ConicRotations
See this applet for the transformation between conic metrics: elliptic, parabolic and hyperbolic.
The same scalar s is used as circular angle, parabolic angle and hyperbolic angle:
- θ = s is the circular angle for R to rotate on the unit circle.
- s is the parabolic angle for S to "rotate" on the unit parabola. This parabolic rotation is the shear mapping with shear factor s = tan(φ) where φ is the shear angle.
- ψs = s is the hyperbolic angle for H to "rotate" on the unit hyperbola. This hyperbolic rotation is the squeeze mapping with squeeze factor k = es where s = ψs is the hyperbolic angle relating to the squeeze angle ψ by tan(ψ) = tanh(ψs).
- For circular and parabolic angle, they are also the arclength of the corresponding conic arc.
- For the hyperbolic case, using Minkowski metric, we also have the "arclength" of the hyperbolic arc equals hyperbolic angle.