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Grinding wheel tool path simulation.

I am completely lost about where to look for answers as I have no experience in this field, I have been given this problem from my supervisor. So, if anyone could point me the right direction as where to look for revelent examples or literatures, it would really helpful. The problem is as follow.
I have to simulate following in labview...
 
Calculate the equation of tool path for a vertical grinding machine with a grinding disk of which the inner diameter is D1 and outer diameter is D2. the rotational speed of omega, w. location of grinding wheel can be defined as P(x,y) on the work piece with dimension of LX and LY with the grinding amount subjected to RwT(R=radius of disk, w= rotational speed T= time).
and so the calculated path should not error of more than 5% on the workpiece.
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Do you need analytical solution or numerical?

For numerical

I would first calculate how much it grinds for a given trajectory.

For example split LX, LY into small squares, move circle along path, probably with constant speed and add grinding amount for each point according to your formula.

This gives you 3D surface - if trajectory is a single point, it will be kind of a cone in a cylinder - it grinds a lot on the outer edge where disk is fast.

Then I would generate trajectories of certain type (rectangular stepping, moving spiral) and calculate how does 3D surface amplitude depends on trajectory params.

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Thank you for your response, Alexander. 

Actually I have to find both analytical and numerical solutions and simulate. Basically what I am looking for is where can I get the algorithm or equation for rectangular stepping or moving spiral path, so that I can implement them in my simulation. With my very limited knowledge in this field, I don't know what or where to look for. (E.g. books or literature or any examples.)

As for the equations, if I can get the tooling path equation, probably I can apply the above material removal from grinder formula to generate a functional simulation. 

I am guessing, I would have to do a numerical analysis to calculate the the error rate, since the analytical value may or may not be very helpful but the reason why I have to find analytical (equations) solution, so I can report them in my simulation as reference. 

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