On Dec 14, 2015 10:30 PM, "Arjen Nienhuis" <<a href="mailto:a.g.nienhuis@gmail.com">a.g.nienhuis@gmail.com</a>> wrote: > > > Yeah... You have to define what exactly you want. A 2D matrix like the ones > > cairo uses can always be decomposed into a concatenation of the following > > matrices: > > > > - transform > > transform is what cairo calls translate right? Err. Yes, I meant translate. > > - rotate > > - skew > > - scale > > > > This has many useful properties, and you can derive those four transformations > > from an arbitrary matrix easily. Here's my derivation: > > > > <a href="https://readable-email.org/list/www-style/topic/better-matrix-decomposition-for-animation">https://readable-email.org/list/www-style/topic/better-matrix-decomposition-for-animation</a> > > > > This also describes the benefits of such decompositions: > > > > <a href="http://research.cs.wisc.edu/graphics/Courses/838-s2002/Papers/polar-decomp.pdf">http://research.cs.wisc.edu/graphics/Courses/838-s2002/Papers/polar-decomp.pdf</a> > > > > If you transform a circle with a matrix, you get an ellipse. If you are > > interested in the major and minor axes of that ellipse, that's a Singular > > Value Decomposition of the 2D matrix. I've put code here for doing that: > > > > <a href="https://github.com/behdad/cairo/blob/color-emoji/doc/tutorial/src/singular.c">https://github.com/behdad/cairo/blob/color-emoji/doc/tutorial/src/singular.c</a> > > > > Cheers, > > > > behdad > > -- > > cairo mailing list > > <a href="mailto:cairo@cairographics.org">cairo@cairographics.org</a> > > <a href="http://lists.cairographics.org/mailman/listinfo/cairo">http://lists.cairographics.org/mailman/listinfo/cairo</a>