interp3d — 3d spline evaluation function
[fp[,dfpdx,dfpdy,dfpdz]]=interp3d(xp,yp,zp,tl,out_mode)
real vectors or matrices of same size
tlist of type "splin3d", defining a 3d tensor spline (called s
in the following)
(optional) string defining the evaluation of s
outside the grid
([xmin,xmax]x[ymin,ymax]x[zmin,zmax])
vector or matrix of same format than xp
, yp
and zp
,
elementwise evaluation of s
on these points.
vectors (or matrices) of same format than xp
, yp
and zp
,
elementwise evaluation of the first derivatives of s
on these points.
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]:
an extrapolation by zero is done
extrapolation by Nan
the extrapolation is defined as follows :
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)
: s
is extended by periodicity.