https://www.latex4technics.com/ is a nice LaTeX editor.
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For the overall approach:
GPU-accelerated Path Rendering Kilgard and Bolz 2012 http://developer.download.nvidia.com/devzone/devcenter/gamegraphics/files/opengl/gpupathrender.pdf
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To determine how many quadratic curves are necessary to approximate a cubic curve, the approach from this paper is used to find the error:
Explicit Error Bound for Quadratic Spline Approximation of Cubic Spline Kim and Ahn 2009 http://ocean.kisti.re.kr/downfile/volume/ksiam/E1TAAE/2009/v13n4/E1TAAE_2009_v13n4_257.pdf
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To fill quadratic and cubic curves, the approach in this paper is used:
Resolution Independent Curve Rendering using Programmable Graphics Hardware Loop and Blinn 2005 http://research.microsoft.com/pubs/78197/p1000-loop.pdf
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To find the distance to a quadratic curve in the fragment shader, this page was helpful:
http://blog.gludion.com/2009/08/distance-to-quadratic-bezier-curve.html
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To solve a depressed cubic equation using Cardano's formula, Wikipedia has some information, but overall is poor. This page is very useful for solving depressed a cubic equation:
http://www.trans4mind.com/personal_development/mathematics/polynomials/cubicAlgebra.htm
This page shows solving a non-depressed cubic:
To Solve a Cubic Equation http://www.codeproject.com/Articles/798474/To-Solve-a-Cubic-Equation
And in this section, there's some code:
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To find the axis of a quadratic curve (which is the point of greatest curvature):
An Inexpensive Bounding Representation for Offsets of Quadratic Curves Ruf 2011 https://www.researchgate.net/profile/Erik_Ruf/publication/221249023_An_Inexpensive_Bounding_Representation_for_Offsets_of_Quadratic_Curves/links/551c1fcd0cf2fe6cbf7684c0.pdf