Is there some standard way of "rotating" a geometric figure in 2D?
Maybe this needs to be in the geometry forum or something?
I'm looking for a Cartesian equation for a rotated ellipse.
h is x-koordinate of the center of the ellipse.
k is y-koordinate of the center of the ellipse.
a is the ellipse axis which is parallell to the x-axis when rotation is zero.
b is the ellipse axis which is parallell to the y-axis when rotation is zero.
phi is the rotation angle.
Here is a cartesian equation for a non-rotated ellipse:
(How do I "put rotation phi" into this?)
Code:(x-h)^2 (y-k)^2 ------- + ------- = 1 a^2 b^2
Here is a parametric form of a rotated ellipse:
x = h+a*cos(t)*cos(phi)-b*sin(t)*sin(phi)
y = k+b*sin(t)*cos(phi)+a*cos(t)*sin(phi)
I'd like to have the x and the y in the same equation, and without the parameter t. I think that this means that I want a Cartesian equation for a rotated ellipse, but I'm sorry if I have misunderstood Cartesian here...
Thanks beforehand and a jolly good weekend to ya' all!
Cheers!
multiplying by this matrix will rotate the graph by the angle theta
where x' and y' are the new rotated coordinates
so now suppose that we have the equations of an ellispe
and
so if we want to rotate the eqations by 45 degrees or we get..
so then
and
I hope this helps.
Actually, you demonstrated how to derive the parametric equations of a rotated ellipse, which I posted, from the parametric equations of a non-rotated ellipse. I can follow the matrix multiplication, yes, but is it possible to put that together in the way I'm looking for:
Joining x and y in one single equation, and getting rid of that t parameter? If I try to substitute and solve from the parametric equation system, I end up with a mess. There must be a much simpler way.
For a non-rotated ellipse, it looks quite simple:
Code:(x-h)^2 (y-k)^2 ------- + ------- = 1 a^2 b^2
How do I turn THAT phi degrees?
Hi,
i also had the same problem. I found the solution at the following link. I do not know whether the external links are allowed on this forum or not...
The Quadratic Curves, Circles and Ellipses FAQ
Look for the question ---
Q21. How do I calculate the coefficients of an arbitary rotated ellipse?
at the above link.
I hope this is what you were also looking for .