plot curve from known coordinates and instantaneous slopes

I would like to plot a sample graph (a rough stress strain curve comparison) with 2 lines where my x,y and instantaneous slopes are known...and basically very roughly interpolate the curve between the two. is this possible?

[monarch]

Example plot: "line 1" would look something like upper aorta and "line 2" would look something like carotid.

Answer 1

[Roger Stafford]

Hint: Suppose your interpolated curve is the following general cubic polynomial with four unknown coefficients:

y = a*x^3+b*x^2+c*x+d

Its slope (derivative) would be:

s = 3*a*x^2+2*b*x+c

Using these two equations, you can write four linear equations that must be satisfied for each of your curves. In each case matlab can solve those four equations for the unknown a, b, c, and d values, and you then have your two interpolated curves (not "lines".)

[monarch]

Thank you, but I'm not sure how to turn the points and slopes I have into a plot given that information. (grey-haired researcher, new to Matlab here...trying to represent some pilot data in graphical form).

[Roger Stafford]

Use the two end y values in the first equation and the two end slope values in the second equation. This gives you your four linear equations in the unknown coefficients a, b, c, and d, which matlab can solve for you. Do this for each curve.