how to find data points of function passed through a distorted "pipe"?

This is not going to be your ordinary question, but hopefully somebody can assist me.

I want to take a function of data points, for instance a random set of points ("rnpi" in my code), and fit it to an upper and lower bounding function, such as a pair of sine waves (AS1 and AS2 in my code). The data point locations will be distorted by the waves, so that a straight line will come out curvy, etc. I am including a diagram showing what I want. How do I do this?

iP = [0, 88];
iB = [30, 74];

npi = 200; % SHOULD BE EQUAL TO LENGTH OF RANDOM PATTERN BELOW

aa1 = iP(1); % MIN OF RANGE
aa2 = iP(2); % MAX OF RANGE

ab1 = iB(1); % MIN OF RANGE
ab2 = iB(2); % MAX OF RANGE

nz1 = 0:pi/npi:4*pi;
nz2 = pi + (0:pi/npi:4*pi);

nr1 = 3/2; % NUMBER OF REPEATS /2
nr2 = 5/2; % NUMBER OF REPEATS /2

AS1 = (1 + cos(pi + nz1*nr1))/2; % 0-1
AS1 = aa1 + (ab1 * AS1); % aa1-ab1

AS2 = (1 + cos((pi*nr2)-(nz2*nr2)))/2; % 0-1
AS2 = ab2 + ((aa2-ab2) * AS2); % ab1-ab2

plot(AS1)
hold on
plot(AS2)
hold off

% NOW TEST WITH A RANDOM PATTERN
rnpi = round(88 * rand(npi,1));

%  THE REST GOES HERE.....................

Answer 1

[John D'Errico]

A difficult question to answer, since so much is left to guess. And the vaguesness of your question suggests all you want is a result that looks qualitatively as you have drawn. Mathematics is not good at subjective things. Sorry.

But is is not difficult to do something that looks vaguely as you have drawn, as simply an interpolation between two curves.

ULim = [74 88];
LLim = [0 30];
XLim = [0 2*pi];

x = linspace(XLim(1),XLim(2));

UpperFcn = @(x) (cos(x)+1)/2*diff(ULim) + ULim(1);
LowerFcn = @(x) (1-(cos(x))/2)*diff(LLim) + LLim(1);

fplot(UpperFcn,XLim)
hold on
fplot(LowerFcn,XLim)

Now just create an interpolated function that trades off the two boundaries.

TFcn = @(x) (x-XLim(1))./diff(XLim);
MidFcn = @(x) (1-TFcn(x)).*UpperFcn(x) + TFcn(x).*LowerFcn(x);
fplot(MidFcn,XLim)

Again, totally subjective. Just a picture that looks vaguely like what you asked about.

[mark palmer]

THanks for attempting to make sense of my vagueness.

What I am looking for is to map the points in the first diagram into the points on the second so that the distance between the points and the barriers retains a similar relative placing. So a point in the middle of 1 would stay in the middle of 2, although it may be a different value if the borders are squeezed in.

Anyway, hope that helps.

[mark palmer]

No worries, I gave it a bit of thought,and it only involves some simple math. Problem solved.