# -*- coding: utf-8 -*-
"""
Module to define particular circular tangents in a closed polygon in
:math:`\\mathbb{R}^2`.
"""
# %%
[docs]class pckCirclesInPolygon:
'''Creates an instance of an object that defines circular particles tangent
in a fractal way inside of a closed polygon in :math:`\\mathbb{R}^2`.
Attributes:
coordinates ((n, 2) `numpy.ndarray`): Coordinates of vertices of the\
polygon.
depth (`int`): Depth fractal for each triangle that compose the\
triangular mesh. If this number is not given, then,\
the fractal generation of circles is done up to a circle\
reachs a radius to lower than the five percent of the\
incircle radius. Large values of `depth` might produce internal\
variables that tend to infinte, then a\
``ValueError`` is produced with a warning message\
``array must not contain infs or NaNs``.
Note:
The class ``pckCirclesInPolygon`` requires\
`NumPy <http://www.numpy.org/>`_,\
`Matplotlib <https://matplotlib.org/>`_ and\
`Triangle <http://dzhelil.info/triangle/>`_
Examples:
>>> from numpy import array
>>> from circlespacking import pckCirclesInPolygon
>>> coords = array([[1, 1], [2, 5], [4.5, 6], [8, 3], [7, 1], [4, 0]])
>>> pckCircles = pckCirclesInPolygon(coords)
>>> pckCircles.__dict__.keys()
dict_keys(['coordinates', 'depth', 'CDT', 'listCircles'])
'''
def __init__(self, coordinates, depth=None):
'''Method for initializing the attributes of the class.'''
self.coordinates = coordinates
self.depth = depth
# initializing methods
self.trianglesMesh()
self.generator()
[docs] def trianglesMesh(self):
'''Method to generate a triangles mesh in a polygon by using
`Constrained Delaunay triangulation\
<https://en.wikipedia.org/wiki/Constrained_Delaunay_triangulation>`_.
Return:
verts ((n, 3, 2) `numpy.ndarray`): Vertices of each triangle that\
compose the triangular mesh. n means the number of triangles;\
(3, 2) means the index vertices and the coordinates (x, y)\
respectively.
Examples:
>>> from numpy import array
>>> from basegeometry import Polygon
>>> from circlespacking import pckCirclesInPolygon
>>> coordinates = array([[1, 1], [2, 5], [4.5, 6], [6, 4], [8, 3],
[7, 1], [4.5, 1], [4, 0]])
>>> polygon = Polygon(coordinates)
>>> boundCoords = polygon.boundCoords
>>> pckCircles = pckCirclesInPolygon(boundCoords)
>>> verts = pckCircles.trianglesMesh()
>>> from numpy import array
>>> from basegeometry import Polygon
>>> from circlespacking import pckCirclesInPolygon
>>> coordinates = array([[2, 2], [2, 6], [8, 6], [8, 2]])
>>> polygon = Polygon(coordinates)
>>> boundCoords= polygon.boundCoords
>>> pckCircles = pckCirclesInPolygon(boundCoords)
>>> verts = pckCircles.trianglesMesh()
'''
import numpy as np
from triangle import triangulate
# polygon area by applying the gauss equation
area = 0.5*abs(sum(self.coordinates[:-1, 0] * self.coordinates[1:, 1] -
self.coordinates[:-1, 1] * self.coordinates[1:, 0]))
index = np.arange(len(self.coordinates[:-1]))
indexSegmts = np.column_stack((index, np.hstack((index[1:], [0]))))
# Max area of the triangles in the Constrained Delaunay triangulation
maxArea = np.random.uniform(0.25 * area)
steinerPts = np.random.uniform(5, 50)
# constrained Delaunay triangulation
self.CDT = triangulate(tri={'vertices': self.coordinates[:-1],
'segments': indexSegmts},
opts='pq20a'+str(maxArea)+'S'+str(steinerPts))
vertsIndex = self.CDT['vertices']
trianglesIndex = self.CDT['triangles']
verts = vertsIndex[trianglesIndex]
return verts
[docs] def generator(self):
'''Method to generate circular particles in each triangle of the
triangular mesh.
Returns:
listCircles (`list` of Circle objects): `list` that contain all\
the circles object packed in the polygon.
Examples:
>>> from numpy import array
>>> from circlespacking import pckCirclesInPolygon
>>> coords = array([[2, 2], [2, 6], [8, 6], [8, 2]])
>>> pckCircles = pckCirclesInPolygon(coords)
>>> lstCircles = pckCircles.generator() # list of circles
'''
from basegeometry import Triangle
vertsTriangles = self.trianglesMesh() # Triangles mesh in polygon
self.listCircles = list()
for vert in vertsTriangles:
self.listCircles += Triangle(vert).packCircles(depth=self.depth,
want2plot=False)
return self.listCircles
[docs] def plot(self, plotTriMesh=False):
'''Method for show a graphic of the circles generated within of the
polyhon.
