WIP: Support for curvilinear coordinates

[darwindarak]

It almost works!

θ = linspace(0,2π,10)
R = linspace(1,3, 10)
ζ = Complex128[r*exp(im*ϕ) for ϕ in θ, r in R]
x, y, z = real(ζ), imag(ζ), abs(ζ)

so z has the form

10x10 Array{Float64,2}:
 1.0  1.22222  1.44444  1.66667  1.88889  2.11111  2.33333  2.55556  2.77778  3.0
 1.0  1.22222  1.44444  1.66667  1.88889  2.11111  2.33333  2.55556  2.77778  3.0
 1.0  1.22222  1.44444  1.66667  1.88889  2.11111  2.33333  2.55556  2.77778  3.0
 1.0  1.22222  1.44444  1.66667  1.88889  2.11111  2.33333  2.55556  2.77778  3.0
 1.0  1.22222  1.44444  1.66667  1.88889  2.11111  2.33333  2.55556  2.77778  3.0
 1.0  1.22222  1.44444  1.66667  1.88889  2.11111  2.33333  2.55556  2.77778  3.0
 1.0  1.22222  1.44444  1.66667  1.88889  2.11111  2.33333  2.55556  2.77778  3.0
 1.0  1.22222  1.44444  1.66667  1.88889  2.11111  2.33333  2.55556  2.77778  3.0
 1.0  1.22222  1.44444  1.66667  1.88889  2.11111  2.33333  2.55556  2.77778  3.0
 1.0  1.22222  1.44444  1.66667  1.88889  2.11111  2.33333  2.55556  2.77778  3.0

which would look like straight lines if plotted in rectangular coordinates. But if the matrices x and y that contain the coordinate points are passed in, we get

There are still a few kinks to work out though. For example:

θ = linspace(0,2π,100);
R = linspace(1,2, 50);
ζ = Complex128[r*exp(im*ϕ) for ϕ in θ, r in R];
x, y = real(ζ), imag(ζ);
z = imag(ζ .+ conj(1./ζ));

results in

[coveralls]

Coverage remained the same when pulling ee1173f on dd/curvilinear_coords into 2d5ca7d on master.

[tomasaschan]

Very cool! I have no idea what the quirks are about, but I'm sure you'll find it =)

I have a couple of concerns about argument types for some of these, but that should be quite easy to fix. I'll comment on the relevant code lines separately.

[tomasaschan]

Do we really need to enforce Vector{Float64} here? I suggest AbstractVector{T}, or even just AbstractVector. I guess the point is to distinguish from the method that takes a matrix below, but since the only important type parameter is the dimension (1 vs 2), we should try to keep everything else as generic as possible.

[darwindarak]

That makes sense. I think the only requirement we need is for the type to have arithmetic functions defined for it.

[coveralls]

Coverage remained the same when pulling ef83904 on dd/curvilinear_coords into 2d5ca7d on master.

[coveralls]

Coverage remained the same when pulling e048006 on dd/curvilinear_coords into 2d5ca7d on master.

[darwindarak]

I think I fixed it, so now we can make plots like this:

without having to do too many coordinate transforms.

[coveralls]

Coverage remained the same when pulling 3b64d19 on dd/curvilinear_coords into 2d5ca7d on master.

[tomasaschan]

Nice!

Still needs documentation, though, even though these examples are a good starting point - I'd need a mathematical description of how to create x and y to understand how to do it for whatever system I'm working in.

[darwindarak]

Yeah, definitely. I'll add the documentation as soon as I can. There are also a few edge cases I want to test out.

[SimonDanisch]

@darwindarak, would be nice to merge this ;)

[darwindarak]

Just rebased on master branch and updated the syntax. @SimonDanisch I haven't used Julia in a while, do you mind taking a look to see if anything needs to be changed? Otherwise I'll merge once the tests go through.

[sjkelly]

This will be helpful to my lab mates. I say lets merge and work out the bugs.

edit: The code looks good!