dMatrix clSpline::GetCoordinates(const dMatrix &uSpec)
{
dMatrix coord;
if(uSpec.GetNumberColumns() != 1 || uSpec.GetNumberRows() == 0)
{
throw clException("clSpline", "GetCoordinates", "Invalid dimensions of matrix uSpec.");
}
else
{
coord.SetNumberRows(uSpec.GetNumberRows());
coord.SetNumberColumns(3);
if(!initialised)
{
Initialise();
}
// Do for all specified u's
for(int i=1; i<=uSpec.GetNumberRows(); i++)
{
if(uSpec(i, 1) < 0 || uSpec(i, 1) > 1)
{
throw clException("clSpline", "GetCoordinates", "Invalid value for uSpec.");
}
else
{
// Now find the position of uSpec
double uu = uSpec(i, 1)*GetSplineLength();
int j = 1;
while((uu - u(j+1, 1) > 0) && (j<u.GetNumberRows()-1))
{
j++;
}
// Now calculate the coefficients
double A = (u(j+1, 1)-uu)/(u(j+1, 1)-u(j,1));
double B = 1-A;
double C = (A*A*A-A)/6 * (u(j+1, 1)-u(j, 1))*(u(j+1, 1)-u(j, 1));
double D = (B*B*B-B)/6 * (u(j+1, 1)-u(j, 1))*(u(j+1, 1)-u(j, 1));
// Finally calculate the coordinates
coord.SetElement(i, 1, A*X(j, 1) + B*X(j+1, 1) + C*X2(j, 1) + D*X2(j+1, 1));
coord.SetElement(i, 2, A*Y(j, 1) + B*Y(j+1, 1) + C*Y2(j, 1) + D*Y2(j+1, 1));
coord.SetElement(i, 3, A*Z(j, 1) + B*Z(j+1, 1) + C*Z2(j, 1) + D*Z2(j+1, 1));
}
}
}
return (coord);
}
void clSpline::FirstDerivatives(void)
{
double deltaU;
double deltaX;
double deltaY;
double deltaZ;
// Get maximum number of rows
int rmax = u.GetNumberRows();
X1.SetNumberRows(rmax); X1.SetNumberColumns(1);
Y1.SetNumberRows(rmax); Y1.SetNumberColumns(1);
Z1.SetNumberRows(rmax); Z1.SetNumberColumns(1);
for(int r=1; r<rmax; r++)
{
deltaU = u.GetElement(r+1, 1) - u.GetElement(r, 1);
if(fabs(deltaU)<PRECISION)
{
deltaU = PRECISION;
//throw clException("clSpline", "FirstDerivatives", "Division by zero.");
}
deltaX = X.GetElement(r+1, 1) - X.GetElement(r, 1);
deltaY = Y.GetElement(r+1, 1) - Y.GetElement(r, 1);
deltaZ = Z.GetElement(r+1, 1) - Z.GetElement(r, 1);
X1.SetElement(r, 1, fabs(deltaX)*(deltaX/deltaU - deltaU*X2(r, 1)/3.0 - deltaU*X2(r+1, 1)/6.0));
Y1.SetElement(r, 1, fabs(deltaY)*(deltaY/deltaU - deltaU*Y2(r, 1)/3.0 - deltaU*Y2(r+1, 1)/6.0));
Z1.SetElement(r, 1, fabs(deltaZ)*(deltaZ/deltaU - deltaU*Z2(r, 1)/3.0 - deltaU*Z2(r+1, 1)/6.0));
}
// Do last control point; work backwards
deltaU = u.GetElement(rmax-1, 1) - u.GetElement(rmax, 1);
if(fabs(deltaU)<PRECISION)
{
deltaU = PRECISION;
//throw clException("clSpline", "FirstDerivatives", "Division by zero.");
}
deltaX = X.GetElement(rmax-1, 1) - X.GetElement(rmax, 1);
deltaY = Y.GetElement(rmax-1, 1) - Y.GetElement(rmax, 1);
deltaZ = Z.GetElement(rmax-1, 1) - Z.GetElement(rmax, 1);
X1.SetElement(rmax, 1, fabs(deltaX)*(deltaX/deltaU - deltaU*X2(rmax, 1)/3.0 - deltaU*X2(rmax-1, 1)/6.0));
Y1.SetElement(rmax, 1, fabs(deltaY)*(deltaY/deltaU - deltaU*Y2(rmax, 1)/3.0 - deltaU*Y2(rmax-1, 1)/6.0));
