ABSTRACT
Given any admissible curve x : I —► H 2, there exists a unique continuous map px : [0, 1] —► H satisfying:
( i) Therefore Xo ipx is a variable-distance offset curve. From <px(0) = 0 and y?x( 1) = 1, it follows px(0) = px( 1) = 0, and (1) implies that for s E [0,1], ||x(<px(s)) — p(s) ||2 = |/0x(s)|, where || • ||2 denotes the Euchdean norm. Hence we define (cf. [3,6]): Definition 3. For each admissible curve x, the map px is called the deviation function of x, and dN(x) := llpxllo© •= maxs6/ |px(s)| the normal distance from x to p.
