[Gmsh] Bump Equation

[Adam Zabriskie]

Hello,

I have been working on duplicating the transfinite bump using layers and
arrays.  I can't seem to figure out the equation or series used to compute
the location of each node on the line.  At first I thought it was a power
series like the transfinite progression is.  That didn't work though.  Below
are the two equations I thought would duplicate bump using layers.  Both
compare the layers with the actual transfinite line to ensure there are the
same number of nodes and the spacing is the same.

n=5; // Number of nodes
p=2; // Progression equations
a=(p-1)/(p^(n-1)-1);
Point(5)={0,-1,0,2};
Point(6)={10,-1,0,2};
Line(3)={5,6};
Transfinite Line{3}=n Using Progression p;

nod[0]=1;
spa[0]=a;
For i In {1:n-2}
   nod[i]=1;
   spa[i]=spa[i-1]+a*p^(i);
EndFor
Point(7)={0,-1.1,0,2};
Extrude {10,0,0} {Point{7}; Layers{nod[],spa[]};}

The next is about the same but for a reverse direction.

n=5; // Number of nodes
p=2; // Progression equations
a=(p-1)/(p^(n-1)-1);
Point(1)={0,0,0,2};
Point(2)={10,0,0,2};
Line(1)={1,2};
Transfinite Line{-1}=n Using Progression p;

nodes[n-2]=1;
spaces[n-2]=1;
For j In {n-3:0:-1}
  nodes[j]=1;
  spaces[j]=spaces[j+1]-a*p^(-j+n-3);
EndFor
Point(3)={0,.1,0,2};
Extrude {10,0,0} {Point{3}; Layers{nodes[],spaces[]};}

If anyone has any code for creating a similar node map using layers which
represents a transfinite line using bump, could you post it?  Or if you know
how Gmsh computes the spacing for each node in bump, then could you post
that?

Thank you,
Adam Z.
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