plot and evaluate this cubic polynomial

I need to evalue this polynomial q(t) = a + b(t - tk1) + c(t - tk1)^2 + d(t - tk1)^3

whit tk1<t<tk2

where a,b,c,d,tk1,tk2 are costant

I think to polyval but it is rigth for : q(t) = a + b*t + c*t^2 + d*t^3 how can evalue and plot my polynomial

thanks

Answer 1

[Benjamin Avants]

I think the easiest thing to do is to first define t as a vector. Choose your resolution and invoke linspace:

numberOfPoints = 1000;
t = linspace(tk1,tk2,numberOfPoints);

then compute q and plot:

q = a + b .* (t - tk1) + c .* (t - tk1).^2 + d .* (t - tk1).^3;
plot(t,q);

[Benjamin Avants]

For clarification, linspace creates a vector from a to b inclusive with n number of evenly spaced points:

a = 1;
b = 5;
n = 5;
linspace(a,b,n)
ans =
[1,2,3,4,5]

[enzo milito]

I tryed your suggestion and run very well, but now I have connect or concatenate two or more different polynomial in different interval time tk1-tk2 tk2-tk3 tk3-tk4 for to obtain one plot from tk1-tk4 and so have you any suggestion ? thanks

[Benjamin Avants]

There are a couple of approaches that will accomplish this. I think the best way is to simply compute each segment for the desired polynomial and then do the following:

combinedQ = [q1,q2,q3];

or

combinedQ = [q1;q2;q3]; % depending on whether q is a row or column vector

and then

totalT = [t1,t2,t3]; % Once again, use semicolons if this doesn't work
plot(totalT,combinedQ);