0

I know there's a formula for getting all points that satisfy an ellipsis:
(A1,A2)=center1
(B1,B2)=center2
R=radius

sqrt((x-A1)^2+(y-A2)^2)+sqrt((x-A1)^2+(y-A2)^2)=R

But is there another formula that reduces the number of variables (5 in this case) or make the variables more efficient (R must be a minimum size depending on A and B)? So that all possible ellipses could be represented as a point in a 4D cube?

user2741831
  • 225

1 Answers1

0

If you would like to characterize an arbitrary ellipse in a two-dimensional plane the number cannot be reduced. It can even increase if the ellipse resides in a higher dimensional space. However if you are interested not in exact location of the ellipse but only in its size and shape, two parameters completely suffice (e.g. the lengths of large and small axes).

user
  • 26,272
  • Yeah I was trying to create a hough transformer, but I needed a 5 dimensional cube for that and was hoping to reduce that, thanks though. I was just thinking if an elipsis with its points further apart but with a smaller radius would be equvalent with one with closer points but bigger radius – user2741831 Dec 01 '19 at 14:07