how to draw piecewise hermite curve.

i know the points. i know tangent at the start and point..how to draw hermite curve.?

[Roger Stafford]

See:

http://en.wikipedia.org/wiki/Cubic_Hermite_spline

Answer 1

[Roger Stafford]

Here's how to draw one "piece". Let (x1,y1) and (x2,y2) be the coordinates of the two end points and m1 and m2 the respective desired derivatives at these two points.

 A = [x1^3,x2^3,3*x1^2,3*x2^2;x1^2,x2^2,2*x1,2*x2;x1,x2,1,1;1,1,0,0];
 C = [y1,y2,m1,m2]/A; % Solve for the four cubic Hermite coefficients

 n = 1000;
 X = linspace(x1,x2,n);
 Y = C*[X.^3;X.^2;X;ones(1,n)];
 plot(X,Y,'y-')   % Plot the cubic between the two given points

I'll leave it to you to figure out how to put together many adjacent pieces.

Answer 2

[John D'Errico]

As Roger showed, you can do it wit some modest effort (not really that hard.) Or you can use a tool that does it for you. Download my SLM toolbox from the file exchange.

For example, to create the cubic hermite segment that at...

x = 0, y = 0, y' = 1
x = 10, y = 5, y' = 2

Do this:

slm.form = 'slm';
slm.degree = 3;
slm.knots = [0;10];
slm.coef = [0 1;5 2];
plotslm(slm)

If you have more segments, just add extra knots, then add extra rows to the coef array.

[Rehanos_boyzee]

how can i know the parametric equation for this slm hermite curve?

[John D'Errico]

F = slmpar(slm,'symabs')
F =
  2×1 cell array
    {1×2 double}
    {1×1 sym   }

>> F{1,1}
ans =
     0    10

>> F{2,1}
ans =
0.02*x^3 - 0.25*x^2 + x

So, on the interval [0,10], the function was as given. With a more complicated spline, there would be multiple intervals, and thuis different polynomial segments.