The relief -modulus- of the function exp(1/z) defined by means of three bidimensional fields [Le relief -module- de la fonction exp(1/z) défini à l'aide de trois champs bidimensionnels].




Nota: the {X,Y,Z} axis colors are {Red,Green,Blue} respectively.


Many surfaces -bidimensional manifolds- in a tridimensional space can be defined using a set of three equations:
                    X = F (u,v)
                         x
                    Y = F (u,v)
                         y
                    Z = F (u,v)
                         z
with:
                    u E [U   ,U   ]
                          min  max
                    v E [V   ,V   ]
                          min  max
[Umin,Umax]x[Vmin,Vmax] then defined a bidimensional rectangular domain D.
                       v ^
                         |
                    V    |...... ---------------------------
                     max |      |+++++++++++++++++++++++++++|
                         |      |+++++++++++++++++++++++++++|
                         |      |+++++++++++++++++++++++++++|
                         |      |+++++++++++++++++++++++++++|
                         |      |+++++++++++++++++++++++++++|
                         |      |+++++++++++++++++++++++++++|
                         |      |+++++++++++++++++++++++++++|
                         |      |+++++++++++++++++++++++++++|
                         |      |+++++++++++++++++++++++++++|
                    V    |...... ---------------------------
                     min |      :                           :
                         |      :                           :
                         O------------------------------------------------->
                                U                           U              u
                                 min                         max

If D is sampled by means of a bidimensional rectangular grid (made of Nu.Nv points), the three {X,Y,Z} coordinates can be defined by means of three rectangular matrices:
                    X = M (i,j)
                         x
                    Y = M (i,j)
                         y
                    Z = M (i,j)
                         z
with:
                    i = f(u,U   ,U   ,N )
                             min  max  u
                    j = g(v,V   ,V   ,N )
                             min  max  v
where 'f' and 'g' denote two obvious linear functions...


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For the relief -modulus- of the function exp(1/z), the three {X,Y,Z} fields/matrices are as follows:




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