
//
// Input, int SAMPLE_NODE_NUM, the number of sample nodes.
//
// Input, double SAMPLE_NODE_XYZ[3*SAMPLE_NODE_NUM], the sample nodes.
//
// Output, double) FEM3D_EVALUATE[FEM_VALUE_DIM*SAMPLE_NODE_NUM],
// the sampled values.
//
{
int j;
double[] p_xyz = new double[3];
double[] b = new double[fem_element_order];
double[] sample_value = new double[fem_value_dim * sample_node_num];
int[] t_node = new int[fem_element_order];
double[] t_xyz = new double[3 * fem_element_order];
//
// For each sample point: find the element T that contains it,
// and evaluate the finite element function there.
//
for (j = 0; j < sample_node_num; j++)
{
p_xyz[0] = sample_node_xyz[0 + j * 3];
p_xyz[1] = sample_node_xyz[1 + j * 3];
p_xyz[2] = sample_node_xyz[2 + j * 3];
//
// Find the element T that contains the point.
//
int step_num = 0;
int t = TetMesh.tet_mesh_search_naive(fem_node_num, fem_node_xyz,
fem_element_order, fem_element_num, fem_element_node,
p_xyz, ref step_num);
//
// Evaluate the finite element basis functions at the point in T.
//
int i;
for (i = 0; i < fem_element_order; i++)
{
t_node[i] = fem_element_node[i + t * fem_element_order];
}
for (i = 0; i < fem_element_order; i++)
{
t_xyz[0 + i * 3] = fem_node_xyz[0 + t_node[i] * 3];
t_xyz[1 + i * 3] = fem_node_xyz[1 + t_node[i] * 3];
t_xyz[2 + i * 3] = fem_node_xyz[2 + t_node[i] * 3];
}
Basis_mn.basis_mn_tet4(t_xyz, 1, p_xyz, ref b);
//
// Multiply by the finite element values to get the sample values.
//
for (i = 0; i < fem_value_dim; i++)
{
sample_value[i + j * fem_value_dim] = 0.0;
int k;
for (k = 0; k < fem_element_order; k++)
{
sample_value[i + j * fem_value_dim] += fem_value[i + t_node[k] * fem_value_dim] * b[k];
}
}
}
return(sample_value);
}
private static void Main(string[] args)
//****************************************************************************80
//
// Purpose:
//
// MAIN is the main program for TET_MESH_L2Q.
//
// Discussion:
//
// TET_MESH_L2Q makes a quadratic tet mesh from a linear one.
//
// Usage:
//
// tet_mesh_l2q prefix
//
// where prefix is the common file prefix:
//
// * prefix_nodes.txt, the node coordinates;
// * prefix_elements.txt, the linear element definitions.
// * prefix_l2q_nodes.txt, the quadratic node coordinates,
// * prefix_l2q_elements.txt, the quadratic element definitions.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 01 October 2009
//
// Author:
//
// John Burkardt
//
{
const int element_order2 = 10;
int node_num2 = 0;
string prefix;
Console.WriteLine("");
Console.WriteLine("TET_MESH_L2Q");
Console.WriteLine(" Read a \"linear\" tet mesh and");
Console.WriteLine(" write out a \"quadratic\" one.");
Console.WriteLine("");
Console.WriteLine(" Read a node file of NODE_NUM1 nodes in 3 dimensions.");
Console.WriteLine(" Read an associated tet mesh of TETRA_NUM");
Console.WriteLine(" tetrahedrons, using 4 nodes per tetrahedron.");
Console.WriteLine("");
Console.WriteLine(" Create new nodes which are midpoints of sides,");
Console.WriteLine(" generate new node and tet mesh data for");
Console.WriteLine(" quadratic 10-node tetrahedrons, and write them out.");
Console.WriteLine("");
//
// Get the filename prefix.
//
try
{
prefix = args[0];
}
catch
{
Console.WriteLine("");
Console.WriteLine("TET_MESH_L2Q:");
Console.WriteLine(" Please enter the filename prefix.");
prefix = Console.ReadLine();
}
//
// Create the filenames.
//
string input_node_filename = prefix + "_nodes.txt";
string input_element_filename = prefix + "_elements.txt";
string output_node_filename = prefix + "_l2q_nodes.txt";
string output_element_filename = prefix + "_l2q_elements.txt";
//
// Read the node data.
//
TableHeader h = typeMethods.r8mat_header_read(input_node_filename);
int dim_num = h.m;
int node_num1 = h.n;
if (dim_num != 3)
{
Console.WriteLine("");
Console.WriteLine("TET_MESH_L2Q - Fatal error!");
Console.WriteLine(" The spatial dimension must be 3.");
Console.WriteLine(" This data has dimension = " + dim_num + "");
return;
}
Console.WriteLine("");
Console.WriteLine(" Read the header of \"" + input_node_filename + "\".");
Console.WriteLine("");
Console.WriteLine(" Spatial dimension = " + dim_num + "");
Console.WriteLine(" Number of nodes = " + node_num1 + "");
double[] node_xyz1 = typeMethods.r8mat_data_read(input_node_filename, dim_num,
node_num1);
Console.WriteLine("");
Console.WriteLine(" Read the data in \"" + input_node_filename + "\".");
typeMethods.r8mat_transpose_print_some(dim_num, node_num1,
node_xyz1, 1, 1, dim_num, 5, " First 5 nodes:");
//
// Read the tet mesh data.
//
h = typeMethods.i4mat_header_read(input_element_filename);
int element_order1 = h.m;
int element_num = h.n;
if (element_order1 != 4)
{
Console.WriteLine("");
Console.WriteLine("TET_MESH_L2Q - Fatal error!");
Console.WriteLine(" The tet mesh must have order 4.");
Console.WriteLine(" This mesh has order " + element_order1 + "");
return;
}
Console.WriteLine("");
Console.WriteLine(" Read the header of \"" + input_element_filename + "\".");
Console.WriteLine("");
Console.WriteLine(" Tetrahedron order = " + element_order1 + "");
Console.WriteLine(" Number of tetras = " + element_num + "");
int[] element_node1 = typeMethods.i4mat_data_read(input_element_filename, element_order1,
element_num);
Console.WriteLine("");
Console.WriteLine(" Read the data in \"" + input_element_filename + "\".");
typeMethods.i4mat_transpose_print_some(element_order1, element_num,
element_node1, 1, 1, element_order1, 5, " First 5 tetrahedrons:");
//
// If the element information is 1-based, make it 0-based.
//
TetMesh.tet_mesh_base_zero(node_num1, element_order1, element_num, ref element_node1);
//
// Compute the quadratic mesh.
