Calculate point in ellipse given a unit vector

[mariano_donat]

Hi to everyone.

I'm detecting collision between two ellipses. I've got my unit vector, my ellipse center and radius (horizontal and vertical). I want to calculate the point that lies in the ellipse on the direction of the unit vector. See the image attached. Suppose the red arrow is my unit vector and I want to get the coordinates of the green colored point. I'm just multiplying my unit vector times my radius plus the center of the ellipse. The formula looks like this:

//Assume unit vector has been already calculated at this stage, ellipseCenter and ellipseRadius has been given
Vector pointInEllipse = VectorMake(unitVector.x * ellipseRadius.x + ellipseCenter.x, unitVector.y * ellipseRadius.y + ellipseCenter.y);

The point I get using the above formula lies on the ellipse, but it's translated on both axis a little bit, translated enough to detect collisions when haven't occurred any.
What am I missing here?

Thank you very much in advance.

 

[LCKurtz]

I've never heard of an ellipse radius. If the equation of the ellipse is

$$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$

what quantity represents the "ellipse radius"?

 

[mariano_donat]

I apologize for that, it's a and b from that equation, ellipseRadius.x = a and ellipseRadius.y = b.

 

[LCKurtz]

I have trouble deciphering your syntax in that programming language. But if you have a unit vector you have the slope m. Assuming the picture is translated to the origin, why not just solve y = mx with the equation of the ellipse? A quick calculation seems to show you just need to calculate something like

$$x=\pm\frac{ab}{\sqrt{m^2+b^2}}$$

 

[CellCoree]

Hello, it seems like you are on the right track with your formula. However, there may be a few things that could be causing the translation in your calculations.

First, make sure that your unit vector is normalized, meaning its magnitude is equal to 1. If it is not, you may need to divide the vector components by its magnitude before multiplying by the radius.

Another possibility is that your ellipse center and radius values are not accurate or consistent. Double check that these values are correct and match up with the image you have provided.

Lastly, check if your coordinate system is consistent. It could be that your unit vector and ellipse center are using different coordinate systems, resulting in the translation you are seeing. Make sure to use the same coordinate system for all calculations.

I hope this helps and good luck with your collision detection!