Slide object across surface of another, like a decal

I'm trying to take an object and slide it across another object, such that it follows the texture of the surface. The effect would be like sliding a decal over the second object; the first object would slip down into gaps, roll over bumps, etc.

How could I accomplish this? I can imagine using rays and colliders to check the distance from any point of the object to the surface below, but I don't see how to get that nice sliding effect without using infinitely many rays and triangles.