//
int[] edge_data = new int[5 * 6 * element_num];
TetMesh_L2Q.tet_mesh_order4_to_order10_size(element_num, element_node1, node_num1,
ref edge_data, ref node_num2);
Console.WriteLine(" Number of quadratic nodes = " + node_num2 + "");
double[] node_xyz2 = new double[dim_num * node_num2];
int[] element_node2 = new int[element_order2 * element_num];
TetMesh_L2Q.tet_mesh_order4_to_order10_compute(element_num, element_node1, node_num1,
node_xyz1, edge_data, ref element_node2, node_num2, ref node_xyz2);
//
// Print a small amount of the quadratic data.
//
typeMethods.r8mat_transpose_print_some(dim_num, node_num2, node_xyz2,
1, 1, dim_num, 5, " First 5 quadratic nodes:");
typeMethods.i4mat_transpose_print_some(element_order2, element_num, element_node2,
1, 1, element_order2, 5, " First 5 quadratic tetras");
//
// Write out the node and tetra data for the quadratic mesh
//
typeMethods.r8mat_write(output_node_filename, dim_num, node_num2, node_xyz2);
Console.WriteLine("");
Console.WriteLine(" Wrote the file \"" + output_node_filename + "\".");
typeMethods.i4mat_write(output_element_filename, element_order2, element_num, element_node2);
Console.WriteLine(" Wrote the file \"" + output_element_filename + "\".");
Console.WriteLine("");
Console.WriteLine("TET_MESH_L2Q:");
Console.WriteLine(" Normal end of execution.");
Console.WriteLine("");
}
private static void Main(string[] args)
//****************************************************************************80
//
// Purpose:
//
// MAIN is the main program for TET_MESH_TET_NEIGHBORS.
//
// Discussion:
//
// TET_MESH_TET_NEIGHBORS manages the tet mesh neighbor calculation.
//
// A tet mesh of order 4 or order 10 may be used.
//
// Usage:
//
// tet_mesh_tet_neighbors prefix
//
// where prefix is the common file prefix:
//
// * prefix_nodes.txt, the node coordinates (not needed by this program);
// * prefix_elements.txt, the linear element definitions.
// * prefix_element_neighbors.txt, the element neighbors.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 27 September 2009
//
// Author:
//
// John Burkardt
//
{
const int node_num = 0;
string prefix;
Console.WriteLine("");
Console.WriteLine("TET_MESH_TET_NEIGHBORS");
Console.WriteLine(" Read a tet mesh dataset of TETRA_NUM");
Console.WriteLine(" tetrahedrons, using 4 or 10 nodes.");
Console.WriteLine("");
Console.WriteLine(" Compute the tet mesh neighbors, and write this");
Console.WriteLine(" information to a file");
Console.WriteLine("");
//
// Get the filename prefix.
//
try
{
prefix = args[0];
}
catch
{
Console.WriteLine("");
Console.WriteLine("TET_MESH_TET_NEIGHBORS:");
Console.WriteLine(" Please enter the filename prefix.");
prefix = Console.ReadLine();
}
//
// Create the filenames.
//
string element_filename = prefix + "_elements.txt";
string neighbor_filename = prefix + "_element_neighbors.txt";
//
// Read the tet mesh data.
//
TableHeader h = typeMethods.i4mat_header_read(element_filename);
int element_order = h.m;
int element_num = h.n;
if (element_order != 4 && element_order != 10)
{
Console.WriteLine("");
Console.WriteLine("TET_MESH_TET_NEIGHBORS - Fatal error!");
Console.WriteLine(" The tet mesh must have order 4 or order 10.");
return;
}
Console.WriteLine("");
Console.WriteLine(" Read the header of \"" + element_filename + "\".");
Console.WriteLine("");
Console.WriteLine(" Tetrahedron order = " + element_order + "");
Console.WriteLine(" Number of tetras = " + element_num + "");
int[] element_node = typeMethods.i4mat_data_read(element_filename, element_order,
element_num);
Console.WriteLine("");
Console.WriteLine(" Read the data in \"" + element_filename + "\".");
typeMethods.i4mat_transpose_print_some(element_order, element_num,
element_node, 1, 1, element_order, 5, " First 5 tetrahedrons:");
//
// Detect and correct 1-based node indexing.
//
TetMesh.tet_mesh_base_zero(node_num, element_order, element_num, ref element_node);
//
// Compute the neighbor information.
//
int[] element_neighbor = TetMesh_Neighbors.tet_mesh_neighbor_tets(element_order, element_num,
element_node);
typeMethods.i4mat_transpose_print_some(4, element_num,
element_neighbor, 1, 1, 4, 5, " First 5 neighbor sets:");
//
// Write the neighbor information to a file.
//
typeMethods.i4mat_write(neighbor_filename, 4, element_num, element_neighbor);
Console.WriteLine("");
Console.WriteLine(" Created the file \"" + neighbor_filename + "\".");
Console.WriteLine("");
Console.WriteLine("TET_MESH_TET_NEIGHBORS:");
Console.WriteLine(" Normal end of execution.");
Console.WriteLine("");
}
private static void Main(string[] args)
//****************************************************************************80
//
// Purpose:
//
// MAIN is the main program for TET_MESH_RCM.
//
// Discussion:
//
// TET_MESH_RCM applies the RCM reordering to a tet mesh.
//
// The user supplies a node file and a tetrahedron file, containing
// the coordinates of the nodes, and the indices of the nodes that
// make up each tetrahedron. Either 4-node or 10-node tetrahedrons may
// be used.
//
// The program reads the data, computes the adjacency information,
// carries out the RCM algorithm to get the permutation, applies
// the permutation to the nodes and tetrahedrons, and writes out
// new node and tetrahedron files that correspond to the RCM permutation.
//
// Note that node data is normally three dimensional, that is,
// each node has an X, Y and Z coordinate. In some applications, it
// may be desirable to specify more information. This program
// will accept node data that includes DIM_NUM entries on each line,
// as long as DIM_NUM is the same for each entry.
//
// Thanks to Xingxing Zhang for pointing out some problems with a
// previous version of this program, 10 May 2011.
//
// Usage:
//
// tet_mesh_rcm prefix
//
// where prefix is the common file prefix:
//
// * prefix_nodes.txt, the node coordinates (input);
// * prefix_elements.txt, the element definitions (input).
// * prefix_rcm_nodes.txt, the new node coordinates (output);
// * prefix_rcm_elements.txt, the new element definitions (output).
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 08 March 2013
//
// Author:
//
// John Burkardt
//
{
int[] adj = new int[1];
int adj_num = 0;
int[] adj_row = new int[1];
const bool debug = false;
int i;
int j;
string prefix;
Console.WriteLine("");
Console.WriteLine("");
Console.WriteLine("TET_MESH_RCM");
Console.WriteLine(" Read a node dataset of NODE_NUM points in 3 dimensions.");
Console.WriteLine(" Read an associated tet mesh dataset of TETRA_NUM");
Console.WriteLine(" tetrahedrons using 4 or 10 nodes.");
Console.WriteLine("");
Console.WriteLine(" Apply the RCM reordering (Reverse Cuthill-McKee).");
Console.WriteLine("");
Console.WriteLine(" Reorder the data and write it out to files.");
Console.WriteLine("");
//
// Get the filename prefix.
