first of all, i am quite new in Python (an programming area) but i wish to learn and convert a function developed by jwpat7. Given a set of points derived from a convex hull
hull= [(560023.44957588764,6362057.3904932579),
(560023.44957588764,6362060.3904932579),
(560024.44957588764,6362063.3904932579),
(560026.94957588764,6362068.3904932579),
(560028.44957588764,6362069.8904932579),
(560034.94957588764,6362071.8904932579),
(560036.44957588764,6362071.8904932579),
(560037.44957588764,6362070.3904932579),
(560037.44957588764,6362064.8904932579),
(560036.44957588764,6362063.3904932579),
(560034.94957588764,6362061.3904932579),
(560026.94957588764,6362057.8904932579),
(560025.44957588764,6362057.3904932579),
(560023.44957588764,6362057.3904932579)]
this script return a print of all possible area following this post problem. The code develop by jwpat7 is:
import math
def mostfar(j, n, s, c, mx, my): # advance j to extreme point
xn, yn = hull[j][0], hull[j][1]
rx, ry = xn*c - yn*s, xn*s + yn*c
best = mx*rx + my*ry
while True:
x, y = rx, ry
xn, yn = hull[(j+1)%n][0], hull[(j+1)%n][1]
rx, ry = xn*c - yn*s, xn*s + yn*c
if mx*rx + my*ry >= best:
j = (j+1)%n
best = mx*rx + my*ry
else:
return (x, y, j)
n = len(hull)
iL = iR = iP = 1 # indexes left, right, opposite
pi = 4*math.atan(1)
for i in range(n-1):
dx = hull[i+1][0] - hull[i][0]
dy = hull[i+1][1] - hull[i][1]
theta = pi-math.atan2(dy, dx)
s, c = math.sin(theta), math.cos(theta)
yC = hull[i][0]*s + hull[i][1]*c
xP, yP, iP = mostfar(iP, n, s, c, 0, 1)
if i==0: iR = iP
xR, yR, iR = mostfar(iR, n, s, c, 1, 0)
xL, yL, iL = mostfar(iL, n, s, c, -1, 0)
area = (yP-yC)*(xR-xL)
print ' {:2d} {:2d} {:2d} {:2d} {:9.3f}'.format(i, iL, iP, iR, area)
the result is:
i iL iP iR Area
0 6 8 0 203.000
1 6 8 0 211.875
2 6 8 0 205.800
3 6 10 0 206.250
4 7 12 0 190.362
5 8 0 1 203.000
6 10 0 4 201.385
7 0 1 6 203.000
8 0 3 6 205.827
9 0 3 6 205.640
10 0 4 7 187.451
11 0 4 7 189.750
12 1 6 8 203.000
i wish to create a single function with the return of Length, Width, and Area of the smallest rectangle. Ex:
Length, Width, Area = get_minimum_area_rectangle(hull)
print Length, Width, Area
18.036, 10.392, 187.451
my questions are:
Thanks in advance
1) solution: one function following the first solution suggest by Scott Hunter, i have a problem to integrate mostfar() inside get_minimum_area_rectangle(). Any suggestion or help are really appreciate because i can learn.
#!/usr/bin/python
import math
def get_minimum_area_rectangle(hull):
# get pi greek
pi = 4*math.atan(1)
# number of points
n = len(hull)
# indexes left, right, opposite
iL = iR = iP = 1
# work clockwise direction
for i in range(n-1):
# distance on x axis
dx = hull[i+1][0] - hull[i][0]
# distance on y axis
dy = hull[i+1][1] - hull[i][1]
# get orientation angle of the edge
theta = pi-math.atan2(dy, dx)
s, c = math.sin(theta), math.cos(theta)
yC = hull[i][0]*s + hull[i][1]*c
from here following the above example of jwpat7 i need to use mostfar(). I have a problem to understand how integrate (sorry for the not right term) mostfar in this point
Here's an example of how to make it a functor object out of your code and use it -- along with a few changes to some other things I felt were worthwhile. A functor is an entity that serves the role of a function but can be operated upon like an object.
In Python there's less of a distinction between the two since functions are already singleton objects, but sometimes it's useful to create an specialized class for one. In this case it allows the helper function to be made into a private class method instead of it being global or nested which you seem to object to doing.
from math import atan2, cos, pi, sin
class GetMinimumAreaRectangle(object):
""" functor to find length, width, and area of the smallest rectangular
area of the given convex hull """
def __call__(self, hull):
self.hull = hull
mostfar = self._mostfar # local reference
n = len(hull)
min_area = 10**100 # huge value
iL = iR = iP = 1 # indexes left, right, opposite
# print ' {:>2s} {:>2s} {:>2s} {:>2s} {:>9s}'.format(
# 'i', 'iL', 'iP', 'iR', 'area')
for i in xrange(n-1):
dx = hull[i+1][0] - hull[i][0] # distance on x axis
dy = hull[i+1][1] - hull[i][1] # distance on y axis
theta = pi-atan2(dy, dx) # get orientation angle of the edge
s, c = sin(theta), cos(theta)
yC = hull[i][0]*s + hull[i][1]*c
xP, yP, iP = mostfar(iP, n, s, c, 0, 1)
if i==0: iR = iP
xR, yR, iR = mostfar(iR, n, s, c, 1, 0)
xL, yL, iL = mostfar(iL, n, s, c, -1, 0)
l, w = (yP-yC), (xR-xL)
area = l*w
# print ' {:2d} {:2d} {:2d} {:2d} {:9.3f}'.format(i, iL, iP, iR, area)
if area < min_area:
min_area, min_length, min_width = area, l, w
return (min_length, min_width, min_area)
def _mostfar(self, j, n, s, c, mx, my):
""" advance j to extreme point """
hull = self.hull # local reference
xn, yn = hull[j][0], hull[j][1]
rx, ry = xn*c - yn*s, xn*s + yn*c
best = mx*rx + my*ry
while True:
x, y = rx, ry
xn, yn = hull[(j+1)%n][0], hull[(j+1)%n][1]
rx, ry = xn*c - yn*s, xn*s + yn*c
if mx*rx + my*ry >= best:
j = (j+1)%n
best = mx*rx + my*ry
else:
return (x, y, j)
if __name__ == '__main__':
hull= [(560023.44957588764, 6362057.3904932579),
(560023.44957588764, 6362060.3904932579),
(560024.44957588764, 6362063.3904932579),
(560026.94957588764, 6362068.3904932579),
(560028.44957588764, 6362069.8904932579),
(560034.94957588764, 6362071.8904932579),
(560036.44957588764, 6362071.8904932579),
(560037.44957588764, 6362070.3904932579),
(560037.44957588764, 6362064.8904932579),
(560036.44957588764, 6362063.3904932579),
(560034.94957588764, 6362061.3904932579),
(560026.94957588764, 6362057.8904932579),
(560025.44957588764, 6362057.3904932579),
(560023.44957588764, 6362057.3904932579)]
gmar = GetMinimumAreaRectangle() # create functor object
print "dimensions and area of smallest enclosing rectangular area:"
print " {:.3f}(L) x {:.3f}(W) = {:.3f} area".format(*gmar(hull)) # use it
Output:
dimensions and area of smallest enclosing rectangular area:
10.393(L) x 18.037(W) = 187.451 area