3 ms·
The rational parametrization looks like the Cayley transform, which IIRC does not cover the whole circle (you can't reach (-1, 0) with a finite mu). Does this h
by chombier 10y ago
The rational parametrization looks like the Cayley transform, which IIRC does not cover the whole circle (you can't reach (-1, 0) with a finite mu). Does this happen here as well?
- grondilu 10y agoIndeed, (-1, 0) can not be reached. I'm thinking of ways to improve it that regard.
- jacobolus 10y agoThis is a stereographic projection representation of an angle. The number should be seen as a point on the real projective line, which includes a point at infinity. If you’re using floating point, you can use the number ∞ for this. You’ll need some special cases in the code for it. Cf. https://en.wikipedia.org/wiki/Stereographic_projection https://en.wikipedia.org/wiki/Stereographic_projection https://en.wikipedia.org/wiki/Tangent_half-angle_substitution https://en.wikipedia.org/wiki/Tangent_half-angle_substitutio... https://en.wikipedia.org/wiki/Real_projective_line https://en.wikipedia.org/wiki/Real_projective_line