Calculating the resistance of a 3D shape between two points If I have an arbitrarily shaped object made of a uniform material of some specified resistivity, how would I go about calculating the resistance between two measurement points with known contact geometry?
Is there a general formula for this? (other than just Maxwell's equations) If so, where would I find a derivation?
Edit: Some simulations re answer below:


 A: Well, yes you can, but it is usually very hard. Here are the steps:


*

*Solve the Laplace equation:
$$ \nabla^2V = 0 \, .$$
In your case, find the general solution in spherical coordinates. Try to use every simplification you can. You might wonder why you don't solve Poisson's equation:
$$ \epsilon\nabla^2V = \rho \, .$$
That's because a conductor is an equal number of lattice positive and moving negative, so you have a net null density of charge.

*Find the electric field with:
$$ E = -\nabla V $$
You should still have a term dependent on your $V_0$, the potential difference between your two points.

*Find the current density with:
$$ J = \sigma E \, .$$

*Find the total current $I$ by integrating over any closed surface containing only one of your two contact point.

*$$V_0 = R I \, !$$
That's it. I have used it to find the resistance for certain geometries when you could do lots of simplifications to find the solution of $V$, but I don't know how it can be applied for more general problems.
A: Not that I am aware of.  The best I could do is to make a numerical simulation.  Make a mesh of points that fill the object, compute the resistance between each neighbor pair, and do a numerical relaxation to determine the potential throughout the object.
