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In this section we describe some functions involving points and geodesics.
Geodesics in the upper half plane are given by circles or lines
which intersect
the real axes at right angles. A geodesic is defined by its two
end points. Points and geodesics can be drawn using the
graphics functions described in the next section.
GeodesicsIntersection(x,y) : [SetCspElt],[SetCspElt] -> SpcHypElt
Computes the intersection in the upper
half plane of the two geodesics x, y,
where x and y are specified by their end points, which must be cusps.
If the geodesics intersect along a line the empty sequence is returned.
In the following example we find and display the intersection points
of some geodesics:
> H := UpperHalfPlaneWithCusps();
> g1 := [H|-1,2];
> g2 := [H|0,6];
> g3 := [H|1,5];
> g4 := [H|2,Infinity()];
> lines := [g1,g2,g3,g4];
> points := [GeodesicsIntersection(x,y,H) : x in lines,y in lines];
> DisplayPolygons(lines cat points,"/tmp/pic.ps":
> Labels := [-1,0,1,2,5,6],Colours := [1,0,0],Show := true);
[ -1.000000000000000000000000000, 6.000000000000000000000000000,
3.328427124746190097603377448, 91 ]
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