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curves.py
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# Copy from https://github.com/PvdPal. Thanks!
import math
def hilbertCurve(iteration, rotation, xOffset=0, yOffset=0):
"""
The Hilbert Curve
This function creates a Hilbert curve of the given size, the higher the given
iteration is, the bigger the size of the Hilbert curve will be. The three
latter variables are needed to make sure the curve has the correct rotation
and offset. This is used to connect the multiple curves correctly.
"""
if(iteration > 1):
if(rotation == 'leftReverse'):
firstExtension = hilbertCurve(iteration - 1, 'topReverse', math.pow(2, iteration - 1) + xOffset, 0 + yOffset)
secondExtension = hilbertCurve(iteration - 1, 'leftReverse', 0 + xOffset, 0 + yOffset)
thirdExtension = hilbertCurve(iteration - 1, 'leftReverse', 0 + xOffset, math.pow(2, iteration - 1) + yOffset)
fourthExtension = hilbertCurve(iteration - 1, 'bottomReverse', math.pow(2, iteration - 1) + xOffset, math.pow(2, iteration - 1) + yOffset)
return firstExtension + secondExtension + thirdExtension + fourthExtension
elif(rotation == 'top'):
firstExtension = hilbertCurve(iteration - 1, 'right', 0 + xOffset, 0 + yOffset)
secondExtension = hilbertCurve(iteration - 1, 'top', 0 + xOffset, math.pow(2, iteration - 1) + yOffset)
thirdExtension = hilbertCurve(iteration - 1, 'top', math.pow(2, iteration - 1) + xOffset, math.pow(2, iteration - 1) + yOffset)
fourthExtension = hilbertCurve(iteration - 1, 'left', math.pow(2, iteration - 1) + xOffset, 0 + yOffset)
return firstExtension + secondExtension + thirdExtension + fourthExtension
elif(rotation == 'rightReverse'):
firstExtension = hilbertCurve(iteration - 1, 'bottomReverse', 0 + xOffset, math.pow(2, iteration - 1) + yOffset)
secondExtension = hilbertCurve(iteration - 1, 'rightReverse', math.pow(2, iteration - 1) + xOffset, math.pow(2, iteration - 1) + yOffset)
thirdExtension = hilbertCurve(iteration - 1, 'rightReverse', math.pow(2, iteration - 1) + xOffset, 0 + yOffset)
fourthExtension = hilbertCurve(iteration - 1, 'topReverse', 0 + xOffset, 0 + yOffset)
return firstExtension + secondExtension + thirdExtension + fourthExtension
elif(rotation == 'bottom'):
firstExtension = hilbertCurve(iteration - 1, 'left', math.pow(2, iteration - 1) + xOffset, math.pow(2, iteration - 1) + yOffset)
secondExtension = hilbertCurve(iteration - 1, 'bottom', math.pow(2, iteration - 1) + xOffset, 0 + yOffset)
thirdExtension = hilbertCurve(iteration - 1, 'bottom', 0 + xOffset, 0 + yOffset)
fourthExtension = hilbertCurve(iteration - 1, 'right', 0 + xOffset, math.pow(2, iteration - 1) + yOffset)
return firstExtension + secondExtension + thirdExtension + fourthExtension
elif(rotation == 'left'):
firstExtension = hilbertCurve(iteration - 1, 'bottom', math.pow(2, iteration - 1) + xOffset, math.pow(2, iteration - 1) + yOffset)
secondExtension = hilbertCurve(iteration - 1, 'left', 0 + xOffset, math.pow(2, iteration - 1) + yOffset)
thirdExtension = hilbertCurve(iteration - 1, 'left', 0 + xOffset, 0 + yOffset)
fourthExtension = hilbertCurve(iteration - 1, 'top', math.pow(2, iteration - 1) + xOffset, 0 + yOffset)
return firstExtension + secondExtension + thirdExtension + fourthExtension
