Ellipse generation algorithm - 2d shape primitives, Computer Graphics

Ellipse Generation Algorithm 

You know that a circle is symmetric in all the octants, while ellipse is symmetric with respect to four quadrants.  Therefore, to draw an ellipse, we need to determine approximating pixels in one quadrant.  We proceed exactly the same way as we did in the case of a circle.  Define a decision parameter and choose the next pixel position depending on the sign of the decision parameter. The decision parameter is defined in terms of the equation of an ellipse.   

As in the case of a circle, let us assume that the ellipse is having centre at the origin.  Consider its perimeter segment in the positive quadrant. Identify the point on the perimeter where the ellipse has tangent line with slope = -1. Then divide the positive quadrant in two regions- Region I where slope  dy/dx > -1  and Region II where slope dy/dx < -1  .  You may notice that for Region I,  y  values of points of the perimeter are decreasing slowly with respect to  x  values, than in Region II.  This means for determining the approximating pixels, we have to do the following.  For each increment in  x  value,  y  will either remain same or be decremented depending on the sign of a decision parameter.  But in Region II, for each decremented  y  value,  x  will either be incremented or will remain the same (compare with two cases of Bresenham line drawing algorithm for slopes  | m | <  1 and   | m | > 1).

Posted Date: 4/26/2013 1:16:13 AM | Location : United States

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