I need a equation or formula on finding a point on ellipse and circle.
Given:
The degree of point,
Ellipse height, width.
Please explain!
Thanks! |
Request for Question Clarification by
mathtalk-ga
on
08 May 2004 14:08 PDT
Hi, alanzhao-ga:
It's not clear what you mean by "degree of point".
Does this refer to the measure of an angle subtended by the ray from
the center of the ellipse to a point on the ellipse and the semi-major
axis (or semi-minor axis) of the ellipse?
In the case of a circle for example, it is common to parameterize a
circle of radius R centered at the origin by:
x = R cos(t)
y = R sin(t)
where t is the angle between the positive x-axis and the ray drawn
from the origin (center) to the point (x,y) on the circle.
A similar parameterization of an ellipse can be given, but the
parameter t would no longer have the simple interpretation of "angle"
as it does in the circular ("constant angular velocity") case.
Note that in general an ellipse need not have axes that are parallel
to the coordinate axes, so that a parameterization can be complicated
by nonstandard orientations as well.
regards, mathtalk-ga
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Clarification of Question by
alanzhao-ga
on
08 May 2004 14:35 PDT
The formula you're given is only for the circle, right?
I need this formula also to works with ellipse.
Thanks!
|
Request for Question Clarification by
mathtalk-ga
on
08 May 2004 15:04 PDT
Hi, alanzhao-ga:
As I tried to explain, there is a simple modification of this pair of
formulas which produces an ellipse of the required width and height.
However it is no longer true that under that modification the
parameter t can be interpreted as the "central angle" between the
positive x-axis and the ray drawn to the point.
It would be helpful if you Clarify:
1) whether the ellipse that you want to draw is centered at the origin
and has the coordinate axes as the major and minor axes of the
ellipse; and if so
2) whether you need the parameter of the formulas to be the angle
between the positive x-axis and the central ray drawn to a point on
the ellipse.
regards, mathtalk-ga
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Clarification of Question by
alanzhao-ga
on
08 May 2004 19:41 PDT
Thanks mathtalk-ga.
I hope I can explain my problem, but please take a look at <a
href="http://www.ilovemimi.com/question.gif" target="_blank">this</a>
Note: because this is a Windows GDI+ programming problem, the degree
increases in clockwise direction.
Thanks!!!
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