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add epsilon to collinearity test, plus a demo

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This commit is contained in:
Johann Dreo 2014-06-02 08:42:57 +02:00
commit 634ed47f42
1 changed files with 45 additions and 4 deletions
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49
geometry.py
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@ -4,6 +4,7 @@ from __future__ import division
import math import math
epsilon = 1e-6 epsilon = 1e-6
# epsilon = 0
def x( point ): def x( point ):
return point[0] return point[0]
@ -49,14 +50,16 @@ def is_point( segment ):
return segment[0] == segment[1] return segment[0] == segment[1]
def collinear( p, q, r ): def collinear( p, q, r, e = epsilon ):
"""Returns True if the 3 given points are collinear. """Returns True if the 3 given points are collinear.
Note: there is a lot of algorithm to test collinearity, the most known involving linear algebra. Note: there is a lot of algorithm to test collinearity, the most known involving linear algebra.
This one has been found in Jonathan Shewchuk's "Lecture Notes on Geometric Robustness". This one has been found in Jonathan Shewchuk's "Lecture Notes on Geometric Robustness".
It is maybe the most elegant one: just arithmetic on x and y, without ifs, sqrt or risk of divide-by-zero error. It is maybe the most elegant one: just arithmetic on x and y, without ifs, sqrt or risk of divide-by-zero error.
""" """
return (x(p)-x(r)) * (y(q)-y(r)) == (x(q)-x(r)) * (y(p)-y(r)) # Without epsilon comparison, this would ends as:
# return (x(p)-x(r)) * (y(q)-y(r)) == (x(q)-x(r)) * (y(p)-y(r))
return abs((x(p)-x(r)) * (y(q)-y(r)) - (x(q)-x(r)) * (y(p)-y(r))) <= e
def line_intersection( seg0, seg1 ): def line_intersection( seg0, seg1 ):
@ -162,6 +165,7 @@ if __name__ == "__main__":
import uberplot import uberplot
import matplotlib.pyplot as plot import matplotlib.pyplot as plot
# intersections demo
if len(sys.argv) > 1: if len(sys.argv) > 1:
scale = 100 scale = 100
nb = int(sys.argv[1]) nb = int(sys.argv[1])
@ -198,11 +202,48 @@ if __name__ == "__main__":
fig = plot.figure() fig = plot.figure()
ax = fig.add_subplot(111) ax = fig.add_subplot(121)
ax.set_aspect('equal')
uberplot.plot_segments( ax, segments, linewidth=0.5, edgecolor = "blue" ) uberplot.plot_segments( ax, segments, linewidth=0.5, edgecolor = "blue" )
uberplot.scatter_points( ax, points, edgecolor="blue", facecolor="blue", s=120, alpha=1, linewidth=1 ) uberplot.scatter_points( ax, points, edgecolor="blue", facecolor="blue", s=120, alpha=1, linewidth=1 )
uberplot.scatter_points( ax, line_inter, edgecolor="none", facecolor="green", s=60, alpha=0.5 ) uberplot.scatter_points( ax, line_inter, edgecolor="none", facecolor="green", s=60, alpha=0.5 )
uberplot.scatter_points( ax, seg_inter, edgecolor="none", facecolor="red", s=60, alpha=0.5 ) uberplot.scatter_points( ax, seg_inter, edgecolor="none", facecolor="red", s=60, alpha=0.5 )
ax.set_aspect('equal')
# collinear test demo
if len(sys.argv) > 1:
scale = 100
nb = int(sys.argv[1])
triangles = []
for t in range(nb):
triangles.append( [ [scale*random.random(),scale*random.random()] for i in range(3)] )
# forced collinear
t = [ [scale*random.random(),scale*random.random()] for i in range(2)]
triangles.append( [t[0],t[1],t[0]] )
else:
triangles = [
[(-60.45085, -24.898983), (-68.54102, -30.776835), (-58.54102, -30.776835)],
[(-68.54102, -0.0), (-65.45085, -9.510565), (-58.54102, -0.0)],
[(-65.45085, 9.510565), (-68.54102, -0.0), (-58.54102, -0.0)],
[(-68.54102, 30.776835), (-60.45085, 24.898983), (-58.54102, 30.776835)],
[(-58.54102, -0.0), (-65.45085, -9.510565), (-55.45085, -9.510565)],
[(-65.45085, -9.510565), (-57.36068, -15.388418), (-55.45085, -9.510565)],
[(-65.45085, 9.510565), (-58.54102, -0.0), (-55.45085, 9.510565)],
[(-65.45085, 9.510565), (-65.45085, 9.510565), (-55.45085, 9.510565)], # is collinear
]
ax = fig.add_subplot(122)
for triangle in triangles:
status="green"
if collinear(*triangle):
status="red"
uberplot.plot_segments( ax, utils.tour(triangle), edgecolor = status )
# ax.set_aspect('equal')
ax.axis('auto')
plot.show() plot.show()