//
try
{
prefix = args[0];
}
catch
{
Console.WriteLine("");
Console.WriteLine("TET_MESH_RCM:");
Console.WriteLine(" Please enter the filename prefix.");
prefix = Console.ReadLine();
}
//
// Create the filenames.
//
string node_filename = prefix + "_nodes.txt";
string element_filename = prefix + "_elements.txt";
string node_rcm_filename = prefix + "_rcm_nodes.txt";
string element_rcm_filename = prefix + "_rcm_elements.txt";
//
// Read the node data.
//
TableHeader h = typeMethods.r8mat_header_read(node_filename);
int dim_num = h.m;
int node_num = h.n;
Console.WriteLine("");
Console.WriteLine(" Read the header of \"" + node_filename + "\".");
Console.WriteLine("");
Console.WriteLine(" Spatial dimension DIM_NUM = " + dim_num + "");
Console.WriteLine(" Number of points NODE_NUM = " + node_num + "");
double[] node_xyz = typeMethods.r8mat_data_read(node_filename, dim_num, node_num);
Console.WriteLine("");
Console.WriteLine(" Read the data in \"" + node_filename + "\".");
typeMethods.r8mat_transpose_print_some(dim_num, node_num, node_xyz, 1, 1, dim_num, 5,
" Coordinates of first 5 nodes:");
//
// Read the tet mesh data.
//
h = typeMethods.i4mat_header_read(element_filename);
int element_order = h.m;
int element_num = h.n;
if (element_order != 4 && element_order != 10)
{
Console.WriteLine("");
Console.WriteLine("TET_MESH_RCM - Fatal error!");
Console.WriteLine(" The tet mesh must have order 4 or order 10.");
return;
}
Console.WriteLine("");
Console.WriteLine(" Read the header of \"" + element_filename + "\".");
Console.WriteLine("");
Console.WriteLine(" Tetrahedron order = " + element_order + "");
Console.WriteLine(" Number of tetras = " + element_num + "");
int[] element_node = typeMethods.i4mat_data_read(element_filename, element_order,
element_num);
Console.WriteLine("");
Console.WriteLine(" Read the data in \"" + element_filename + "\".");
typeMethods.i4mat_transpose_print_some(element_order, element_num,
element_node, 1, 1, element_order, 5, " First 5 tetrahedrons:");
//
// If the element information is 1-based, make it 0-based.
//
int base_user = TetMesh.tet_mesh_base_zero(node_num, element_order,
element_num, ref element_node);
if (base_user != 0 && base_user != 1)
{
Console.WriteLine("");
Console.WriteLine("TET_MESH_RCM - Fatal error!");
Console.WriteLine(" The input data does not seem to be 0-based or 1-based.");
}
switch (element_order)
{
//
// Following code depends on the element order.
//
case 4:
{
//
// Count the number of adjacencies.
// Set up the ADJ_ROW adjacency pointer array.
//
adj_row = new int[node_num + 1];
TetMesh.tet_mesh_order4_adj_count(node_num, element_num, element_node,
ref adj_num, ref adj_row);
if (debug || node_num < 10)
{
Console.WriteLine("");
Console.WriteLine(" ADJ_NUM = " + adj_num + "");
typeMethods.i4vec_print(node_num + 1, adj_row, " ADJ_ROW:");
}
//
// Set up the ADJ adjacency array.
//
adj = TetMesh.tet_mesh_order4_adj_set(node_num, element_num, element_node,
adj_num, adj_row);
switch (node_num)
{
case < 10:
AdjacencyMatrix.adj_print(node_num, adj_num, adj_row, adj, " ADJ");
break;
}
break;
}
case 10:
{
//
// Count the number of adjacencies.
// Set up the ADJ_ROW adjacency pointer array.
//
adj_row = new int[node_num + 1];
TetMesh.tet_mesh_order10_adj_count(node_num, element_num, element_node,
ref adj_num, ref adj_row);
if (debug || node_num < 10)
{
Console.WriteLine("");
Console.WriteLine(" ADJ_NUM = " + adj_num + "");
typeMethods.i4vec_print(node_num + 1, adj_row, " ADJ_ROW:");
}
//
// Set up the ADJ adjacency array.
//
adj = TetMesh.tet_mesh_order10_adj_set(node_num, element_num, element_node,
ref adj_num, ref adj_row);
switch (node_num)
{
case < 10:
AdjacencyMatrix.adj_print(node_num, adj_num, adj_row, adj, " ADJ");
break;
}
break;
}
}
//
// Compute the bandwidth.
//
int bandwidth = AdjacencyMatrix.adj_bandwidth(node_num, adj_num, adj_row, adj);
Console.WriteLine("");
Console.WriteLine(" ADJ bandwidth = " + bandwidth + "");
//
// GENRCM computes the RCM permutation.
//
int[] perm = GenRCM.genrcm(node_num, adj_num, adj_row, adj);
//
// Compute the inverse permutation.
//
int[] perm_inv = typeMethods.perm_inverse3(node_num, perm);
switch (node_num)
{
case < 10:
{
Console.WriteLine("");
Console.WriteLine(" I PERM[I] INVERSE[I]");
Console.WriteLine("");
for (i = 0; i < node_num; i++)
{
Console.WriteLine(" " + i.ToString().PadLeft(8)
+ " " + perm[i].ToString().PadLeft(8)
+ " " + perm_inv[i].ToString().PadLeft(8) + "");
}
break;
}
}
//
// Compute the bandwidth of the permuted array.
//
bandwidth = AdjacencyMatrix.adj_perm_bandwidth(node_num, adj_num, adj_row, adj,
perm, perm_inv);
Console.WriteLine("");
Console.WriteLine(" ADJ bandwidth after RCM permutation = " + bandwidth + "");
//
// Permute the nodes in NODE_XYZ.
//
int base_internal = 0;
typeMethods.r8col_permute(dim_num, node_num, perm, base_internal, node_xyz);
//
// Permute the node indices in ELEMENT_NODE.
//
for (j = 0; j < element_num; j++)
{
for (i = 0; i < element_order; i++)
{
int node = element_node[i + j * element_order];
element_node[i + j * element_order] = perm_inv[node];
}
}
switch (base_user)
{
//
// If the user base was 1, restore it!
//
case 1:
{
for (i = 0; i < element_num; i++)
{
for (j = 0; j < element_order; j++)
{
element_node[i + j * element_order] += 1;
}
}
Console.WriteLine("");
Console.WriteLine(" Output files will use the same 1-based ordering used by the input.");
break;
}
}
//
// Write the node and element data.
