how to draw piecewise hermite curve.
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i know the points. i know tangent at the start and point..how to draw hermite curve.?
Answers (2)
Roger Stafford
on 23 Aug 2014
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.
0 Comments
John D'Errico
on 24 Aug 2014
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.
2 Comments
John D'Errico
on 10 May 2020
Edited: John D'Errico
on 10 May 2020
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.
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