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?

• whuber: Please tell us precisely how you could not get correct results. What were the inputs and what were the outputs?
• Mike T: To quickly answer one of your questions: angular units are radians.

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):
enter image description here

about the anchor point on (1,0):
enter image description here

about the anchor point on (0.5,0.5):
enter image description here

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:
enter image description here
enter image description here

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)

• Developer: Note that ar is array (numpy or scipy) and also note that cnt is an array i.e., array([0,0]). All these are necessary to avoid problems with multiplication of lists in Python.
• Harry: I could not get it to work. I have a list of points and one anchor point I would like to get the rotated location of the points calculated per the angle specified.
• Harry: I have used this code:
• whuber: Once more, @Harry: exactly how does your attempt at a solution not "work"? We need something to go on here if we're going to do any better than guessing!
• Harry: def RotateAxis(AnchorX,AnchorY,inputx,inputy, WindDirection): x = inputx - AnchorX y = inputy - AnchorY resultx1 = x * cos(radians(WindDirection)) resultx2 = y * sin(radians(WindDirection)) resultx = resultx1 + resultx2 + AnchorX resulty1 = x * sin(radians(WindDirection)) resulty2 = y * cos(radians(WindDirection)) resulty = resulty1 + resulty2 + AnchorY return (resultx,resulty)