//
typeMethods.r8mat_write(node_rcm_filename, dim_num, node_num, node_xyz);
Console.WriteLine("");
Console.WriteLine(" Created the file \"" + node_rcm_filename + "\".");
typeMethods.i4mat_write(element_rcm_filename, element_order, element_num, element_node);
Console.WriteLine(" Created the file \"" + element_rcm_filename + "\".");
Console.WriteLine("");
Console.WriteLine("TET_MESH_RCM:");
Console.WriteLine(" Normal end of execution.");
Console.WriteLine("");
}
private static void Main(string[] args)
//****************************************************************************80
//
// Purpose:
//
// MAIN is the main program for TET_MESH_TO_GMSH.
//
// Discussion:
//
// TET_MESH_TO_GMSH converts a tet mesh, using 4 or 10 node
// tetrahedral elements, to a Gmsh file.
//
// Usage:
//
// tet_mesh_to_gmsh prefix
//
// where prefix is the common file prefix:
//
// * prefix_nodes.txt, the node coordinates;
// * prefix_elements.txt, the linear element definitions.
// * prefix.msh, the Gmsh msh file.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 31 May 2013
//
// Author:
//
// John Burkardt
//
// Reference:
//
// Christophe Geuzaine, Jean-Francois Remacle,
// Gmsh: a three-dimensional finite element mesh generator with
// built-in pre- and post-processing facilities,
// International Journal for Numerical Methods in Engineering,
// Volume 79, Number 11, pages 1309-1331, 2009.
//
{
string prefix;
Console.WriteLine("");
Console.WriteLine("TET_MESH_TO_GMSH;");
Console.WriteLine(" Convert a linear or quadratic tet mesh to Gmsh format");
Console.WriteLine("");
Console.WriteLine(" Read \"prefix\"_nodes.txt, node coordinates.");
Console.WriteLine(" Read \"prefix\"_elements.txt, 4 or 10 node element definitions.");
Console.WriteLine("");
Console.WriteLine(" Create \"prefix\".msh, a corresponding Gmsh mesh file.");
Console.WriteLine("");
//
// Get the filename prefix.
//
try
{
prefix = args[0];
}
catch
{
Console.WriteLine("");
Console.WriteLine("TET_MESH_TO_GMSH;:");
Console.WriteLine(" Please enter the filename prefix.");
prefix = Console.ReadLine();
}
//
// Create the filenames.
//
string node_filename = prefix + "_nodes.txt";
string element_filename = prefix + "_elements.txt";
string gmsh_filename = prefix + ".msh";
//
// Read the node data.
//
TableHeader h = typeMethods.r8mat_header_read(node_filename);
int dim_num = h.m;
int node_num = h.n;
if (dim_num != 3)
{
Console.WriteLine("");
Console.WriteLine("TET_MESH_TO_GMSH; - Fatal error!");
Console.WriteLine(" The spatial dimension must be 3.");
return;
}
Console.WriteLine("");
Console.WriteLine(" Read the header of \"" + node_filename + "\".");
Console.WriteLine("");
Console.WriteLine(" Spatial dimension = " + dim_num + "");
Console.WriteLine(" Number of nodes = " + node_num + "");
double[] node_xyz = typeMethods.r8mat_data_read(node_filename, dim_num, node_num);
Console.WriteLine("");
Console.WriteLine(" Read the data in \"" + node_filename + "\".");
typeMethods.r8mat_transpose_print_some(dim_num, node_num,
node_xyz, 1, 1, dim_num, 5, " First 5 nodes:");
//
// Read the element data.
//
h = typeMethods.i4mat_header_read(element_filename);
int element_order = h.m;
int element_num = h.n;
switch (element_order)
{
case 4:
break;
case 10:
break;
case 20:
break;
default:
Console.WriteLine("");
Console.WriteLine("TET_MESH_TO_GMSH; - Fatal error!");
Console.WriteLine(" The tet mesh must have order 4, 10, or 20.");
return;
}
Console.WriteLine("");
Console.WriteLine(" Read the header of \"" + element_filename + "\".");
Console.WriteLine("");
Console.WriteLine(" Element order = " + element_order + "");
Console.WriteLine(" Number of elements = " + element_num + "");
int[] element_node = typeMethods.i4mat_data_read(element_filename, element_order,
element_num);
Console.WriteLine("");
Console.WriteLine(" Read the data in \"" + element_filename + "\".");
typeMethods.i4mat_transpose_print_some(element_order, element_num,
element_node, 1, 1, element_order, 5, " First 5 elements:");
//
// Use 1-based indexing.
//
TetMesh.tet_mesh_base_one(node_num, element_order, element_num, ref element_node);
//
// Write the Gmsh file.
//
Burkardt.GMesh.IO.gmsh_write(gmsh_filename, dim_num, node_num, node_xyz, element_order,
element_num, element_node);
Console.WriteLine("");
Console.WriteLine(" Created GMSH file \"" + gmsh_filename + "\".");
Console.WriteLine("");
Console.WriteLine("TET_MESH_TO_GMSH;");
Console.WriteLine(" Normal end of execution.");
Console.WriteLine("");
}
private static void Main(string[] args)
//****************************************************************************80
//
// Purpose:
//
// MAIN is the main program for TET_MESH_QUALITY.
//
// Discussion:
//
// TET_MESH_QUALITY determines quality measures for a tet mesh.
//
// Usage:
//
// tet_mesh_quality prefix
//
// where prefix is the common file prefix:
//
// * prefix_nodes.txt contains the node coordinates;
// * prefix_elements.txt contains the element definitions.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 27 September 2009
//
// Author:
//
// John Burkardt
//
{
int i;
string prefix;
double value_max = 0;
double value_mean = 0;
double value_min = 0;
double value_var = 0;
Console.WriteLine("");
Console.WriteLine("");
Console.WriteLine("TET_MESH_QUALITY");
Console.WriteLine(" Compute tet mesh quality measures.");
Console.WriteLine("");
//
// Get the filename prefix.
//
try
{
prefix = args[0];
}
catch
{
Console.WriteLine("");
Console.WriteLine("TET_MESH_QUALITY:");
Console.WriteLine(" Please enter the file prefix.");
prefix = Console.ReadLine();
}
//
// Create the filenames.
//
string node_filename = prefix + "_nodes.txt";
string element_filename = prefix + "_elements.txt";
//
// Read the node data.
