Rotating the polygon about anchor point using Python script

Question

I know there would be no tool in ArcPy module as such but might have in third party modules. I however tried taking the vertices of the polygon and moving using the below formula. But did not get the correct output coordinate values and polygon thus generated is weird.

I have tried this function

def RotateAxis(AnchorX,AnchorY,inputx,inputy, WindDirection):
    x = inputx - AnchorX
    y = inputy - AnchorY
    resultx = (x * math.cos(WindDirection)) - (y * math.sin(WindDirection)) + AnchorX
    resulty = (x * math.sin(WindDirection)) + (y * math.cos(WindDirection)) + AnchorY
    return (resultx,resulty)

where Anchor is the origin and WindDirection is the angle which I tried taking in radians as well as degrees but could not get correct results.

I tried with projected coordinates that didn't work either. Is there any suggestion?

Answer 1

You may use the following function:

def Rotate2D(pts,cnt,ang=pi/4):
    '''pts = {} Rotates points(nx2) about center cnt(2) by angle ang(1) in radian'''
    return dot(pts-cnt,ar([[cos(ang),sin(ang)],[-sin(ang),cos(ang)]]))+cnt

It works well as can be seen in the following figures: about the anchor point on (0,0):

about the anchor point on (1,0):

about the anchor point on (0.5,0.5):

Update:
Well here is the full code, you must be able to generate the exact results as here:

from __future__ import division                 #to avoid integer devision problem
import scipy
import pylab

#just for fun making further development easier and with joy
pi     = scipy.pi
dot    = scipy.dot
sin    = scipy.sin
cos    = scipy.cos
ar     = scipy.array
rand   = scipy.rand
arange = scipy.arange
plot   = pylab.plot
show   = pylab.show
axis   = pylab.axis
grid   = pylab.grid
title  = pylab.title
rad    = lambda ang: ang*pi/180                 #lovely lambda: degree to radian

#the function
def Rotate2D(pts,cnt,ang=pi/4):
    '''pts = {} Rotates points(nx2) about center cnt(2) by angle ang(1) in radian'''
    return dot(pts-cnt,ar([[cos(ang),sin(ang)],[-sin(ang),cos(ang)]]))+cnt

#the code for test
pts = ar([[0,0],[1,0],[1,1],[0.5,1.5],[0,1]])
plot(*pts.T,lw=5,color='k')                     #points (poly) to be rotated
for ang in arange(0,2*pi,pi/8):
    ots = Rotate2D(pts,ar([0.5,0.5]),ang)       #the results
    plot(*ots.T)
axis('image')
grid(True)
title('Rotate2D about a point')
show()

The results are:

Good luck!

Appendices:

>>> pts
array([[ 0. ,  0. ],
       [ 1. ,  0. ],
       [ 1. ,  1. ],
       [ 0.5,  1.5],
       [ 0. ,  1. ]])
>>> pts.shape
(5, 2)
>>> anchor = ar([0.5,0.5])
>>> anchor
array([ 0.5,  0.5])
>>> ots = Rotate2D(pts,anchor,ang=rad(45))
>>> ots
array([[ 0.5       , -0.20710678],
       [ 1.20710678,  0.5       ],
       [ 0.5       ,  1.20710678],
       [-0.20710678,  1.20710678],
       [-0.20710678,  0.5       ]])
>>> ots.shape
(5, 2)
>>> '''a single point'''
'a single point'
>>> pts = ar([3.1,1.3])
>>> pts.shape
(2,)
>>> ots = Rotate2D(pts,anchor,ang=rad(30))
>>> ots
array([ 2.35166605,  2.49282032])
>>> ots.shape
(2,)
>>> dts = ots.reshape(-1,2)
>>> dts
array([[ 2.35166605,  2.49282032]])
>>> dts.shape
(1, 2)