// get shape functions and optionally derivatives wrt x and y, but derivatives only work
// if it is a regular array. Shape functions are general
void Lagrange2D::ShapeFunction(Vector *xi,int getDeriv,double *sfxn,
double *xDeriv,double *yDeriv,double *zDeriv) const
{
sfxn[0]=0.25 * (xi->x-1.)*xi->x * (xi->y-1.)*xi->y; // (-1,-1)
sfxn[1]=0.25 * (xi->x+1.)*xi->x * (xi->y-1.)*xi->y; // (1,-1)
sfxn[2]=0.25 * (xi->x+1.)*xi->x * (xi->y+1.)*xi->y; // (1,1)
sfxn[3]=0.25 * (xi->x-1.)*xi->x * (xi->y+1.)*xi->y; // (-1,1)
sfxn[4]=0.5 * (1.-xi->x*xi->x) * (xi->y-1.)*xi->y; // (0,-1)
sfxn[5]=0.5 * (xi->x+1.)*xi->x * (1.-xi->y*xi->y); // (1,0)
sfxn[6]=0.5 * (1.-xi->x*xi->x) * (xi->y+1.)*xi->y; // (0,1)
sfxn[7]=0.5 * (xi->x-1.)*xi->x * (1.-xi->y*xi->y); // (-1,0)
sfxn[8]=(1.-xi->x*xi->x) * (1.-xi->y*xi->y); // (0,0)
if(getDeriv)
{ xDeriv[0]=0.5 * (2.*xi->x-1.) * (xi->y-1.)*xi->y/GetDeltaX(); // (-1,-1)
xDeriv[1]=0.5 * (2.*xi->x+1.) * (xi->y-1.)*xi->y/GetDeltaX(); // (1,-1)
xDeriv[2]=0.5 * (2.*xi->x+1.) * (xi->y+1.)*xi->y/GetDeltaX(); // (1,1)
xDeriv[3]=0.5 * (2.*xi->x-1.) * (xi->y+1.)*xi->y/GetDeltaX(); // (-1,1)
xDeriv[4]=(-2.*xi->x) * (xi->y-1.)*xi->y/GetDeltaX(); // (0,-1)
xDeriv[5]=(2.*xi->x+1.) * (1.-xi->y*xi->y)/GetDeltaX(); // (1,0)
xDeriv[6]=(-2.*xi->x) * (xi->y+1.)*xi->y/GetDeltaX(); // (0,1)
xDeriv[7]=(2.*xi->x-1.) * (1.-xi->y*xi->y)/GetDeltaX(); // (-1,0)
xDeriv[8]=2.0 * (-2.*xi->x) * (1.-xi->y*xi->y)/GetDeltaX(); // (0,0)
yDeriv[0]=0.5 * (xi->x-1.)*xi->x * (2.*xi->y-1.)/GetDeltaY(); // (-1,-1)
yDeriv[1]=0.5 * (xi->x+1.)*xi->x * (2.*xi->y-1.)/GetDeltaY(); // (1,-1)
yDeriv[2]=0.5 * (xi->x+1.)*xi->x * (2.*xi->y+1.)/GetDeltaY(); // (1,1)
yDeriv[3]=0.5 * (xi->x-1.)*xi->x * (2.*xi->y+1.)/GetDeltaY(); // (-1,1)
yDeriv[4]=(1.-xi->x*xi->x) * (2.*xi->y-1.)/GetDeltaY(); // (0,-1)
yDeriv[5]=(xi->x+1.)*xi->x * (-2.*xi->y)/GetDeltaY(); // (1,0)
yDeriv[6]=(1.-xi->x*xi->x) * (2.*xi->y+1.)/GetDeltaY(); // (0,1)
yDeriv[7]=(xi->x-1.)*xi->x * (-2.*xi->y)/GetDeltaY(); // (-1,0)
yDeriv[8]=2.0 * (1.-xi->x*xi->x) * (-2.*xi->y)/GetDeltaY(); // (0,0)
}
}
/**
* Calculate the average dy/dx over the whole window. This may only
* be called after HasEnoughData() has returned true.
*/
gcc_pure
double DeriveAverage() const {
auto delta_x = GetDeltaX();
auto delta_y = GetDeltaY();
return delta_y / delta_x;
}
/**
* Calculate the average dy/dx over the whole window. This may only
* be called after HasEnoughData() has returned true.
*/
gcc_pure
fixed DeriveAverage() const {
const fixed delta_x = GetDeltaX();
const fixed delta_y = GetDeltaY();
return delta_y / delta_x;
}