//
TableHeader h = typeMethods.r8mat_header_read(node_filename);
int dim_num = h.m;
int node_num = h.n;
Console.WriteLine("");
Console.WriteLine(" Read the header of \"" + node_filename + "\".");
Console.WriteLine("");
Console.WriteLine(" Spatial dimension DIM_NUM = " + dim_num + "");
Console.WriteLine(" Number of points NODE_NUM = " + node_num + "");
if (dim_num != 3)
{
Console.WriteLine("");
Console.WriteLine("TET_MESH_QUALITY - Fatal error!");
Console.WriteLine(" Dataset must have spatial dimension 3.");
return;
}
double[] node_xyz = typeMethods.r8mat_data_read(node_filename, dim_num, node_num);
Console.WriteLine("");
Console.WriteLine(" Read the data in \"" + node_filename + "\".");
typeMethods.r8mat_transpose_print_some(dim_num, node_num, node_xyz, 1, 1, 5, 5,
" 5 by 5 portion of data read from file:");
//
// Read the tetra data.
//
h = typeMethods.i4mat_header_read(element_filename);
int element_order = h.m;
int element_num = h.n;
if (element_order != 4)
{
Console.WriteLine("");
Console.WriteLine("TET_MESH_QUALITY - Fatal error!");
Console.WriteLine(" Data is not for a 4 node tet mesh.");
return;
}
Console.WriteLine("");
Console.WriteLine(" Read the header of \"" + element_filename + "\".");
Console.WriteLine("");
Console.WriteLine(" Element order = " + element_order + "");
Console.WriteLine(" Number of elements = " + element_num + "");
int[] element_node = typeMethods.i4mat_data_read(element_filename, element_order,
element_num);
Console.WriteLine("");
Console.WriteLine(" Read the data in \"" + element_filename + "\".");
typeMethods.i4mat_transpose_print_some(element_order, element_num,
element_node, 1, 1, element_order, 10, " Portion of ELEMENT_NODE:");
//
// If the element information is 1-based, make it 0-based.
//
TetMesh.tet_mesh_base_zero(node_num, element_order, element_num, ref element_node);
//
// Compute and print the quality measures.
//
Console.WriteLine("");
Console.WriteLine(" Minimum Mean Maximum Variance");
Console.WriteLine("");
TetMesh.tet_mesh_quality1(node_num, node_xyz, element_order, element_num,
element_node, ref value_min, ref value_mean, ref value_max, ref value_var);
Console.WriteLine(" Quality measure 1 = "
+ " " + value_min.ToString(CultureInfo.InvariantCulture).PadLeft(10)
+ " " + value_mean.ToString(CultureInfo.InvariantCulture).PadLeft(10)
+ " " + value_max.ToString(CultureInfo.InvariantCulture).PadLeft(10)
+ " " + value_var.ToString(CultureInfo.InvariantCulture).PadLeft(10) + "");
TetMesh.tet_mesh_quality2(node_num, node_xyz, element_order, element_num,
element_node, ref value_min, ref value_mean, ref value_max, ref value_var);
Console.WriteLine(" Quality measure 2 = "
+ " " + value_min.ToString(CultureInfo.InvariantCulture).PadLeft(10)
+ " " + value_mean.ToString(CultureInfo.InvariantCulture).PadLeft(10)
+ " " + value_max.ToString(CultureInfo.InvariantCulture).PadLeft(10)
+ " " + value_var.ToString(CultureInfo.InvariantCulture).PadLeft(10) + "");
TetMesh.tet_mesh_quality3(node_num, node_xyz, element_order, element_num,
element_node, ref value_min, ref value_mean, ref value_max, ref value_var);
Console.WriteLine(" Quality measure 3 = "
+ " " + value_min.ToString(CultureInfo.InvariantCulture).PadLeft(10)
+ " " + value_mean.ToString(CultureInfo.InvariantCulture).PadLeft(10)
+ " " + value_max.ToString(CultureInfo.InvariantCulture).PadLeft(10)
+ " " + value_var.ToString(CultureInfo.InvariantCulture).PadLeft(10) + "");
TetMesh.tet_mesh_quality4(node_num, node_xyz, element_order, element_num,
element_node, ref value_min, ref value_mean, ref value_max, ref value_var);
Console.WriteLine(" Quality measure 4 = "
+ " " + value_min.ToString(CultureInfo.InvariantCulture).PadLeft(10)
+ " " + value_mean.ToString(CultureInfo.InvariantCulture).PadLeft(10)
+ " " + value_max.ToString(CultureInfo.InvariantCulture).PadLeft(10)
+ " " + value_var.ToString(CultureInfo.InvariantCulture).PadLeft(10) + "");
TetMesh.tet_mesh_quality5(node_num, node_xyz, element_order, element_num,
element_node, ref value_min, ref value_mean, ref value_max, ref value_var);
Console.WriteLine(" Quality measure 5 = "
+ " " + value_min.ToString(CultureInfo.InvariantCulture).PadLeft(10)
+ " " + value_mean.ToString(CultureInfo.InvariantCulture).PadLeft(10)
+ " " + value_max.ToString(CultureInfo.InvariantCulture).PadLeft(10)
+ " " + value_var.ToString(CultureInfo.InvariantCulture).PadLeft(10) + "");
int[] node_order = TetMesh.tet_mesh_node_order(element_order, element_num, element_node,
node_num);
int histo_num = typeMethods.i4vec_max(node_num, node_order);
int[] histo_gram = typeMethods.i4vec_histogram(node_num, node_order, histo_num);
Console.WriteLine("");
Console.WriteLine(" Here is a numerical histogram of the order of");
Console.WriteLine(" each node in the mesh, that is, the number of");
Console.WriteLine(" tetrahedrons that include that node as a vertex.");
Console.WriteLine("");
Console.WriteLine(" For a regular mesh, most nodes would have the");
Console.WriteLine(" same order.");
Console.WriteLine("");
Console.WriteLine(" Order Number of Nodes");
Console.WriteLine("");
for (i = 0; i <= histo_num; i++)
{
if (histo_gram[i] != 0)
{
Console.WriteLine(" " + i.ToString(CultureInfo.InvariantCulture).PadLeft(6)
+ " " + histo_gram[i].ToString(CultureInfo.InvariantCulture).PadLeft(6) + "");
}
}
Console.WriteLine("");
Console.WriteLine("TET_MESH_QUALITY:");
Console.WriteLine(" Normal end of execution.");
Console.WriteLine("");
}
private static void Main(string[] args)
//****************************************************************************80
//
// Purpose:
//
// MAIN is the main program for TET_MESH_VOLUMES.
//
// Discussion:
//
// TET_MESH_VOLUMES determines the element volumes of a tet mesh.
//
// Usage:
//
// tet_mesh_volumes prefix
//
// where
//
// * prefix_nodes.txt contains nodal coordinates;
// * prefix_elements.txt contains the element definitions;
// * prefix_volumes.txt will contain the element volumes.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 13 August 2009
//
// Author:
//
// John Burkardt
//
{
int element;
string prefix;
double[] tetra = new double[3 * 4];
Console.WriteLine("");
Console.WriteLine("");
Console.WriteLine("TET_MESH_VOLUMES");
Console.WriteLine(" Compute volume of each tetrahedron in a tet mesh..");
Console.WriteLine("");
//
// Get the filename prefix.
