How do you draw a circle or circular arc using Bresenham’s algorithm with the ability to start at an arbitrary point along the circle? It’s definitely possible, it’s just that it requires more computation up-front, here’s how.
What factors are you given?
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The current point.
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The starting angle, vectors are preferred.
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The radius. This may be expressed in the starting angle vector.
So now we need to compute the non-trivial starting parameters. y0
aned y^2 are easy to directly compute from the current point and
angle vector. What about y_odd? Well, remember the sum of odd
numbers formula to iteratively compute y.
(y + 1)^2 == y^2 + 2*y + 1
So now this means that we simply compute (2 * y + 1) to get y_odd.
And for proper rounding, we add one more on top of that.
Computing x0 and x^2? That is almost as easy, but remember we
must be subtracting from the radius. So, after making that adjustment
the rest of the parameters can be computed with ease.