I'm a little confused on why inside/outside tests are hard in this case. Couldn't we plug in the coordinates of our point and check if the last coordinate matches the output? Why is this representation different?
Is this just difficult because we don't know if a point is inside the hole of the torus as opposed to outside of the torus? Couldn't we have another function for the hole of the torus, and do two inside outside tests?
Is it that implicit surfaces are easier to represent within our code, but then at runtime the values are all converted to explicit in a way?
are we able to tell which expression works better as soon as we see the problem, but not based on experience? also are these two expressions always interchangeable?
Does the difficulty in this case come from the non-convexness of this geometry?
What is the benefit of modeling geometry as such and dealing with difficult formulas when we can use triangle approximations?