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# bsplin3val

3d spline arbitrary derivative evaluation function

### Calling Sequence

[dfp]=bsplin3val(xp,yp,zp,tl,der)

### Arguments

- 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)- der
vector with 3 components

`[ox,oy,oz]`

defining which derivative of`s`

to compute.- dfp
vector or matrix of same format than

`xp`

,`yp`

and`zp`

, elementwise evaluation of the specified derivative of`s`

on these points.

### Description

While the function interp3d may
compute only the spline `s`

and its first derivatives,
`bsplin3val`

may compute any derivative of
`s`

. The derivative to compute is specified by the
argument `der=[ox,oy,oz]`

:

So `der=[0 0 0]`

corresponds to
*s*, `der=[1 0 0]`

to
*ds/dx*, `der=[0 1 0]`

to
*ds/dy*, `der=[1 1 0]`

to
*d2s/dxdy*, etc...

For a point with coordinates
*(xp(i),yp(i),zp(i))* outside the grid, the function
returns 0.

### Examples

deff("v=f(x,y,z)","v=cos(x).*sin(y).*cos(z)"); deff("v=fx(x,y,z)","v=-sin(x).*sin(y).*cos(z)"); deff("v=fxy(x,y,z)","v=-sin(x).*cos(y).*cos(z)"); deff("v=fxyz(x,y,z)","v=sin(x).*cos(y).*sin(z)"); deff("v=fxxyz(x,y,z)","v=cos(x).*cos(y).*sin(z)"); n = 20; // n x n x n interpolation points x = linspace(0,2*%pi,n); y=x; z=x; // interpolation grid [X,Y,Z] = ndgrid(x,y,z); V = f(X,Y,Z); tl = splin3d(x,y,z,V,[5 5 5]); // compute f and some derivates on a point // and compare with the spline interpolant xp = grand(1,1,"unf",0,2*%pi); yp = grand(1,1,"unf",0,2*%pi); zp = grand(1,1,"unf",0,2*%pi); f_e = f(xp,yp,zp) f_i = bsplin3val(xp,yp,zp,tl,[0 0 0]) fx_e = fx(xp,yp,zp) fx_i = bsplin3val(xp,yp,zp,tl,[1 0 0]) fxy_e = fxy(xp,yp,zp) fxy_i = bsplin3val(xp,yp,zp,tl,[1 1 0]) fxyz_e = fxyz(xp,yp,zp) fxyz_i = bsplin3val(xp,yp,zp,tl,[1 1 1]) fxxyz_e = fxxyz(xp,yp,zp) fxxyz_i = bsplin3val(xp,yp,zp,tl,[2 1 1])

### Authors

- R.F. Boisvert, C. De Boor (code from the CMLIB fortran lib)
- B. Pincon (scilab interface)

## Comments

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