Data Points Joined by Spiral !!
 

Hello;

I've non-monotonic analytically derived data points: (x,y)i, i=1, n
I would like to join the points by a smooth curve with the following
constraints:
a. points are joined in the same order, i.e.; pnt# 1, pnt# 2, ..., pnt# n
b. the curve progresses in clockwise direction ONLY starting at pnt # 1
c. the curve does not cross itself
d. the curve has a minimum possible turns
e. the curve has a known (dy/dx) at pnt # n

By examining the data, the points appear to lie on a spiral of some kind.

Here're two sets of data points for illustration purposes
(Ref. HTK006,T*=0.08,T*=0.05):
SET # 1:
n = 5, (dy/dx) at pnt# 5 = - 4.1343
pnt#1 x = - 0.2062 , y = 0.9369
pnt#2 x = - 0.1937 , y = 0.9454
pnt#3 x = - 0.2043 , y = 0.9263
pnt#4 x = - 0.1797 , y = 0.9640
pnt#5 x = - 0.1542 , y = 0.9309

SET # 2:
n = 4, (dy/dx) at pnt# 4 = - 8.6897
pnt#1 x = - 0.1206 , y = 0.9698
pnt#2 x = - 0.1292 , y = 0.9470
pnt#3 x = - 0.1282 , y = 0.9785
pnt#4 x = - 0.0974 , y = 0.9508

(n=3 and n=10 are generally the min and max data points per set)

How can one develop such spiral ???

Your expert opinion would be greatly appreciated.

(Excel 2003 SP2, Windows XP)