Z1.SetElement(rmax, 1, fabs(deltaZ)*(deltaZ/deltaU - deltaU*Z2(rmax, 1)/3.0 - deltaU*Z2(rmax-1, 1)/6.0));
}
void VectorCurve::loadData()
{
int xcol = d_table->colIndex(d_x_column);
int ycol = d_table->colIndex(title().text());
int endXCol = d_table->colIndex(d_end_x_a);
int endYCol = d_table->colIndex(d_end_y_m);
int rows = abs(d_end_row - d_start_row) + 1;
QVector<double> X(rows), Y(rows), X2(rows), Y2(rows);
int size = 0;
for (int i = d_start_row; i <= d_end_row; i++)
{
QString xval = d_table->text(i, xcol);
QString yval = d_table->text(i, ycol);
QString xend = d_table->text(i, endXCol);
QString yend = d_table->text(i, endYCol);
if (!xval.isEmpty() && !yval.isEmpty() && !xend.isEmpty() && !yend.isEmpty())
{
Y[size] = yval.toDouble();
X[size] = xval.toDouble();
Y2[size] = yend.toDouble();
X2[size] = xend.toDouble();
size++;
}
}
if (!size)
return;
X.resize(size); Y.resize(size); X2.resize(size); Y2.resize(size);
setData(X.data(), Y.data(), size);
foreach(DataCurve *c, d_error_bars)
c->setData(X.data(), Y.data(), size);
setVectorEnd(X2, Y2);
}
void cpp_wrap_Y2(const double* gamma_,
const double* vM_,
const unsigned int& m,
const unsigned int& n,
double* Y2_) {
Y2(gamma_,vM_,m,n,Y2_);
}
dMatrix clSpline::GetSecondDerivatives(void)
{
dMatrix dummy;
if(!initialised)
{
Initialise();
}
dummy.SetNumberRows(X2.GetNumberRows());
dummy.SetNumberColumns(3);
for(int i=1; i<=X2.GetNumberRows(); i++)
{
dummy.SetElement(i, 1, fabs(X2(i, 1)) < PRECISION ? 0.0 : X2(i, 1));
dummy.SetElement(i, 2, fabs(Y2(i, 1)) < PRECISION ? 0.0 : Y2(i, 1));
dummy.SetElement(i, 3, fabs(Z2(i, 1)) < PRECISION ? 0.0 : Z2(i, 1));
}
return(dummy);
}
void VectorCurve::loadData() {
if (!plot())
return;
int xcol = d_table->colIndex(d_x_column);
int ycol = d_table->colIndex(title().text());
int endXCol = d_table->colIndex(d_end_x_a);
int endYCol = d_table->colIndex(d_end_y_m);
int rows = abs(d_end_row - d_start_row) + 1;
QVector<double> X(rows), Y(rows), X2(rows), Y2(rows);
int size = 0;
QLocale locale = plot()->locale();
for (int i = d_start_row; i <= d_end_row; i++) {
QString xval = d_table->text(i, xcol);
QString yval = d_table->text(i, ycol);
QString xend = d_table->text(i, endXCol);
QString yend = d_table->text(i, endYCol);
if (!xval.isEmpty() && !yval.isEmpty() && !xend.isEmpty() &&
!yend.isEmpty()) {
bool valid_data = true;
X[size] = locale.toDouble(xval, &valid_data);
if (!valid_data)
continue;
Y[size] = locale.toDouble(yval, &valid_data);
if (!valid_data)
continue;
X2[size] = locale.toDouble(xend, &valid_data);
if (!valid_data)
continue;
Y2[size] = locale.toDouble(yend, &valid_data);
if (valid_data)
size++;
}
}
if (!size)
return;
X.resize(size);
Y.resize(size);
X2.resize(size);
Y2.resize(size);
setData(X.data(), Y.data(), size);
