mat Scheme::implicitScheme(int nSteps, double tSteps, double(*u_s)(double))
{
//input: nSteps (# of interior points), time, tSteps, u_s(x)
double deltaX = 1.0 / (nSteps + 1);
double deltaT = 1.0 / tSteps;
double alpha = deltaT / pow(deltaX,2);
vec v(nSteps), vNext(nSteps), u(nSteps);
int printIndex = tSteps / 10;
mat M(printIndex, nSteps);
int index = 0;
for( int i = 0; i < nSteps; i++)
{
double x = (i + 1) * deltaX;
vNext[i] = v[i] = -u_s(x);
}
// Boundary conditions
v[0] = vNext[0] = v[nSteps] = vNext[nSteps] = 0;
double a = -alpha; // diagonal element
double b = 1 + 2*alpha; // off-diagonal element
Solver solv = Solver();
for(int t = 1; t <= tSteps; t++)
{
solv.tridiagonalSolver(a, b, v, vNext);
// Initial conditions
vNext[0] = vNext[nSteps] = 0;
v = vNext;
for (int i = 0; i < nSteps; i++)
{
double x = (i + 1) * deltaX;
u[i] = v[i] + u_s(x);
}
// Print to file !
if (t % 10 == 0)
{
for (int i = 0; i < nSteps; i++)
M(index, i) = u[i];
index++;
}
}
for (int i = 0; i < printIndex; i++)
{
for (int j = 0; j < nSteps; j++)
printf("%f \t", M(i, j));
}
return M;
}
mat Scheme::explicitScheme(int nSteps, double tSteps, double(*u_s)(double))
{
//input: nSteps , time, u_s(x)
double deltaX = 1.0 / (float)(nSteps + 1);
double alpha = 0.4;
double deltaT = alpha * pow(deltaX, 2);
//double
tSteps = 1.0 / deltaT;
vec v(nSteps), vNext(nSteps), u(nSteps);
int printIndex = tSteps / 10;
mat M(printIndex, nSteps);
int index = 0;
//Initialization
for (int i = 1; i < nSteps; i++)
{
double x = (i + 1) * deltaX;
v(i) = -u_s(x);
}
// Boundary conditions
v[0] = vNext[0] = 0;
v[nSteps] = vNext[nSteps] = 0;
//
for(int t = 1; t <= tSteps; t ++)
{
if ((t - 1) % 204 == 0)
{
for (int i = 0; i < nSteps; i++)
printf("%f \t", v(i));
printf("\n");
}
for(int i = 1; i < nSteps; i++ )
{
vNext[i] = (1 - 2 * alpha) * v[i];
double truc = vNext[i]; // XX
if( i > 0 )
vNext[i] += alpha * v[i-1]; // else += 0
if( i < nSteps )
vNext[i] += alpha * v[i+1]; // else += 0
}
v = vNext;
/*if ((t - 1) % 204 == 0)
{
for (int i = 0; i < nSteps; i++)
printf("%f \t", v(i));
printf("\n");
}*/
for (int i = 0; i < nSteps; i++)
{
double x = (i + 1) * deltaX;
u[i] = v[i] + u_s(x);
}
// Print to file !
if (t % 10 == 0)
{
for (int i = 0; i < nSteps; i++)
M(index, i) = u[i];
index++;
}
}
for (int i = 0; i < printIndex; i++)
{
for (int j = 0; j < nSteps; j++)
printf("%f \t", M(i, j));
}
return M;
}
mat Scheme::crankNicolsonScheme(int nSteps, double tSteps, double(*u_s)(double))
{
//input: nSteps (# of interior points), time, tSteps, u_s(x)
double deltaX = 1.0 / (nSteps + 1);
double deltaT = 1.0 / tSteps;
double alpha = deltaT / pow(deltaX,2);
vec v(nSteps), w(nSteps), u(nSteps);
int printIndex = tSteps / 10;
mat M(printIndex, nSteps);
int index = 0;
for(int i = 0; i < nSteps; i++)
{
double x = (i + 1) * deltaX;
v[i] = -u_s(x);
}
// Boundary conditions
v[0] = w[0] = v[nSteps] = w[nSteps] = 0;
double a = 2 * (1 + alpha); // diagonal element
double b = -alpha; // off-diagonal element
Solver solv = Solver();
for(int t = 1; t <= tSteps; t++)
{
for( int i = 0; i < nSteps; i++ )
{
w[i] = 2 * (1 - alpha) * v[i];
if( i > 0 )
w[i] += alpha * v[i - 1]; // else += 0
if( i < nSteps - 1 )
w[i] += alpha * v[i + 1]; // else += 0
}
solv.tridiagonalSolver(a, b, w, v);
// Boundary conditions:
v[0] = v[nSteps] = 0;
for (int i = 0; i < nSteps; i++)
{
double x = (i + 1) * deltaX;
u[i] = v[i] + u_s(x);
}
// Print to file !
