Let e,, e„, and e be unit tangent vectors to the d), 6, and the hull 



-cp -0 -n 



ce normal coordinates, resf 

 computed using Equation (24) by 



surface normal coordinates, respectively. Then e„ and e are easily 



-6 -n 



3r 



3i" 



(26) 



9r 



8r dr 

 ^ "" 99 



(27) 



3r 9r 

 91 "" 96 



where | | • | | denotes the length of the vector. The requirement that the (fi 

 and 9 coordinates be orthogonal imposes the condition that 



e, = e X e 

 -9 -n -q 



(28) 



The increment of arc along the curve (p = constant, dr| ,, can be 

 written as 



9r 9r 



(29) 



and by virtue of orthogonality 



dr L = 



(30) 



The derivative (ds/d9) , can be obtained from Equation (30) by 



ds 



I 9x ^x d^ _9^ j 



V 99 9s 99 9s/ 



(31) 



+ 1 



16 