//
try
{
prefix = args[0];
}
catch
{
Console.WriteLine("");
Console.WriteLine("TET_MESH_VOLUMES:");
Console.WriteLine(" Please enter the filename prefix.");
prefix = Console.ReadLine();
}
//
// Create the filenames.
//
string node_filename = prefix + "_nodes.txt";
string element_filename = prefix + "_elements.txt";
string volume_filename = prefix + "_volumes.txt";
//
// Read the node data.
//
TableHeader h = typeMethods.r8mat_header_read(node_filename);
int dim_num = h.m;
int node_num = h.n;
Console.WriteLine("");
Console.WriteLine(" Read the header of \"" + node_filename + "\".");
Console.WriteLine("");
Console.WriteLine(" Spatial dimension DIM_NUM = " + dim_num + "");
Console.WriteLine(" Number of points NODE_NUM = " + node_num + "");
if (dim_num != 3)
{
Console.WriteLine("");
Console.WriteLine("TET_MESH_VOLUMES - Fatal error!");
Console.WriteLine(" Dataset must have spatial dimension 3.");
return;
}
double[] node_xyz = typeMethods.r8mat_data_read(node_filename, dim_num, node_num);
Console.WriteLine("");
Console.WriteLine(" Read the data in \"" + node_filename + "\".");
typeMethods.r8mat_transpose_print_some(dim_num, node_num, node_xyz, 1, 1, 5, 5,
" 5 by 5 portion of data read from file:");
//
// Read the tetra data.
//
h = typeMethods.i4mat_header_read(element_filename);
int element_order = h.m;
int element_num = h.n;
if (element_order != 4)
{
Console.WriteLine("");
Console.WriteLine("TET_MESH_VOLUMES - Fatal error!");
Console.WriteLine(" Data is not for a 4 node tet mesh.");
return;
}
Console.WriteLine("");
Console.WriteLine(" Read the header of \"" + element_filename + "\".");
Console.WriteLine("");
Console.WriteLine(" Tetrahedron order = " + element_order + "");
Console.WriteLine(" Number of tetras = " + element_num + "");
int[] element_node = typeMethods.i4mat_data_read(element_filename, element_order,
element_num);
Console.WriteLine("");
Console.WriteLine(" Read the data in \"" + element_filename + "\".");
typeMethods.i4mat_transpose_print_some(element_order, element_num,
element_node, 1, 1, element_order, 10, " Portion of ELEMENT_NODE:");
//
// If the element information is 1-based, make it 0-based.
//
TetMesh.tet_mesh_base_zero(node_num, element_order, element_num, ref element_node);
//
// Compute and print the quality measures.
//
double[] volume = new double[element_num];
for (element = 0; element < element_num; element++)
{
int j;
for (j = 0; j < 4; j++)
{
int i;
for (i = 0; i < 3; i++)
{
int node = element_node[j + element * element_order];
tetra[i + j * 3] = node_xyz[i + node * 3];
}
}
volume[element] = Tetrahedron.tetrahedron_volume(tetra);
}
double volume_max = typeMethods.r8vec_max(element_num, volume);
double volume_min = typeMethods.r8vec_min(element_num, volume);
double volume_ave = typeMethods.r8vec_mean(element_num, volume);
double volume_tot = typeMethods.r8vec_sum(element_num, volume);
double volume_var = typeMethods.r8vec_variance(element_num, volume);
Console.WriteLine("");
Console.WriteLine(" Minimum: " + volume_min + "");
Console.WriteLine(" Average: " + volume_ave + "");
Console.WriteLine(" Maximum: " + volume_max + "");
Console.WriteLine(" Total: " + volume_tot + "");
Console.WriteLine(" Variance: " + volume_var + "");
typeMethods.r8mat_write(volume_filename, 1, element_num, volume);
Console.WriteLine("");
Console.WriteLine(" Full list of volumes written to \"" + volume_filename + "\".");
Console.WriteLine("");
Console.WriteLine("TET_MESH_VOLUMES:");
Console.WriteLine(" Normal end of execution.");
Console.WriteLine("");
}
public static double[] projection(int fem_node_num, double[] fem_node_xyz,
int fem_element_order, int fem_element_num, int[] fem_element_node,
int[] fem_element_neighbor, int fem_value_dim, double[] fem_value,
int sample_node_num, double[] sample_node_xyz)
//****************************************************************************80
//
// Purpose:
//
// PROJECTION evaluates an FEM function on a T3 or T6 triangulation.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 27 August 2009
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int FEM_NODE_NUM, the number of nodes.
//
// Input, double FEM_NODE_XYZ[3*FEM_NODE_NUM], the coordinates
// of the nodes.
//
// Input, int FEM_ELEMENT_ORDER, the order of the elements.
//
// Input, int FEM_ELEMENT_NUM, the number of elements.
//
// Input, int FEM_ELEMENT_NODE(FEM_ELEMENT_ORDER,FEM_ELEMENT_NUM), the
// nodes that make up each element.
//
// Input, int FEM_ELEMENT_NEIGHBOR[4*FEM_ELEMENT_NUM], the
// index of the neighboring element on each side, or -1 if no neighbor there.
//
// Input, int FEM_VALUE_DIM, the "dimension" of the values.
//
// Input, double FEM_VALUE[FEM_VALUE_DIM*FEM_NODE_NUM], the
// finite element coefficient values at each node.
//
// Input, int SAMPLE_NODE_NUM, the number of sample nodes.
//
// Input, double SAMPLE_NODE_XYZ[3*SAMPLE_NODE_NUM], the sample nodes.
//
// Output, double PROJECTION[FEM_VALUE_DIM*SAMPLE_NODE_NUM],
// the sampled values.
//
{
int face = 0;
int j;
double[] p_xyz = new double[3];
int step_num = 0;
double[] b = new double[fem_element_order];
double[] sample_value = new double[fem_value_dim * sample_node_num];
double[] t_xyz = new double[3 * fem_element_order];
//
// For each sample point: find the element T that contains it,
// and evaluate the finite element function there.
//
for (j = 0; j < sample_node_num; j++)
{
p_xyz[0] = sample_node_xyz[0 + 3 * j];
p_xyz[1] = sample_node_xyz[1 + 3 * j];
p_xyz[2] = sample_node_xyz[2 + 3 * j];
//
// Find the triangle T that contains the point.
