Improved SDF objective function.
For two colliding SDFs `A` and `B`, the function is `(A+B)+abs(max(A,B))`. This can also be written as `clearance + abs(intersection)`. This function has the following properties:
- On the penetrating surface, it is equal to `A+B`, i.e. the clearance field which is the penetration depth.
- The object boundary is a set of local minima in 3D space, since `abs(max(A, B))>0` away from the surface.
- Along the penetrating surface, the maximum penetration is a local minimum of the clearance since this field is orthogonal to the midsurface field `A-B`, which acts as a support plane for the contact.
[Level sets of the improved function for two colliding circles](https://www.wolframalpha.com/input?i=plot+sqrt%28x%5E2%2By%5E2%29-1+%2B+sqrt%28%28x-1%29%5E2%2B%28y-1%29%5E2%29-1+%2B+max%28max%28sqrt%28x%5E2%2By%5E2%29-1%2C+sqrt%28%28x-1%29%5E2%2B%28y-1%29%5E2%29-1%29%2C+0%29+-+min%28max%28sqrt%28x%5E2%2By%5E2%29-1%2C+sqrt%28%28x-1%29%5E2%2B%28y-1%29%5E2%29-1%29%2C+0%29+).
PiperOrigin-RevId: 585106580
Change-Id: I5b18a1ef262ceb0a1ab8abcad8acfd6dc1992e2c
Alessio Quaglino
d070b1893e