http://nodename.com/blog/2005/11/02/graphing-a-parametric-function-using-quad-curves/ Thu, 05 Jan 2012 17:15:00 +0000 hourly 1 http://wordpress.org/?v=3.0 http://nodename.com/blog/2005/11/02/graphing-a-parametric-function-using-quad-curves/comment-page-1/#comment-71 Patrick Mineault Wed, 02 Nov 2005 23:22:17 +0000 http://nodename.com/blog/?p=32#comment-71 Using it to draw parametric functions was actually going to be my next blog post, but looks like you beat me to it :) Nice stuff. Some functions which have very pathological behaviour are bound to be difficult to draw properly, like sin(1/x). In that case, because of the rapid succession of cycles near 0, at some point the graphing function will sample two points where one has a large positive derivative and another point with a large negative derivative and while the intersection is between the two points, it's way, way off. I think one reasonable way to solve this is adding a check if the derivatives are too different between two very close points, and if so, revert to a line drawing mode. That wasn't really my point however, since it was more for drawing 'nice' functions so they render well without having a bunch of lines on screen. Note that the algo can be retrofitted to AS1 and ECMAScript to be used as a JSFL tool (like Keith Peter's sinewave tool) Using it to draw parametric functions was actually going to be my next blog post, but looks like you beat me to it :) Nice stuff. Some functions which have very pathological behaviour are bound to be difficult to draw properly, like sin(1/x). In that case, because of the rapid succession of cycles near 0, at some point the graphing function will sample two points where one has a large positive derivative and another point with a large negative derivative and while the intersection is between the two points, it’s way, way off. I think one reasonable way to solve this is adding a check if the derivatives are too different between two very close points, and if so, revert to a line drawing mode. That wasn’t really my point however, since it was more for drawing ‘nice’ functions so they render well without having a bunch of lines on screen. Note that the algo can be retrofitted to AS1 and ECMAScript to be used as a JSFL tool (like Keith Peter’s sinewave tool)

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