I want to know how thickness is defined.
Let me start with the simplest shape due to its symmetry. This is a circle. Assume a circle with radius of 1. If we draw a circle with the same center and radius 2, we will have created a ring with thickness 1.
How can we extend this to different shapes? For example let's take a rectangle with length of sides a=1 and b=2. I can think of 2 ways to create a ring of thickness 1.
- create a rectangle with length of sizes 2 and 3.
- create a shape like previous rectangle, but the corners would be rounded. That'a because the thickness in the corners would be $\sqrt2$, not 1.
So my definition of thickness something like
- The minimum distance between any point of the inner shape and any point of the outer shape should be 1.
- there should be no point (A) in inner shape where there is no point (B) in outer circle such as AB=1.
- there should be no point (A) in outer shape where there is no point (B) in inner circle such as AB=1.
Can this be correct? Assuming that above is correct:
If inner shape is circle $(x-a)^2+(y-b)^2=r^2$, then the outer shape should be $(x-a)^2+(y-b)^2=(r+1)^2$.
How about if the inner shape is an ellipsis? Or a square?