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morphing a sequence of numbers
Posted:
Jul 10, 1996 11:01 PM


hi,
i need some help on two somewhat related topics. for the first scenario, i have a sequence of n, positive numbers. now, i would like to constrain the first and nth number to two arbitrary, positive values through some type of transform that keeps positive the remaining n2 numbers in the middle.
in other words:
Given: x[a .. b], x[j] > 0 for j=[a,b], A' and B' Find: F such that x'[j] = F{x[j]} for j=[a,b] and x'[a] = A' and x'[b] = B', and x[j] > 0 for j=[a,b]
are there are restrictions on A' and B'?
now, for my second question i'll illustrate it with a diagram. say i have the following two curves i'd like to smoothly connect.
* ** ** ** * AND * * * *
note each curve has six points. i'd like to generate a final curve consisting of twelve points by just specifying the value of the first and last point. granted i could set the 6th point and the 1st point of the left and right curve, respectively, to their average, and just apply my soughtfor F (if it exists) from above. perhaps, there's a better method?
i know that there are multiresolution methods for modifying the sweep of a curve at a low resolution, and then adding back in all the detail. however, would they guarantee that all points remain positive?
thanks for any advice in advance,
jon