foreach (DataCurve *c, d_error_bars)
c->setData(X.data(), Y.data(), size);
setVectorEnd(X2, Y2);
}
int main(int argc, char** argv) {
int l=5;
TinyVector<double,3> pos(0.1,0.3,-0.45), deltax(0.0001,0.0,0.0), deltay(0.0,0.0001,0.0), deltaz(0.0,0.0,0.0001), tpos, g;
if(argc>1) l = atoi(argv[1]);
if(argc>4) {
pos[0] = atof(argv[2]);
pos[1] = atof(argv[3]);
pos[2] = atof(argv[4]);
}
SphericalTensor<double,TinyVector<double,3> > Y1(l,true), Y2(l,true), Yp(l,true), Ym(l,true);
Y1.evaluate(pos);
std::cout.setf(std::ios::scientific, std::ios::floatfield);
for(int lm=0; lm<Y1.size(); lm++) {
std::cout << lm << std::endl;
std::cout << std::setw(20) << std::setprecision(12) << Y1.Ylm[lm]
<< std::setprecision(12) << Y1.gradYlm[lm] << std::endl;
//std::cout << std::setw(20) << std::setprecision(12) << Y2.Ylm[lm]
// << std::setprecision(12) << Y2.gradYlm[lm] << std::endl;
}
// for(int lm=0; lm<Y1.size(); lm++) {
// tpos = pos+deltax; Yp.evaluate(tpos);
// tpos = pos-deltax; Ym.evaluate(tpos);
// g[0] = (Yp.Ylm[lm]-Ym.Ylm[lm])/0.0002;
// tpos = pos+deltay; Yp.evaluate(tpos);
// tpos = pos-deltay; Ym.evaluate(tpos);
// g[1] = (Yp.Ylm[lm]-Ym.Ylm[lm])/0.0002;
// tpos = pos+deltaz; Yp.evaluate(tpos);
// tpos = pos-deltaz; Ym.evaluate(tpos);
// g[2] = (Yp.Ylm[lm]-Ym.Ylm[lm])/0.0002;
// std::cout << lm << std::endl;
// std::cout << std::setw(20) << std::setprecision(12) << Y1.Ylm[lm]
// << std::setprecision(12) << Y1.gradYlm[lm] - g << std::endl;
// }
}
function<RT(ArgT...)> Y2(function<RT(function<RT(ArgT...)>, ArgT...)> f) {
return [f](ArgT&& ...arg)->RT{ return f(Y2(f), forward<ArgT>(arg) ...); };
}
void bench_r2d_proj()
{
Pt2di sz(120,50);
Im2D_REAL8 MNT(sz.x,sz.y,0.0);
Im2D_REAL8 X1(sz.x,sz.y,0.0);
Im2D_REAL8 Y1(sz.x,sz.y,0.0);
Im2D_REAL8 X2(sz.x,sz.y,0.0);
Im2D_REAL8 Y2(sz.x,sz.y,0.0);
ELISE_COPY(MNT.all_pts(),frandr(),MNT.out());
ELISE_COPY
(
MNT.all_pts(),
proj_cav(MNT.in(),0.5,2.0),
Virgule(X1.out(),Y1.out())
);
ELISE_COPY
(
MNT.lmr_all_pts(Pt2di(1,0)),
proj_cav(MNT.in(),0.5,2.0),
Virgule(X2.out(),Y2.out())
);
REAL dif;
ELISE_COPY
(
MNT.all_pts(),
Max(Abs(X1.in()-X2.in()),Abs(Y1.in()-Y2.in())),
VMax(dif)
);
BENCH_ASSERT(dif<epsilon);
ELISE_COPY
(
MNT.all_pts(),
(2*PI)*phasis_auto_stereogramme(MNT.in(),10.5,2.0),
X1.out()
);
ELISE_COPY
(
MNT.lmr_all_pts(Pt2di(1,0)),
(2*PI)*phasis_auto_stereogramme(MNT.in(),10.5,2.0),
X2.out()
);
ELISE_COPY
(
MNT.all_pts(),
Max
(
Abs(cos(X1.in())-cos(X2.in())),
Abs(sin(X1.in())-sin(X2.in()))
),
VMax(dif)
);
BENCH_ASSERT(dif<epsilon);
}
double C_Rect::diagonale(void) const
{
double x = X2() - X1();
double y = Y2() - Y1();
return double(sqrt(x*x+y*y));
}
/* readonly attribute nsIDOMSVGAnimatedLength y2; */
NS_IMETHODIMP SVGLinearGradientElement::GetY2(nsIDOMSVGAnimatedLength * *aY2)
{
*aY2 = Y2().get();
return NS_OK;
}