Parameters:
plotTriMesh (`bool`): Variable to check if it also want to show\
the graph of the triangles mesh. The default value is ``False``
Examples:
.. plot::
from numpy import array
from basegeometry import Polygon
from circlespacking import pckCirclesInPolygon
coordinates = array([[1, 1], [2, 5], [4.5, 6], [8, 3], [7, 1],
[4, 0]])
polygon = Polygon(coordinates)
boundCoords = polygon.boundCoords
pckCircles = pckCirclesInPolygon(boundCoords, depth=5)
pckCircles.plot(plotTriMesh=True)
>>> from numpy import array
>>> from basegeometry import Polygon
>>> from circlespacking import pckCirclesInPolygon
>>> coordinates = array([[1, 1], [2, 5], [4.5, 6], [6, 4], [8, 3],
[7, 1], [4.5, 1], [4, 0]])
>>> polygon = Polygon(coordinates)
>>> boundCoords = polygon.boundCoords
>>> pckCircles = pckCirclesInPolygon(boundCoords)
>>> pckCircles.plot()
>>> from slopegeometry import AnthropicSlope
>>> from circlespacking import pckCirclesInPolygon
>>> slopeGeometry = AnthropicSlope(12, [1, 1.5], 10, 10)
>>> boundCoords = slopeGeometry.boundCoords
>>> pckCircles = pckCirclesInPolygon(boundCoords)
>>> pckCircles.plot(plotTriMesh=True)
.. plot::
from numpy import array
from slopegeometry import NaturalSlope
from circlespacking import pckCirclesInPolygon
surfaceCoords = array([[-2.4900, 18.1614],
[0.1022, 17.8824],
[1.6975, 17.2845],
[3.8909, 15.7301],
[5.8963, 14.3090],
[8.1183, 13.5779],
[9.8663, 13.0027],
[13.2865, 3.6058],
[20.2865, 3.6058],
[21.4347, 3.3231],
[22.2823, 2.7114],
[23.4751, 2.2252],
[24.6522, 1.2056],
[25.1701, 0.2488]])
slopeGeometry = NaturalSlope(surfaceCoords)
boundCoords = slopeGeometry.boundCoords
pckCircles = pckCirclesInPolygon(boundCoords)
pckCircles.plot(plotTriMesh=True)
'''
import numpy as np
import matplotlib.pyplot as plt
from triangle import plot as tplot
# plotting
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(np.hstack((self.coordinates[:, 0], self.coordinates[0, 0])),
np.hstack((self.coordinates[:, 1], self.coordinates[0, 1])),
'-k', lw=1.5, label='Polygon')
ax.axis('equal')
ax.set_xlabel('$x$ distance')
ax.set_ylabel('$y$ distance')
ax.grid(ls='--', lw=0.5)
for circle in self.listCircles:
ax.add_patch(plt.Circle(circle.center, circle.radius, fill=False,
lw=1, ec='black'))
# plotting triangular mesh
if plotTriMesh:
fig = plt.figure()
ax = fig.add_subplot(111)
ax.grid(ls='--', lw=0.5)
tplot.plot(ax, **self.CDT)
ax.axis('equal')
return
[docs] def frecuencyHist(self):
'''Method to show the histogram of the diameters of the circular
particles packed in a closed polygon in :math:`\\mathbb{R}^2`.
Examples:
.. plot::
from numpy import array
from basegeometry import Polygon
from circlespacking import pckCirclesInPolygon
coordinates = array([[1, 1], [2, 5], [4.5, 6], [6, 4], [8, 3],
[7, 1], [4.5, 1], [4, 0]])
polygon = Polygon(coordinates)
boundCoords = polygon.boundCoords
pckCircles = pckCirclesInPolygon(boundCoords, 10)
pckCircles.frecuencyHist()
'''
import numpy as np
import math
import matplotlib.pyplot as plt
# Obtaining diameters histogram
n = len(self.listCircles) # simple size
# Number of bins according to Sturges equation
numBins = math.floor(1 + math.log(n, 2))
diams = [circle.diameter for circle in self.listCircles]
bins = np.linspace(min(diams), max(diams), numBins)
# plotting
plt.style.use('seaborn-white')
fig = plt.figure()
ax = fig.add_subplot(111)
ax.hist(diams, bins)
ax.grid(ls='--', lw=0.5)
ax.set_xlabel('Diameters')
ax.set_ylabel('Frecuency')
return
[docs] def loglogDiagram(self):
'''Method to show the log-log graph of the diameters and quantities
of circular particles packed in a closed polygon in
:math:`\\mathbb{R}^2`.
Examples:
.. plot::
from numpy import array
from basegeometry import Polygon
from circlespacking import pckCirclesInPolygon
coordinates = array([[1, 1], [2, 5], [4.5, 6], [6, 4], [8, 3],
[7, 1], [4.5, 1], [4, 0]])
polygon = Polygon(coordinates)
boundCoords = polygon.boundCoords
pckCircles = pckCirclesInPolygon(boundCoords, 10)
pckCircles.loglogDiagram()
'''
import matplotlib.pyplot as plt
import numpy as np
import math
# Obtaining diameters histogram
n = len(self.listCircles) # simple size
# Number of bins according to Sturges equation
numBins = math.floor(1 + math.log(n, 2))
diams = [circle.diameter for circle in self.listCircles]
bins = np.linspace(min(diams), max(diams), numBins)
hist, binEdges = np.histogram(diams, bins)
nonZeroIndx = [i for i, k in enumerate(hist) if k != 0]
histRed = hist[nonZeroIndx]
histRedRel = [float(k)/n * 100 for k in histRed]
nonZeroIndx4Bins = [k+1 for k in nonZeroIndx]
binEdgesRed = binEdges[nonZeroIndx4Bins]
d = binEdgesRed
nD = histRedRel
# plotting
fig = plt.figure()
ax = fig.add_subplot(111)
ax.loglog(d, nD, 'ko', basex=2)
ax.grid(ls='--', lw=0.5)
return
# %%
'''
BSD 2 license.
Copyright (c) 2018, Universidad Nacional de Colombia, Andres Ariza-Triana
and Ludger O. Suarez-Burgoa.
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:
1. Redistributions of source code must retain the above copyright notice,
this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR
CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
'''