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I have a UIView with bounds (w, h) and I am trying to calculate angles and point on a ellipse which is centred at view's mid point i.e. centre is (w * 0.5, h * 0.5). I continuously change the size of view and ellipse so following values are from console for a instance of values.

For this instance, (w, h) = (150.000000, 300.799988) and radii are (rx, ry) = (52.500000, 105.279999)

Now, I try to find angle of point P1(x,y)(30.784275, 93.637390) on this ellipse using following code:

CGFloat angle = atan2((y - (h * 0.5)), (x - (w * 0.5)));
if (angle < 0)
{
   angle += 2 * M_PI;
}

The angle value I get is 4.050611.

Since I was not getting my desired output I just tried to find the point on ellipse from above angle using code below:

framePoint.x = (w * 0.5) + (rx * cosf(angle));
framePoint.y = (h * 0.5) + (ry * sinf(angle));

And surprisingly I got point as (42.737656,67.344543).

I just went ahead and did one more iteration of same process. I calculated angle from above point and got angle as 4.341885 and new point from this latest angle as (55.990501,52.263786).

I know something is wrong with my calculation formulas but I am not able to pin point it.

Also if above ellipse is a circle i.e. when rx = ry, all the points and angle are equal. So it kind of work for circle but not for ellipse.

So, I want to know exactly where I went wrong.

blancos
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  • 1. check your atan2 usage (I use mine atanxy instead here: http://stackoverflow.com/a/21697187/2521214 ) if the operands are dx,dy or dy,dx 2. you can use also mine atanxy and compare the results 3. check if your cos,sin atan2 use the same units (rad,deg) 3. try to add brackets `(`,`)` to coordinate computation to rule out wrong operand priority compiler bug (it happens to me few times in past since i bracketing what i can just to be sure) – Spektre Oct 17 '14 at 07:05
  • @Spektre : I double checked everything. Tried with your atanxy also. atanxy behaves differently but still gives wrong values. I want to know the problem with the code I posted because clearly my math is wrong somewhere. – blancos Oct 17 '14 at 08:23
  • Got mi a while to get what your problem is... Added answer. The basic things are the worst bugs :) you can stair at them forever ... fresh set of eyes usually helps – Spektre Oct 17 '14 at 10:02

1 Answers1

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yes now I see it what you mean

You are obtaining E angle from ellipse via E=atan2(...) and using it in equation where you need Mangle x=x0+rx*cos(M), y=... where:

  • M is mean circular angle
  • E is ellipse angle

ellipse/circle angles

It is analogy to Kepler's equation luckily for you you do not need to match speeds around main focus point so In order to obtain the M angle:

  1. scale one axis to convert ellipse to circle

  2. compute the angle there

    so if your axis aligned ellipse is (x0,y0,rx,ry) and input point on ellipse is (x1,y1) then if I am not mistaken it should be like this:

    M=atan2((y1-y0)*rx/ry,x1-x0)

    or

    M=atan2(y1-y0,(x1-x0)*ry/rx)

  3. compute your point using M

    x=x0+rx*cos(M)
y=y0+ry*sin(M)

[notes]

  • the X coordinate of both points should be the same (image was hand drawed in paint)
  • it does not matter which axis you scale and which not

See also similar:

Spektre
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