Erosion Thickness on Medial Axes of 3D Shapes

We first make a note on the use of infimum instead of minimum in Equation 4 of the paper. This is because BT may only exist in the limit. An example is shown in Figure 1, where M is made up of a horizontal sheet and a vertical, cylindrical sheet close to the horizontal sheet’s boundary. The two sheets meet at a non-manifold seam with a circular shape (dotted curve). The shortest exposing tree at a point x located behind the cylinder would be a single path γ to the boundary that lies infinitely close to a portion of the seam (red). Note that γ cannot exactly lie on the seam, or otherwise it would need to spawn paths onto the cylinder (as required by an exposing tree), whose lengths would be much longer. The infimum allows us to capture the length of γ as if it follows the seam.