Does the camera calibration take into consideration other type of x,y corrected relations that can include other fctors like k1, k2, p1, p2, p3, p4 instead of only k1, k1, p1, p2, k3

edit

So instead of using the following:

Xcorrected=x(1+k1*r^2+k2*r^4+k3*r^6)
Ycorrected=y(1+k1*r^2+k2*r^4+k3*r^6)

I want to use:

Xcorrected=Xd+(Xd-Xc)*(k1*r^2+k2*r^4)+(P1(r^2+2*(Xd-Xc)^2)+2P2(Xd-Xc)*(Yd-Yc))*(1+P3*r^2+P4*r^4)
Ycorrected=Yd+(Yd-Xc)*(k1*r^2+k2*r^4)+(2*P1(Xd-Xc)*(Yd-Yc)+P1(r^2+2*(Yd-Yc)^2)*(1+P3*r^2+P4*r^4)

And if not how can I do that??