How to avoid rounding off errors in parametrization?
显示 更早的评论
Hello everyone. I am parametrizing the function of a conic: Ax^2 + By^2 + Cxy + Dx + Ey + F = 0
The goal is to get the equation to the form: x^2/a^2 + y^2/b^2 = 1
One of the steps of the parametrization corresponds to rotating and scaling about the origin, i.e., eliminate the component of xy.
This is not working very well due to roundoff errors. Being C ~= 0, here is what I have to do:
x->qx+y; y->qy-x
where
q = sqrt(((B-A)/C)^2+1) + (B-A)/C;
When I do this replacement, the xy component doesn't really disappear, it actually becomes something like
1E-5*x*y
This corrupts all of the following algorithm of the parametrization. Any ideas of how to avoid this probelm?
Thank You.
采纳的回答
Roger Stafford
2014-7-28
编辑：Roger Stafford
2014-7-28
First you need to get to translate to get rid of the D*x and E*y terms which I assume you have already done, which brings you to the form
A*x1^2 + B*y1^2 + C*x1*y1 + F1 = 0
Then instead of rotating with x->qx+y; y->qy-x, do this:
x1 = x2*cos(a)-y2*sin(a)
y1 = x2*sin(a)+y2*cos(a)
The coefficient of x2*y2 will then be
(B-A)*sin(2*a)+C*cos(2*a)
which you set to zero to eliminate the x2*y2 term. This gives
tan((2*a) = C/(A-B)
which you can solve with
a = 1/2*atan2(C,A-B)
Then you are nearly there.
2 个评论
Roger Stafford
2014-7-28
Yes, eliminating the D and E terms can be done either way.
更多回答（0 个）
类别
在 帮助中心 和 File Exchange 中查找有关 Programming 的更多信息
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!
Translated by 
