Coverage for local/lib/python2.7/site-packages/sage/plot/hyperbolic_polygon.py : 77%

""" 

Polygons and triangles in hyperbolic geometry 

AUTHORS: 

- Hartmut Monien (2011-08) 

- Vincent Delecroix (2014-11) 

""" 

#***************************************************************************** 

# Copyright (C) 2011 Hartmut Monien <monien@th.physik.uni-bonn.de>, 

# 2014 Vincent Delecroix <20100.delecroix@gmail.com>, 

# 2015 Stefan Kraemer <skraemer@th.physik.uni-bonn.de> 

# 

# Distributed under the terms of the GNU General Public License (GPL) 

# 

# This code is distributed in the hope that it will be useful, 

# but WITHOUT ANY WARRANTY; without even the implied warranty of 

# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 

# General Public License for more details. 

# 

# The full text of the GPL is available at: 

# 

# http://www.gnu.org/licenses/ 

#***************************************************************************** 

from __future__ import print_function 

from sage.plot.bezier_path import BezierPath 

from sage.plot.misc import options, rename_keyword 

from sage.rings.all import CC 

class HyperbolicPolygon(BezierPath): 

""" 

Primitive class for hyberbolic polygon type. 

See ``hyperbolic_polygon?`` for information about plotting a hyperbolic 

polygon in the complex plane. 

INPUT: 

- ``pts`` -- coordinates of the polygon (as complex numbers) 

- ``options`` -- dict of valid plot options to pass to constructor 

EXAMPLES: 

Note that constructions should use :func:`hyperbolic_polygon` or 

:func:`hyperbolic_triangle`:: 

sage: from sage.plot.hyperbolic_polygon import HyperbolicPolygon 

sage: print(HyperbolicPolygon([0, 1/2, I], {})) 

Hyperbolic polygon (0.000000000000000, 0.500000000000000, 1.00000000000000*I) 

""" 

def __init__(self, pts, options): 

""" 

Initialize HyperbolicPolygon. 

EXAMPLES:: 

sage: from sage.plot.hyperbolic_polygon import HyperbolicPolygon 

sage: print(HyperbolicPolygon([0, 1/2, I], {})) 

Hyperbolic polygon (0.000000000000000, 0.500000000000000, 1.00000000000000*I) 

""" 

pts = [CC(_) for _ in pts] 

self.path = [] 

self._hyperbolic_arc(pts[0], pts[1], True) 

for i in range(1, len(pts) - 1): 

self._hyperbolic_arc(pts[i], pts[i + 1]) 

self._hyperbolic_arc(pts[-1], pts[0]) 

BezierPath.__init__(self, self.path, options) 

self._pts = pts 

def _repr_(self): 

""" 

String representation of HyperbolicPolygon. 

TESTS:: 

sage: from sage.plot.hyperbolic_polygon import HyperbolicPolygon 

sage: HyperbolicPolygon([0, 1/2, I], {})._repr_() 

'Hyperbolic polygon (0.000000000000000, 0.500000000000000, 1.00000000000000*I)' 

""" 

return "Hyperbolic polygon ({})".format(", ".join(map(str, self._pts))) 

def _hyperbolic_arc(self, z0, z3, first=False): 

""" 

Function to construct Bezier path as an approximation to 

the hyperbolic arc between the complex numbers z0 and z3 in the 

hyperbolic plane. 

""" 

z0, z3 = (CC(z0), CC(z3)) 

p = (abs(z0)*abs(z0)-abs(z3)*abs(z3))/(z0-z3).real()/2 

r = abs(z0-p) 

if abs(z3-z0)/r < 0.1: 

self.path.append([(z0.real(), z0.imag()), (z3.real(), z3.imag())]) 

return 

if z0.imag() == 0 and z3.imag() == 0: 

p = (z0.real()+z3.real())/2 

zm = CC(p, r) 

self._hyperbolic_arc(z0, zm, first) 

self._hyperbolic_arc(zm, z3) 

return 

else: 

zm = ((z0+z3)/2-p)/abs((z0+z3)/2-p)*r+p 

t = (8*zm-4*(z0+z3)).imag()/3/(z3-z0).real() 

z1 = z0 + t*CC(z0.imag(), (p-z0.real())) 

z2 = z3 - t*CC(z3.imag(), (p-z3.real())) 

if first: 

self.path.append([(z0.real(), z0.imag()), 

(z1.real(), z1.imag()), 

(z2.real(), z2.imag()), 

(z3.real(), z3.imag())]) 

first = False 

else: 

self.path.append([(z1.real(), z1.imag()), 

(z2.real(), z2.imag()), 

(z3.real(), z3.imag())]) 

@rename_keyword(color='rgbcolor') 

@options(alpha=1, fill=False, thickness=1, rgbcolor="blue", zorder=2, 

linestyle='solid') 

def hyperbolic_polygon(pts, **options): 

r""" 

Return a hyperbolic polygon in the hyperbolic plane with vertices ``pts``. 

Type ``?hyperbolic_polygon`` to see all options. 

INPUT: 

- ``pts`` -- a list or tuple of complex numbers 

OPTIONS: 

- ``alpha`` -- default: 1 

- ``fill`` -- default: ``False`` 

- ``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 polygon with coordinates `-1`, `3i`, `2+2i`, `1+i`:: 

sage: hyperbolic_polygon([-1,3*I,2+2*I,1+I]) 

Graphics object consisting of 1 graphics primitive 

.. PLOT:: 

P = hyperbolic_polygon([-1,3*I,2+2*I,1+I]) 

sphinx_plot(P) 

With more options:: 

sage: hyperbolic_polygon([-1,3*I,2+2*I,1+I], fill=True, color='red') 

Graphics object consisting of 1 graphics primitive 

.. PLOT:: 

P = hyperbolic_polygon([-1,3*I,2+2*I,1+I], fill=True, color='red') 

sphinx_plot(P) 

""" 

from sage.plot.all import Graphics 

g = Graphics() 

g._set_extra_kwds(g._extract_kwds_for_show(options)) 

g.add_primitive(HyperbolicPolygon(pts, options)) 

g.set_aspect_ratio(1) 

return g 

def hyperbolic_triangle(a, b, c, **options): 

""" 

Return a hyperbolic triangle in the hyperbolic plane with vertices ``(a,b,c)``. 

Type ``?hyperbolic_polygon`` to see all options. 

INPUT: 

- ``a, b, c`` -- complex numbers in the upper half complex plane 

OPTIONS: 

- ``alpha`` -- default: 1 

- ``fill`` -- default: ``False`` 

- ``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 triangle with coordinates `0, 1/2+i\sqrt{3}/2` and 

`-1/2+i\sqrt{3}/2`:: 

sage: hyperbolic_triangle(0, -1/2+I*sqrt(3)/2, 1/2+I*sqrt(3)/2) 

Graphics object consisting of 1 graphics primitive 

.. PLOT:: 

P = hyperbolic_triangle(0, 0.5*(-1+I*sqrt(3)), 0.5*(1+I*sqrt(3))) 

sphinx_plot(P) 

A hyperbolic triangle with coordinates `0, 1` and `2+i` and a dashed line:: 

sage: hyperbolic_triangle(0, 1, 2+i, fill=true, rgbcolor='red', linestyle='--') 

Graphics object consisting of 1 graphics primitive 

.. PLOT:: 

P = hyperbolic_triangle(0, 1, 2+i, fill=true, rgbcolor='red', linestyle='--') 

sphinx_plot(P) 

""" 

return hyperbolic_polygon((a, b, c), **options)