Coverage for local/lib/python2.7/site-packages/sage/plot/hyperbolic_arc.py : 72%

""" 

Arcs in hyperbolic geometry 

AUTHORS: 

- Hartmut Monien (2011 - 08) 

""" 

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

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

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

# 2016 Javier Honrubia <jhonrubia6@uned.es> 

# 

# 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.colors import to_mpl_color 

from sage.plot.misc import options, rename_keyword 

from sage.rings.all import CC 

class HyperbolicArc(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) 

""" 

def __init__(self, A, B, options): 

A, B = (CC(A), CC(B)) 

if A.imag()<0: 

raise ValueError("%s is not a valid point in the UHP model"%(A)) 

if B.imag()<0: 

raise ValueError("%s is not a valid point in the UHP model"%(B)) 

self.path = [] 

self._hyperbolic_arc(A, B, True); 

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

self.A, self.B = (A, B) 

def _repr_(self): 

""" 

String representation of HyperbolicArc. 

TESTS:: 

sage: from sage.plot.hyperbolic_arc import HyperbolicArc 

sage: HyperbolicArc(0, 1/2+I*sqrt(3)/2, {})._repr_() 

'Hyperbolic arc (0.000000000000000, 0.500000000000000 + 0.866025403784439*I)' 

""" 

return "Hyperbolic arc (%s, %s)" % (self.A, self.B) 

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_arc(a, b, **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 

""" 

from sage.plot.all import Graphics 

g = Graphics() 

g._set_extra_kwds(g._extract_kwds_for_show(options)) 

g.add_primitive(HyperbolicArc(a, b, options)) 

g.set_aspect_ratio(1) 

return g