elif(rotation == 'topReverse'):
firstExtension = hilbertCurve(iteration - 1, 'leftReverse', math.pow(2, iteration - 1) + xOffset, 0 + yOffset)
secondExtension = hilbertCurve(iteration - 1, 'topReverse', math.pow(2, iteration - 1) + xOffset, math.pow(2, iteration - 1) + yOffset)
thirdExtension = hilbertCurve(iteration - 1, 'topReverse', 0 + xOffset, math.pow(2, iteration - 1) + yOffset)
fourthExtension = hilbertCurve(iteration - 1, 'rightReverse', 0 + xOffset, 0 + yOffset)
return firstExtension + secondExtension + thirdExtension + fourthExtension
elif(rotation == 'right'):
firstExtension = hilbertCurve(iteration - 1, 'top', 0 + xOffset, 0 + yOffset)
secondExtension = hilbertCurve(iteration - 1, 'right', math.pow(2, iteration - 1) + xOffset, 0 + yOffset)
thirdExtension = hilbertCurve(iteration - 1, 'right', math.pow(2, iteration - 1) + xOffset, math.pow(2, iteration - 1) + yOffset)
fourthExtension = hilbertCurve(iteration - 1, 'bottom', 0 + xOffset, math.pow(2, iteration - 1) + yOffset)
return firstExtension + secondExtension + thirdExtension + fourthExtension
elif(rotation == 'bottomReverse'):
firstExtension = hilbertCurve(iteration - 1, 'rightReverse', 0 + xOffset, math.pow(2, iteration - 1) + yOffset)
secondExtension = hilbertCurve(iteration - 1, 'bottomReverse', 0 + xOffset, 0 + yOffset)
thirdExtension = hilbertCurve(iteration - 1, 'bottomReverse', math.pow(2, iteration - 1) + xOffset, 0 + yOffset)
fourthExtension = hilbertCurve(iteration - 1, 'leftReverse', math.pow(2, iteration - 1) + xOffset, math.pow(2, iteration - 1) + yOffset)
return firstExtension + secondExtension + thirdExtension + fourthExtension
else:
if(rotation == 'left'):
return [(1 + xOffset, 1 + yOffset),
(0 + xOffset, 1 + yOffset),
(0 + xOffset, 0 + yOffset),
(1 + xOffset, 0 + yOffset)]
elif(rotation == 'top'):
return [(0 + xOffset, 0 + yOffset),
(0 + xOffset, 1 + yOffset),
(1 + xOffset, 1 + yOffset),
(1 + xOffset, 0 + yOffset)]
elif(rotation == 'right'):
return [(0 + xOffset, 0 + yOffset),
(1 + xOffset, 0 + yOffset),
(1 + xOffset, 1 + yOffset),
(0 + xOffset, 1 + yOffset)]
elif(rotation == 'bottom'):
return [(1 + xOffset, 1 + yOffset),
(1 + xOffset, 0 + yOffset),
(0 + xOffset, 0 + yOffset),
(0 + xOffset, 1 + yOffset)]
elif(rotation == 'leftReverse'):
return [(1 + xOffset, 0 + yOffset),
(0 + xOffset, 0 + yOffset),
(0 + xOffset, 1 + yOffset),
(1 + xOffset, 1 + yOffset)]
elif(rotation == 'topReverse'):
return [(1 + xOffset, 0 + yOffset),
(1 + xOffset, 1 + yOffset),
(0 + xOffset, 1 + yOffset),
(0 + xOffset, 0 + yOffset)]
elif(rotation == 'rightReverse'):
return [(0 + xOffset, 1 + yOffset),
(1 + xOffset, 1 + yOffset),
(1 + xOffset, 0 + yOffset),
(0 + xOffset, 0 + yOffset)]
elif(rotation == 'bottomReverse'):
return [(0 + xOffset, 1 + yOffset),
(0 + xOffset, 0 + yOffset),
(1 + xOffset, 0 + yOffset),
(1 + xOffset, 1 + yOffset)]
def mooreCurve(iteration, rotation, xOffset=0, yOffset=0):
"""
The Moore Curve
This function creates a Moore curve of the given size, the higher the given
iteration is, the bigger the size of the Moore curve will be. The three
latter variables are needed to make sure the curve has the correct rotation
and offset. This is used to connect the multiple curves correctly.
