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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) |
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