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Topic: morphing a sequence of numbers
Replies: 0

 Jon Rong-Wei Yi Posts: 2 Registered: 12/12/04
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 n-2 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 sought-for 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?