"""
if(iteration > 1):
if(rotation == 'right'):
firstExtension = hilbertCurve(iteration - 1, 'top', 0 + xOffset, math.pow(2, iteration - 1) + yOffset)
secondExtension = hilbertCurve(iteration - 1, 'top', math.pow(2, iteration - 1) + xOffset, math.pow(2, iteration - 1) + yOffset)
thirdExtension = hilbertCurve(iteration - 1, 'bottom', math.pow(2, iteration - 1) + xOffset, 0 + yOffset)
fourthExtension = hilbertCurve(iteration - 1, 'bottom', 0 + xOffset, 0 + yOffset)
return firstExtension + secondExtension + thirdExtension + fourthExtension
elif(rotation == 'top'):
firstExtension = hilbertCurve(iteration - 1, 'leftReverse', 0 + xOffset, 0 + yOffset)
secondExtension = hilbertCurve(iteration - 1, 'leftReverse', 0 + xOffset, math.pow(2, iteration - 1) + yOffset)
thirdExtension = hilbertCurve(iteration - 1, 'rightReverse', math.pow(2, iteration - 1) + xOffset, math.pow(2, iteration - 1) + yOffset)
fourthExtension = hilbertCurve(iteration - 1, 'rightReverse', math.pow(2, iteration - 1) + xOffset, 0 + yOffset)
return firstExtension + secondExtension + thirdExtension + fourthExtension
elif(rotation == 'left'):
firstExtension = hilbertCurve(iteration - 1, 'bottom', math.pow(2, iteration - 1) + xOffset, 0 + yOffset)
secondExtension = hilbertCurve(iteration - 1, 'bottom', 0 + xOffset, 0 + yOffset)
thirdExtension = hilbertCurve(iteration - 1, 'top', 0 + xOffset, math.pow(2, iteration - 1) + yOffset)
fourthExtension = hilbertCurve(iteration - 1, 'top', math.pow(2, iteration - 1) + xOffset, math.pow(2, iteration - 1) + yOffset)
return firstExtension + secondExtension + thirdExtension + fourthExtension
elif(rotation == 'bottom'):
firstExtension = hilbertCurve(iteration - 1, 'rightReverse', math.pow(2, iteration - 1) + xOffset, math.pow(2, iteration - 1) + yOffset)
secondExtension = hilbertCurve(iteration - 1, 'rightReverse', math.pow(2, iteration - 1) + xOffset, 0 + yOffset)
thirdExtension = hilbertCurve(iteration - 1, 'leftReverse', 0 + xOffset, 0 + yOffset)
fourthExtension = hilbertCurve(iteration - 1, 'leftReverse', 0 + xOffset, math.pow(2, iteration - 1) + yOffset)
return firstExtension + secondExtension + thirdExtension + fourthExtension
elif(rotation == 'rightReverse'):
firstExtension = hilbertCurve(iteration - 1, 'bottomReverse', 0 + xOffset, 0 + yOffset)
secondExtension = hilbertCurve(iteration - 1, 'bottomReverse', math.pow(2, iteration - 1) + xOffset, 0 + yOffset)
thirdExtension = hilbertCurve(iteration - 1, 'topReverse', math.pow(2, iteration - 1) + xOffset, math.pow(2, iteration - 1) + yOffset)
fourthExtension = hilbertCurve(iteration - 1, 'topReverse', 0 + xOffset, math.pow(2, iteration - 1) + yOffset)
return firstExtension + secondExtension + thirdExtension + fourthExtension
elif(rotation == 'topReverse'):
firstExtension = hilbertCurve(iteration - 1, 'right', math.pow(2, iteration - 1) + xOffset, 0 + yOffset)