if (t % 10 == 0)
{
for (int i = 0; i < nSteps; i++)
M(index, i) = u[i];
index++;
}
}
for (int i = 0; i < printIndex; i++)
{
for (int j = 0; j < nSteps; j++)
printf("%f \t", M(i, j));
}
return M;
}
void exportTerrain::printPolygonData(const MFnMesh &theMesh,const bool phy)
{
MStatus status;
MPointArray vertices;
MIntArray perPolyVertices, numVerticesPerPoly;
MVector tNorm;
MVectorArray perVertexNormals, normals;
MItMeshPolygon itPoly( theMesh.object() );
long numPolygons = theMesh.numPolygons();
long numVertices = theMesh.numVertices();
theMesh.getPoints(vertices);
fout << "Vertices: " << endl;
fout << "Number of Vertices: " << numVertices << endl;
fout << vertices << endl;
fout << "Number of polygons: " << numPolygons << endl;
fout << "Polygon Connection List:" << endl;
fout << "[";
for(int i = 0; i < numPolygons - 1; ++i){
fout << i << ": ";
status = theMesh.getPolygonVertices(i, perPolyVertices);
fout << perPolyVertices;
fout << ", " << endl;
}
//last is a special case
fout << numPolygons -1 << ": ";
status = theMesh.getPolygonVertices(numPolygons -1, perPolyVertices);
fout << perPolyVertices;
fout << "]" << endl;
//Per Vertex Normals
for(i=0; i < numVertices; ++i){
theMesh.getVertexNormal( i, tNorm);
perVertexNormals.append(tNorm);
}
fout << "Per Vertex Normals: \n";
fout << perVertexNormals << endl;
/* //per vertex per polygon Normals
//Not supported by the Reaper graphic engine
fout << "Normals" << endl;
i = 0;
fout << "[ ";
while (!itPoly.isDone() ){
itPoly.getNormals(normals);
fout << i << ": " << normals << endl;
++i;
itPoly.next();
}
fout << " ]" << endl;
*/
if( !phy ){
//Texture coordinate information
MIntArray ids;
int index;
MFloatArray Us, Vs;
theMesh.getUVs(Us,Vs);
MFloatArray u_s(numVertices),v_s(numVertices);
MIntArray numuvs(numVertices,0);
//Now the tactic is:
//Iterate over all polygons, and for each vertex read out the UV out of the list
//Insert that in two float arrays, and keep track of how many uvs
//that have been inserted. At last divd the us and vs by the number you
//already go there
//Shared uvs will look strange, but it is the average uvs that is shown
//Make sure to model using no shared uvs
for(i = 0;i<numPolygons;++i){
MIntArray polyVertices;
theMesh.getPolygonVertices(i,polyVertices);
for(int j = 0;j<polyVertices.length();++j){
int uv_id;
theMesh.getPolygonUVid(i,j,uv_id);
u_s[polyVertices[j]] += Us[uv_id];
v_s[polyVertices[j]] += Vs[uv_id];
numuvs[polyVertices[j]]+=1;
}
}
for(int k = 0;k<numVertices;++k){
u_s[k] /= numuvs[k];
v_s[k] /= numuvs[k];
}
fout << "Texture Coordinates: \n";
fout << "[" ;
for(index = 0;index < (u_s.length() - 1); ++index){
fout << index << ": [" << u_s[index] << ", " <<
v_s[index] << "]," << endl;
}
//last is a special case
fout << index << ": [" << u_s[index] << ", " <<
v_s[index] << "]";
fout << "]" << endl;
//Color data, for coloring. Make sure
MItMeshVertex vertexIt(theMesh.object());
MColor color;
std::vector<MColor> colorArray;
while (!vertexIt.isDone() ){
vertexIt.getColor(color);
colorArray.push_back(color);
vertexIt.next();
}
fout << "PerVertexColors: \n";
fout << "[" ;
for(index = 0;index < colorArray.size()-1; ++index){
fout << index << ": " << colorArray[index] << "," << endl;
}
//last is a special case
fout << index << ": " << colorArray[index];
fout << "]" << endl;
}
}
