interp3d - 3d spline evaluation function

Calling Sequence

[fp[,dfpdx,dfpdy,dfpdz]]=interp3d(xp,yp,zp,tl,out_mode)

Parameters

• xp, yp, zp : real vectors or matrices of same size
• tl : tlist of type "splin3d", defining a 3d tensor spline (called s in the following)
• out_mode : (optionnal) string defining the evaluation of s outside the grid ([xmin,xmax]x[ymin,ymax]x[zmin,zmax])
• fp : vector or matrix of same format than xp , yp and zp , elementwise evaluation of s on these points.
• dfpdx, dfpdy, dfpdz : vectors (or matrices) of same format than xp , yp and zp , elementwise evaluation of the first derivatives of s on these points.

Description

Given a tlist tl defining a 3d spline function (see splin3d ) this function evaluates s (and ds/dx, ds/dy, ds/dz if needed) at (xp(i),yp(i),zp(i)) :

      zp(i) = s(xp(i),yp(i))   
      dzpdx(i) = ds/dx(xp(i),yp(i),zp(i))
      dzpdy(i) = ds/dy(xp(i),yp(i),zp(i))  
      dzpdz(i) = ds/dz(xp(i),yp(i),zp(i))
         

The out_mode parameter defines the evaluation rule for extrapolation, i.e. for (xp(i),yp(i),zp(i)) not in [xmin,xmax]x[ymin,ymax]x[zmin,zmax]:

     s(x,y) = s(proj(x,y)) where proj(x,y) is nearest point 
                           of [x(1),x(nx)]x[y(1),y(ny)] from (x,y)
         

Examples

// see the examples of the splin3d help page
 

See Also

splin3d ,   bsplin3val ,  

Authors

R.F. Boisvert, C. De Boor (code from the CMLIB fortran lib)

B. Pincon (scilab interface)