<p>The classic book <em>Computer Graphics: Principles and Practice</em> (second edition) by Foley, van Dam, et al. describes such an algorithm in section 19.2.</p>

<p>The explanation in the book seems to come from an MSc thesis, <a href="http://cs.brown.edu/research/pubs/theses/masters/1989/dasilva.pdf">Raster Algorithms for 2D Primitives</a> by Dilip Da Silva. </p>

<p>See also these papers:</p>

<ul>
<li><p><a href="http://dx.doi.org/10.1145/282918.282943">Curve-drawing algorithms for raster displays</a> by Van Aken and Novak (<em>ACM TOG</em>, 1985). </p></li>
<li><p><a href="http://doi.ieeecomputersociety.org/10.1109/38.506">A tracking algorithm for implicitly defined curves</a> by Chandler (<em>IEEE Computer Graphics and Applications</em>, 1988).</p></li>
</ul>

CC BY-SA 3.0
2015-09-15T16:14:06.920Z
2015-09-15T16:31:12.100Z
2015-09-15T16:31:12.100Z
lhf
<p>Back in the day when you often had to write your own low level rendering algorithms we all used to learn the Bresenham algorithms for lines and circles.</p>

<p>It was almost trivially easy to extend the Bresenham circle algorithm to cover ellipses whose axes were parallel to the X and Y axes.</p>

<p>But it always eluded me if there was some Bresenham-style way to render an arbitrary ellipse whose axes were at some arbitrary angle.</p>

<p>Does such a scanline method for rotated ellipses exist?</p>

<rendering><algorithm><curve><scanline>
Is there some kind of Bresenham algorithm or equivalent for scanline rendering a rotated ellipse?
hippietrail
# Is there some kind of Bresenham algorithm or equivalent for scanline rendering a rotated ellipse?

(Asked by: username_0 on 2015-09-15)

Back in the day when you often had to write your own low level rendering algorithms we all used to learn the Bresenham algorithms for lines and circles.

It was almost trivially easy to extend the Bresenham circle algorithm to cover ellipses whose axes were parallel to the X and Y axes.

But it always eluded me if there was some Bresenham-style way to render an arbitrary ellipse whose axes were at some arbitrary angle.

Does such a scanline method for rotated ellipses exist?

**Tags:** rendering, algorithm, curve, scanline


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## 1 answers

### Answer by username_1 on 2015-09-15. Score: 9

The classic book *Computer Graphics: Principles and Practice* (second edition) by Foley, van Dam, et al. describes such an algorithm in section 19.2.

The explanation in the book seems to come from an MSc thesis, [Raster Algorithms for 2D Primitives](http://cs.brown.edu/research/pubs/theses/masters/1989/dasilva.pdf) by Dilip Da Silva.

See also these papers:

* [Curve-drawing algorithms for raster displays](http://dx.doi.org/10.1145/282918.282943) by Van Aken and Novak (*ACM TOG*, 1985).
* [A tracking algorithm for implicitly defined curves](http://doi.ieeecomputersociety.org/10.1109/38.506) by Chandler (*IEEE Computer Graphics and Applications*, 1988).


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