//
int t = TetMesh.tet_mesh_search_delaunay(fem_node_num, fem_node_xyz,
fem_element_order, fem_element_num, fem_element_node,
fem_element_neighbor, p_xyz, ref face, ref step_num);
switch (t)
{
case -1:
Console.WriteLine("");
Console.WriteLine("PROJECTION - Fatal error!");
Console.WriteLine(" Search failed.");
return(null);
}
//
// Evaluate the finite element basis functions at the point in T.
//
int t_node;
int i;
for (i = 0; i < fem_element_order; i++)
{
t_node = fem_element_node[i + t * fem_element_order];
t_xyz[0 + i * 3] = fem_node_xyz[0 + t_node * 3];
t_xyz[1 + i * 3] = fem_node_xyz[1 + t_node * 3];
t_xyz[2 + i * 3] = fem_node_xyz[2 + t_node * 3];
}
Basis_mn.basis_mn_tet4(t_xyz, 1, p_xyz, ref b);
//
// Multiply by the finite element values to get the sample values.
//
for (i = 0; i < fem_value_dim; i++)
{
double dot = 0.0;
int k;
for (k = 0; k < fem_element_order; k++)
{
t_node = fem_element_node[k + t * fem_element_order];
dot += fem_value[i + t_node * fem_value_dim] * b[k];
}
sample_value[i + j * fem_value_dim] = dot;
}
}
return(sample_value);
}
private static void Main(string[] args)
//****************************************************************************80
//
// Purpose:
//
// MAIN is the main program for TET_MESH_TO_XML.
//
// Discussion:
//
// TET_MESH_TO_XML converts a tet mesh, using 4 or 10 node
// tetrahedral elements, to a DOLFIN XML mesh file.
//
// Usage:
//
// tet_mesh_to_xml prefix
//
// where prefix is the common file prefix:
//
// * prefix_nodes.txt, the node coordinates;
// * prefix_elements.txt, the linear element definitions.
// * prefix.xml, the DOLFIN XML mesh file.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 04 June 2013
//
// Author:
//
// John Burkardt
//
// Reference:
//
// Anders Logg, Kent-Andre Mardal, Garth Wells,
// Automated Solution of Differential Equations by the Finite Element
// Method: The FEniCS Book,
// Lecture Notes in Computational Science and Engineering,
// Springer, 2011,
// ISBN13: 978-3642230981
//
{
string prefix;
Console.WriteLine("");
Console.WriteLine("TET_MESH_TO_XML;");
Console.WriteLine(" Convert a tet mesh to DOLFIN XML format");
Console.WriteLine("");
Console.WriteLine(" Read \"prefix\"_nodes.txt, node coordinates.");
Console.WriteLine(" Read \"prefix\"_elements.txt, 4, 10 or 20 node element definitions.");
Console.WriteLine("");
Console.WriteLine(" Create \"prefix\".xml, a corresponding DOLFIN XML mesh file.");
Console.WriteLine("");
//
// Get the filename prefix.
//
try
{
prefix = args[0];
}
catch
{
Console.WriteLine("");
Console.WriteLine("TET_MESH_TO_XML:");
Console.WriteLine(" Please enter the filename prefix.");
prefix = Console.ReadLine();
}
//
// Create the filenames.
//
string node_filename = prefix + "_nodes.txt";
string element_filename = prefix + "_elements.txt";
string xml_filename = prefix + ".xml";
//
// Read the node data.
//
TableHeader h = typeMethods.r8mat_header_read(node_filename);
int dim_num = h.m;
int node_num = h.n;
if (dim_num != 3)
{
Console.WriteLine("");
Console.WriteLine("TET_MESH_TO_XML; - Fatal error!");
Console.WriteLine(" The spatial dimension must be 3.");
return;
}
Console.WriteLine("");
Console.WriteLine(" Read the header of \"" + node_filename + "\".");
Console.WriteLine("");
Console.WriteLine(" Spatial dimension = " + dim_num + "");
Console.WriteLine(" Number of nodes = " + node_num + "");
double[] node_xyz = typeMethods.r8mat_data_read(node_filename, dim_num, node_num);
Console.WriteLine("");
Console.WriteLine(" Read the data in \"" + node_filename + "\".");
typeMethods.r8mat_transpose_print_some(dim_num, node_num,
node_xyz, 1, 1, dim_num, 5, " First 5 nodes:");
//
// Read the element data.
//
h = typeMethods.i4mat_header_read(element_filename);
int element_order = h.m;
int element_num = h.n;
switch (element_order)
{
case 4:
break;
case 10:
break;
case 20:
break;
default:
Console.WriteLine("");
Console.WriteLine("TET_MESH_TO_XML - Fatal error!");
Console.WriteLine(" The tet mesh must have order 4, 10, or 20.");
return;
}
Console.WriteLine("");
Console.WriteLine(" Read the header of \"" + element_filename + "\".");
Console.WriteLine("");
Console.WriteLine(" Element order = " + element_order + "");
Console.WriteLine(" Number of elements = " + element_num + "");
int[] element_node = typeMethods.i4mat_data_read(element_filename, element_order,
element_num);
Console.WriteLine("");
Console.WriteLine(" Read the data in \"" + element_filename + "\".");
typeMethods.i4mat_transpose_print_some(element_order, element_num,
element_node, 1, 1, element_order, 5, " First 5 elements:");
//
// Use 0-based indexing.
//
TetMesh.tet_mesh_base_zero(node_num, element_order, element_num, ref element_node);
//
// Write the DOLFIN XML file.
//
XML.xml_write(xml_filename, dim_num, node_num, node_xyz, element_order,
element_num, element_node);
Console.WriteLine("");
Console.WriteLine(" Created XML file \"" + xml_filename + "\".");
Console.WriteLine("");
Console.WriteLine("TET_MESH_TO_XML;");
Console.WriteLine(" Normal end of execution.");
Console.WriteLine("");
}
private static void Main(string[] args)
//****************************************************************************80
//
// Purpose:
//
// MAIN is the main program for FEM3D_PROJECT.
//
// Discussion:
//
// FEM3D_PROJECT reads files defining a sampling of a (scalar or vector)
// function of 3 arguments, and a list of nodes and tetrahedral elements
// to use for a finite element representation of the data.
//
// It computes a set of finite element coefficients to be associated with
// the given finite element mesh, and writes that information to a file
// so that an FEM representation is formed by the node, element and value
// files.
//
// Usage:
//
// fem3d_project sample_prefix fem_prefix
//
// where 'sample_prefix' is the common prefix for the SAMPLE files:
//
// * sample_prefix_nodes.txt, the node coordinates where samples were taken,
// * sample_prefix_elements.txt, the 4 nodes that make up each element;
// * sample_prefix_values.txt, the sample values.
//
// and 'fem_prefix' is the common prefix for the FEM files:
//
// * fem_prefix_nodes.txt, the node coordinates.
// * fem_prefix_elements.txt, the 4 nodes that make up each element;
// * fem_prefix_values.txt, the values defined at each node (output).
