Mathematica derivation of signed-distance coordinates for surfaces from Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces

We provide an elementary derivation of an orthogonal coordinate system for boundary layers around evolving smooth surfaces and curves based on the signed-distance function. We go beyond previous works on the signed-distance function and collate useful vector calculus identities for these coordinates. These results provided code enable consistent accounting of geometric effects to arbitrary order for boundary layer asymptotics in a wide range of physical systems.