# This example can be boiled down to a more simplistic example
# to show the problem, but bu including the upper and lower
# bound ellipses, it demonstrates how significant this error
# is to our plots.
import math
from pylab import *
from matplotlib.patches import Ellipse, Arc
# given a point x, y
x = 2692.440
y = 6720.850
# get is the radius of a circle through this point
r = math.sqrt( x*x+y*y )
# show some comparative circles
delta = 6
##################################################
def custom_ellipse( ax, x, y, major, minor, theta, numpoints = 750, **kwargs ):
xs = []
ys = []
incr = 2.0*math.pi / numpoints
incrTheta = 0.0
while incrTheta <= (2.0*math.pi):
a = major * math.cos( incrTheta )
b = minor * math.sin( incrTheta )
l = math.sqrt( ( a**2 ) + ( b**2 ) )
phi = math.atan2( b, a )
incrTheta += incr
xs.append( x + ( l * math.cos( theta + phi ) ) )
ys.append( y + ( l * math.sin( theta + phi ) ) )
# end while
incrTheta = 2.0*math.pi
a = major * math.cos( incrTheta )
b = minor * math.sin( incrTheta )
l = sqrt( ( a**2 ) + ( b**2 ) )
phi = math.atan2( b, a )
xs.append( x + ( l * math.cos( theta + phi ) ) )
ys.append( y + ( l * math.sin( theta + phi ) ) )
ellipseLine = ax.plot( xs, ys, **kwargs )
##################################################
# make the axes
ax1 = subplot( 311, aspect='equal' )
ax1.set_aspect( 'equal', 'datalim' )
# make the lower-bound ellipse
diam = (r - delta) * 2.0
lower_ellipse = Ellipse( (0.0, 0.0), diam, diam, 0.0, fill=False, edgecolor="darkgreen" )
ax1.add_patch( lower_ellipse )
# make the target ellipse
diam = r * 2.0
target_ellipse = Ellipse( (0.0, 0.0), diam, diam, 0.0, fill=False, edgecolor="darkred" )
ax1.add_patch( target_ellipse )
# make the upper-bound ellipse
diam = (r + delta) * 2.0
upper_ellipse = Ellipse( (0.0, 0.0), diam, diam, 0.0, fill=False, edgecolor="darkblue" )
ax1.add_patch( upper_ellipse )
# make the target
diam = delta * 2.0
target = Ellipse( (x, y), diam, diam, 0.0, fill=False, edgecolor="#DD1208" )
ax1.add_patch( target )
# give it a big marker
ax1.plot( [x], [y], marker='x', linestyle='None', mfc='red', mec='red', markersize=10 )
##################################################
# make the axes
ax = subplot( 312, aspect='equal' , sharex=ax1, sharey=ax1)
ax.set_aspect( 'equal', 'datalim' )
# make the lower-bound arc
diam = (r - delta) * 2.0
lower_arc = Arc( (0.0, 0.0), diam, diam, 0.0, fill=False, edgecolor="darkgreen" )
ax.add_patch( lower_arc )
# make the target arc
diam = r * 2.0
target_arc = Arc( (0.0, 0.0), diam, diam, 0.0, fill=False, edgecolor="darkred" )
ax.add_patch( target_arc )
# make the upper-bound arc
diam = (r + delta) * 2.0
upper_arc = Arc( (0.0, 0.0), diam, diam, 0.0, fill=False, edgecolor="darkblue" )
ax.add_patch( upper_arc )
# make the target
diam = delta * 2.0
target = Arc( (x, y), diam, diam, 0.0, fill=False, edgecolor="#DD1208" )
ax.add_patch( target )
# give it a big marker
ax.plot( [x], [y], marker='x', linestyle='None', mfc='red', mec='red', markersize=10 )
##################################################
# now lets do the same thing again using a custom ellipse function
# make the axes
ax = subplot( 313, aspect='equal', sharex=ax1, sharey=ax1 )
ax.set_aspect( 'equal', 'datalim' )
# make the lower-bound ellipse
custom_ellipse( ax, 0.0, 0.0, r-delta, r-delta, 0.0, color="darkgreen" )
# make the target ellipse
custom_ellipse( ax, 0.0, 0.0, r, r, 0.0, color="darkred" )
# make the upper-bound ellipse
custom_ellipse( ax, 0.0, 0.0, r+delta, r+delta, 0.0, color="darkblue" )
# make the target
custom_ellipse( ax, x, y, delta, delta, 0.0, color="#BB1208" )
# give it a big marker
ax.plot( [x], [y], marker='x', linestyle='None', mfc='red', mec='red', markersize=10 )
# give it a big marker
ax.plot( [x], [y], marker='x', linestyle='None', mfc='red', mec='red', markersize=10 )
##################################################
# lets zoom in to see the area of interest
ax1.set_xlim(2650, 2735)
ax1.set_ylim(6705, 6735)
savefig("ellipse")
show()
