#### monirg

##### Well-known Member

- Joined
- Jan 11, 2005

- Messages
- 629

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.