Arcs in hyperbolic geometry¶
AUTHORS:
- Hartmut Monien (2011 - 08)
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class
sage.plot.hyperbolic_arc.HyperbolicArc(A, B, options)¶ Bases:
sage.plot.bezier_path.BezierPathPrimitive class for hyberbolic arc type. See
hyperbolic_arc?for information about plotting a hyperbolic arc in the complex plane.INPUT:
a, b- coordinates of the hyperbolic arc in the complex planeoptions- dict of valid plot options to pass to constructor
EXAMPLES:
Note that constructions should use
hyperbolic_arc:sage: from sage.plot.hyperbolic_arc import HyperbolicArc sage: print(HyperbolicArc(0, 1/2+I*sqrt(3)/2, {})) Hyperbolic arc (0.000000000000000, 0.500000000000000 + 0.866025403784439*I)
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sage.plot.hyperbolic_arc.hyperbolic_arc(a, b, rgbcolor='blue', thickness=1, zorder=2, alpha=1, linestyle='solid', fill=False, **options)¶ Plot an arc from a to b in hyperbolic geometry in the complex upper half plane.
INPUT:
a, b- complex numbers in the upper half complex plane connected bye the arc
OPTIONS:
alpha- default: 1thickness- default: 1rgbcolor- default: ‘blue’linestyle- (default:'solid') The style of the line, which is one of'dashed','dotted','solid','dashdot', or'--',':','-','-.', respectively.
Examples:
Show a hyperbolic arc from 0 to 1:
sage: hyperbolic_arc(0, 1) Graphics object consisting of 1 graphics primitive
Show a hyperbolic arc from 1/2 to \(i\) with a red thick line:
sage: hyperbolic_arc(1/2, I, color='red', thickness=2) Graphics object consisting of 1 graphics primitive
Show a hyperbolic arc form \(i\) to \(2 i\) with dashed line:
sage: hyperbolic_arc(I, 2*I, linestyle='dashed') Graphics object consisting of 1 graphics primitive sage: hyperbolic_arc(I, 2*I, linestyle='--') Graphics object consisting of 1 graphics primitive