An instance of this class represents an approximate isometric map $p\colon\Delta\to EX^*$, together with data relating $p$ to the canonical map $q\colon\Delta\to EX^*$. Here $\Delta$ is given the standard hyperbolic metric, and $EX^*$ is given the rescaled metric that has curvature $-1$. We refer to the point $p(0)$ as the centre of the chart. Note that this class extends the class E_chart, so documentation for that class should be read in conjunction with documentation for this one.
Extends: E_chartIf the centre is $q(c_{Hk}(t))$, then this field should be set to $t$.
Field: alpha::CC0This should be set so that $p(z)=q(\lambda(z-\alpha)/(1-\overline{\alpha}z)$
Field: lambda::CC0This should be set so that $p(z)=q(\lambda(z-\alpha)/(1-\overline{\alpha}z)$
Field: beta::CC0This should be set so that $\beta = -\lambda\alpha$, so $p(0)=q(\beta)$. However, in some cases we will work out $\beta$ first, and only set $\alpha$ and $\lambda$ later.
Field: grid_index::integerThe map $z\mapsto\lambda(z-\alpha)/(1-\overline{\alpha}z)$
The inverse of the map $z\mapsto\lambda(z-\alpha)/(1-\overline{\alpha}z)$
The map $z\mapsto\lambda(z-\alpha)/(1-\overline{\alpha}z)$, composed with the standard isomorphism $\mathbb{R}^2\to\mathbb{C}$
The inverse map $z\mapsto\lambda(z-\alpha)/(1-\overline{\alpha}z)$, composed with the standard isomorphism $\mathbb{C}\to\mathbb{R}^2$