[XP1,XP2]=VL_WTPS(PHI,YP) computes the thin-plate spline (TPS) specified by the basis PHI and the warped control point Yp.

Yp is a 2xK matrix with one column per control point and the basis PHI is calculated by means of the VL_TPS function.

The thin-palte spline is defined on a domain X1,X2 and specified by a set of points Y and their warp YP. The spline passes interpolates exaclty the control points.

The parameters X1,X2 and Y are used to compute the basis PHI. This operation is fairily slow, but computing the spline for a given Yp is then very quick, as the operation is just a linear combination of the basis.

Example

To calculate the warped grid [X1,X2] by moving the control points Y to the control points YP use:

  [xp1,xp2]=VL_WTPS(VL_TPS(x1,x2,Y),Yp).