hi all , i have to create an ellispe the inputs are major axis , minor axis , and the angle of the major axis the ellipse needs to be tilted. thanks aviral
Construct the formula for the ellipse in standard position, and then use an affine transformation to rotate it. Better yet, if you need to draw it to screen, construct the parametric formula for the ellipse and transform that.
A circle in standard position is given thus:
x = r cos(t)
y = r sin(t)
t = 0..1
Change it to an ellipse by substituting the major and minor axes into the position of r in the x and y equations:
x = r_maj * cos(t)
y = r_min * sin(t)
Then multiply by the transformation matrix
[ [ cos(a), sin(a)] [-sin(a), cos(a)] ]
To rotate the whole thing counterclockwise by angle 'a'.
* [[cos(a),sin(a)][-sin(a),cos(a)]] =
Which, after tedious and error-prone-when-done-by-hand matrix multiplication, gives
x = r_maj*cos(t)*cos(a) + r_min*sin(t)*-sin(a)
y = r_maj*cos(t)*sin(a) + r_min*sin(t)*cos(a)
This is just a quick answer; there are probably better and faster ways to get the points on an ellipse, but this'll definitely draw the right shape. If you're drawing pixel-by-pixel the line may look a bit chunky in places, since you'll be simply painting every pixel ever occupies for 0<=t<=1. There are probably algorithms extant to smooth that behavior out and produce better "single-pixel-wide" lines.
