[R] interpolation and extremum location of a surface‏

[Clement LAUZIN]

Hello,
 
I have a x,y,z file.Z is not corresponding to a simple analytical function of x and y (see below).
I am trying to find the minimum location of this surface and the z value corresponding to this location by a spline interpolation or from a polynomial fit.
I tried with the akima package but as the location of the point I am looking for (the minimum) is outside of the convex hull it's not giving any answer.
If someone has any idea or any suggestion?
 
Thank you in advance Pierre 
 
 
x    y    z
4.1 60 -152.1719593
4.1 75 -171.136801
4.1 90 -170.4604774
4.2 60 -168.7745552
4.2 75 -174.9667333
4.2 90 -172.1853334
4.3 60 -173.7736418
4.3 75 -171.6712745
4.3 90 -167.6662458
4.05 60 -137.8379387
4.15 60 -162.2264066
4.25 60 -172.4453286
4.35 60 -173.2123715
4.05 67.5 -158.8239625
4.1 67.5 -167.314534
4.15 67.5 -172.586182
4.2 67.5 -175.2217594
4.25 67.5 -175.7162683
4.3 67.5 -174.4890566
4.35 67.5 -171.8940061
4.05 75 -165.4388778
4.15 75 -174.1460392
4.25 75 -174.022344
4.35 75 -168.2149168
4.05 82.5 -166.4026077
4.1 82.5 -170.9199652
4.15 82.5 -172.9923449
4.2 82.5 -173.0803255
4.25 82.5 -171.5739101
4.3 82.5 -168.8024715
4.35 82.5 -165.0431276
4.05 90 -166.2592978
4.15 90 -172.2861302
4.25 90 -170.5383652
4.35 90 -163.8389615