Plot a curve with its derivatives

I have data with the following information and coordinates (not the actual numbers, just an example):

X Y dY/dX d2Y/dX2

4 0.3 5e-4 4.1e-5

5 0.4 1e-4 3e-4

In the example, there are only two points, but in the data, I have over 1000. I would like to plot the curve defined by the x and y-coordinates while maintaining the 1st and 2nd derivatives at each point. Is there a way to do this in matlab? I am not looking to use a linear fit curve. Each x-y value is given its own 1st and 2nd derivative.

[KSSV]

What do youmean by while maintaining the 1st and 2nd derivatives at each point ?

[Alexandra McClernon Ownbey]

If I plot a curve in matlab (or any software) with x-y coordinates, it basically interpolates a line (via e.g. taylor series) between the points to make it continuous. So if I have 4 points that I plot, I get a curve; however, the slope (derivative) at those points are then defined by whatever interpolation or curve the software uses to connect the points. I would like to define what the slope is at each point.

These points are 2nd order accurate, I would like to maintain that accuracy. If I just input points to plot, I lose my accuracy.

I don't think I can create a function for the points - they are coordinates for a nozzle.

[Alexandra McClernon Ownbey]

The only thing I can think of is to use taylor series to add points just after and before the points i have to make sure the derivative is correct

Answer 1

[J. Alex Lee]

As far as I know, matlab's plot function will draw a straight line (linear interpolation) between adjacent points.

For your case, at every point you have a fully specified parabola, so you can draw as refined a plot as you would like around each point.

You could try plotting the parabola around each point, say from mid-way between it and the previous, and mid-way between it and the next, and look at the result. I suspect you won't get a continuous curve though.

I think that at best you will be able to find x-positions between the specified points where the parabolas will meet, but they will not be ensured to have matched slopes (and definitely not 2nd derivatives).

[Alexandra McClernon Ownbey]

I just ended up using taylor series to approximate coordinates above and below each given coordinate using a extremely small dx.