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# Arcs in hyperbolic geometry

AUTHORS:

- Hartmut Monien (2011 - 08)

class `sage.plot.hyperbolic_arc.``HyperbolicArc`(A, B, options)

  Bases: `sage.plot.bezier_path.BezierPath`

  Primitive 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 plane
  - `options` - 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)

`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: 1
  - `thickness` - default: 1
  - `rgbcolor` - 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

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