Creating a spline (curve) parallel to an existing spline (curve)

Hi,

I have attached an I_chart. This is a discrete dataset.

If I have a different starting values (intial values) for d and i, how do I create a new plot (line or curve) parallel to the existing dataset.

I tried curve fitting, it didn't work if the fit is not good for the existing dataset.

In short, I want to create mutiple splines (from different initial values) parallel to the existing spline, and read their values.

Thanks for your help.

Cheers!

KD

Answer 1

[Image Analyst]

What exactly does "parallel" mean to you? Do you just want to shift it up or down by some amount, like this?

data = readmatrix('I_chart.xlsx');
x = data(:, 1);
y = data(:, 2);
plot(x, y, 'b.-')
grid on;
y2 = y + 0.1;
hold on;
plot(x, y2, 'r.-')
legend('Original', 'Shifted')

[John D'Errico]

I was going to say EXACTLY the same thing, i.e., what exactly does parallel mean here. The point being, two straight lines can be parallel, but two curves cannot be parallel by the usual definition. At the very least, we could define multiple ways the curves COULD be parallel, so the solution is non-unique.

A simple x or y translation is trivial, but I have a funny feeling the question may be to find a new curve that is offset at a constant distance away, so an orthogonal distance to the first curve. That of course is a bit more difficult.

[Kanchan]

Thanks for your responses. Let me elaborate a little more.

The data I vs.d (actually a nomograpgh) starts from an intial d0, I0 (0.1, 0.9185).

So, if I have a different d0, I0 (e.g., 0.2, 1.2), I will have to draw another spline starting from (0.2, 1.2) following the same curvature of the spline which started from (0.1, 0.918543).

Both d0 and I0 may change depending upon the system. The initial d0-I0 will define the new system and hence a new spline.

I have attached a schematic what exactly I am looking for.

I know using the word "parallel" was improper and misleading.

Thanks,

KD

[Torsten]

s1(x) = s0(x-(d1-d0)) + I1-I0 

(d0,I0) = (0.1, 0.9185)
(d1,I1) = (0.2, 1.2)

[Kanchan]

An update:

I think I did it; a very crude way

by calculating slope and delta-x at each x. I am calculating delta-x also because the increment is not uniform.

Then, use slope values, delta-x values, new x0, and y0 calculate a new set of x and y.

The graph looks like this (I used log-log plot). The original plot is the thick black line.