An ellipse that is centered at the origin (0, 0) can be described using Cartesia

Question

An ellipse that is centered at the origin (0, 0) can be described using Cartesian 2-D coordinates (x, y) (x/a)^2 + (y/b)^2 = 1 where a and b are called the semi-major (distance from origin to maximum x extent) and semi-minor (distance from origin to maximum y extent) axes, respectively, as shown in the figure below: (x, y) (0, 0) Derive and explain two different and complete rendering algorithms for an ellipse with semi-major axis a and semi-minor axis b, and whose centre point is located at the origin. This is an entirely 2-dimensional problem One of the algorithms must be based on a technique for treating neighboring discrete pixels, while the other algorithm must be based on the solution of a mathematical function (such as square-root function, or a trigonometric function) Discuss the relative merits of each of the two algorithms derived, comparing and contrasting each with the other and focusing on complexity

Explanation / Answer

you can draw an ellipse using Bresenham ellipse drawing algorithm. let see how

1.      Start and just Initialize the graphics mode according to your selection.

3.    then we have the center point as (a1,b1)

4. then you can have he length of semi-major, Semi-minor axes as a & b

5. then we wiill calculate s =pi/180

6.      Initialize i=0

7.      compute d= i*t

8.      compute x=a1+b1*sin(d), y=y1+bcos(d)

9.      plot(x,y)

10. now you can increment i by 1

11. Repeat steps 6 to 9 until i<360

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