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 25 August 2009
//
// Author:
//
// John Burkardt
//
{
string fem_prefix;
int i;
int j;
string sample_prefix;
Console.WriteLine("");
Console.WriteLine("FEM3D_PROJECT");
Console.WriteLine("");
Console.WriteLine(" Read files defining a sampling of a function of 3 arguments.");
Console.WriteLine(" Read files defining a finite element mesh.");
Console.WriteLine(" Project the sample data onto the mesh, and");
Console.WriteLine(" write a file of FEM coefficient values.");
//
// Get the number of command line arguments.
//
try
{
sample_prefix = args[0];
}
catch
{
Console.WriteLine("");
Console.WriteLine("Enter the sample file prefix:");
sample_prefix = Console.ReadLine();
}
try
{
fem_prefix = args[1];
}
catch
{
Console.WriteLine("");
Console.WriteLine("Enter the FEM file prefix:");
fem_prefix = Console.ReadLine();
}
//
// Create the filenames.
//
string sample_node_filename = sample_prefix + "_nodes.txt";
string sample_element_filename = sample_prefix + "_elements.txt";
string sample_value_filename = sample_prefix + "_values.txt";
string fem_node_filename = fem_prefix + "_nodes.txt";
string fem_element_filename = fem_prefix + "_elements.txt";
string fem_value_filename = fem_prefix + "_values.txt";
//
// Read the SAMPLE NODE, ELEMENT and VALUE data.
//
TableHeader h = typeMethods.r8mat_header_read(sample_node_filename);
int sample_node_dim = h.m;
int sample_node_num = h.n;
Console.WriteLine("");
Console.WriteLine(" Sample node spatial dimension is " + sample_node_dim + "");
Console.WriteLine(" Sample node number is " + sample_node_num + "");
if (sample_node_dim != 3)
{
Console.WriteLine("");
Console.WriteLine("FEM3D_PROJECT - Fatal error!");
Console.WriteLine(" Spatial dimension of the sample nodes is not 3.");
return;
}
double[] sample_node_xyz = typeMethods.r8mat_data_read(sample_node_filename, sample_node_dim,
sample_node_num);
h = typeMethods.i4mat_header_read(sample_element_filename);
int sample_element_order = h.m;
int sample_element_num = h.n;
Console.WriteLine("");
Console.WriteLine(" Sample element order is " + sample_element_order + "");
Console.WriteLine(" Sample element number is " + sample_element_num + "");
if (sample_element_order != 4)
{
Console.WriteLine("");
Console.WriteLine("FEM3D_PROJECT - Fatal error!");
Console.WriteLine(" The sample element order must be 4.");
return;
}
int[] sample_element_node = typeMethods.i4mat_data_read(sample_element_filename,
sample_element_order, sample_element_num);
int element_min = typeMethods.i4mat_min(sample_element_order, sample_element_num,
sample_element_node);
switch (element_min)
{
case 1:
{
Console.WriteLine("");
Console.WriteLine(" Converting 1-based sample element array to 0 base.");
for (j = 0; j < sample_element_num; j++)
{
for (i = 0; i < sample_element_order; i++)
{
sample_element_node[i + j * sample_element_order] -= 1;
}
}
break;
}
}
h = typeMethods.r8mat_header_read(sample_value_filename);
int sample_value_dim = h.m;
int sample_value_num = h.n;
Console.WriteLine("");
Console.WriteLine(" The sample value dimension is " + sample_value_dim + "");
Console.WriteLine(" The sample value number is " + sample_value_num + "");
if (sample_value_num != sample_node_num)
{
Console.WriteLine("");
Console.WriteLine("FEM3D_PROJECT - Fatal error!");
Console.WriteLine(" Number of sample values and nodes differ.");
return;
}
double[] sample_value = typeMethods.r8mat_data_read(sample_value_filename, sample_value_dim,
sample_value_num);
//
// Create the sample element neighbor array.
//
int[] sample_element_neighbor = TetMesh.tet_mesh_neighbor_tets(sample_element_order,
sample_element_num, sample_element_node);
Console.WriteLine("");
Console.WriteLine(" The element neighbor array has been computed.");
//
// Read the FEM NODE and ELEMENT data.
//
h = typeMethods.r8mat_header_read(fem_node_filename);
int fem_node_dim = h.m;
int fem_node_num = h.n;
Console.WriteLine("");
Console.WriteLine(" The FEM node dimension is " + fem_node_dim + "");
Console.WriteLine(" The FEM node number is " + fem_node_num + "");
if (fem_node_dim != 3)
{
Console.WriteLine("");
Console.WriteLine("FEM3D_PROJECT - Fatal error!");
Console.WriteLine(" Spatial dimension of the nodes is not 3.");
return;
}
double[] fem_node_xyz = typeMethods.r8mat_data_read(fem_node_filename, fem_node_dim, fem_node_num);
h = typeMethods.i4mat_header_read(fem_element_filename);
int fem_element_order = h.m;
int fem_element_num = h.n;
Console.WriteLine(" The FEM element order is " + fem_element_order + "");
Console.WriteLine(" The FEM element number is " + fem_element_num + "");
if (fem_element_order != 4)
{
Console.WriteLine("");
Console.WriteLine("FEM3D_PROJECT - Fatal error!");
Console.WriteLine(" The FEM element order is not 4.");
return;
}
int[] fem_element_node = typeMethods.i4mat_data_read(fem_element_filename, fem_element_order,
fem_element_num);
element_min = typeMethods.i4mat_min(fem_element_order, fem_element_num,
fem_element_node);
switch (element_min)
{
case 1:
{
Console.WriteLine("");
Console.WriteLine(" Converting 1-based FEM element array to 0 base.");
for (j = 0; j < fem_element_num; j++)
{
for (i = 0; i < fem_element_order; i++)
{
fem_element_node[i + j * fem_element_order] -= 1;
}
}
break;
}
}
//
// Compute the FEM values.
//
double[] fem_value = FEM_3D_Transfer.fem3d_transfer(sample_node_num, sample_element_order,
sample_element_num, sample_value_dim, sample_value_num,
sample_node_xyz, sample_element_node, sample_element_neighbor, sample_value,
fem_node_num, fem_element_order,
fem_element_num, sample_value_dim, fem_node_num,
fem_node_xyz, fem_element_node);
//
// Write the FEM values.
//
typeMethods.r8mat_write(fem_value_filename, sample_value_dim, fem_node_num,
fem_value);
Console.WriteLine("");
Console.WriteLine(" FEM value data written to \"" + fem_value_filename + "\"");
//
// Terminate.
//
Console.WriteLine("");
Console.WriteLine("FEM3D_PROJECT");
Console.WriteLine(" Normal end of execution.");
Console.WriteLine("");
}