Class EH_atlas_edge

An instance of this class represents a pair of charts whose centres are close together. We can triangulate $F_{16}$ using the chart centres as 0-simplices, and these pairs as 1-simplices.

As part of the data of an atlas, we have a list of edges, numbered from 0 to $n-1$ say. If this is the $i$'th edge in the list, then this grid_index field should be set equal to $i$.

If this edge links chart number $i$ to chart number $j$ (with $istart_index should be $i$ and end_index should be $j$.

If this edge links chart number $i$ to chart number $j$ (with $istart_index should be $i$ and end_index should be $j$.

Suppose that this edge links chart number $i$ to chart number $j$, and chart $j$ is given by $p:C\to EX^*$. There will then be a small number $z$ such that $p(z)$ is the centre of chart $i$, and this $z$ should be stored in the start_z field.

Suppose that this edge links chart number $i$ to chart number $j$, and chart $i$ is given by $p:C\to EX^*$. There will then be a small number $z$ such that $p(z)$ is the centre of chart $j$, and this $z$ should be stored in the end_z field.

If this edge lies along one of the four curves that bound F16, then this field should be set to the index of the relevant curve (0,1,3 or 5).

This is the hyperbolic distance between the beta fields of the two charts. If everything is accurate, it should be the same as the EH_length field.

This is an estimate of the distance between the centres of the two charts, with respect to the rescaled metric on $EX^*$. If everything is accurate, it should be the same as the H_length field.

If this edge lies along one of the four curves that bound $F_{16}$, then this method will return the appropriate colour. Edges that do not lie on a boundary curve will be coloured grey.