secondExtension = hilbertCurve(iteration - 1, 'right', math.pow(2, iteration - 1) + xOffset, math.pow(2, iteration - 1) + yOffset)
thirdExtension = hilbertCurve(iteration - 1, 'left', 0 + xOffset, math.pow(2, iteration - 1) + yOffset)
fourthExtension = hilbertCurve(iteration - 1, 'left', 0 + xOffset, 0 + yOffset)
return firstExtension + secondExtension + thirdExtension + fourthExtension
elif(rotation == 'leftReverse'):
firstExtension = hilbertCurve(iteration - 1, 'topReverse', math.pow(2, iteration - 1) + xOffset, math.pow(2, iteration - 1) + yOffset)
secondExtension = hilbertCurve(iteration - 1, 'topReverse', 0 + xOffset, math.pow(2, iteration - 1) + yOffset)
thirdExtension = hilbertCurve(iteration - 1, 'bottomReverse', 0 + xOffset, 0 + yOffset)
fourthExtension = hilbertCurve(iteration - 1, 'bottomReverse', math.pow(2, iteration - 1) + xOffset, 0 + yOffset)
return firstExtension + secondExtension + thirdExtension + fourthExtension
elif(rotation == 'bottomReverse'):
firstExtension = hilbertCurve(iteration - 1, 'left', 0 + xOffset, math.pow(2, iteration - 1) + yOffset)
secondExtension = hilbertCurve(iteration - 1, 'left', 0 + xOffset, 0 + yOffset)
thirdExtension = hilbertCurve(iteration - 1, 'right', math.pow(2, iteration - 1) + xOffset, 0 + yOffset)
fourthExtension = hilbertCurve(iteration - 1, 'right', math.pow(2, iteration - 1) + xOffset, math.pow(2, iteration - 1) + yOffset)
return firstExtension + secondExtension + thirdExtension + fourthExtension
else:
if(rotation == 'left'):
return [(1 + xOffset, 1 + yOffset),
(0 + xOffset, 1 + yOffset),
(0 + xOffset, 0 + yOffset),
(1 + xOffset, 0 + yOffset)]
elif(rotation == 'top'):
return [(0 + xOffset, 0 + yOffset),
(0 + xOffset, 1 + yOffset),
(1 + xOffset, 1 + yOffset),
(1 + xOffset, 0 + yOffset)]
elif(rotation == 'right'):
return [(0 + xOffset, 0 + yOffset),
(1 + xOffset, 0 + yOffset),
(1 + xOffset, 1 + yOffset),
(0 + xOffset, 1 + yOffset)]
elif(rotation == 'bottom'):
return [(1 + xOffset, 1 + yOffset),
(1 + xOffset, 0 + yOffset),
(0 + xOffset, 0 + yOffset),
(0 + xOffset, 1 + yOffset)]
elif(rotation == 'leftReverse'):
return [(1 + xOffset, 0 + yOffset),
(0 + xOffset, 0 + yOffset),
(0 + xOffset, 1 + yOffset),
(1 + xOffset, 1 + yOffset)]
elif(rotation == 'topReverse'):
return [(1 + xOffset, 0 + yOffset),
(1 + xOffset, 1 + yOffset),
(0 + xOffset, 1 + yOffset),
(0 + xOffset, 0 + yOffset)]
elif(rotation == 'rightReverse'):
return [(0 + xOffset, 1 + yOffset),
(1 + xOffset, 1 + yOffset),
(1 + xOffset, 0 + yOffset),
(0 + xOffset, 0 + yOffset)]
elif(rotation == 'bottomReverse'):
return [(0 + xOffset, 1 + yOffset),
(0 + xOffset, 0 + yOffset),
(1 + xOffset, 0 + yOffset),
(1 + xOffset, 1 + yOffset)]
def z_orderCurve(iteration, xOffset=0, yOffset=0):
"""
The Z-order Curve
This function creates a z-order curve of the given size, the higher the given
iteration is, the bigger the size of the z-order curve will be. The three
latter variables are needed to make sure the curve has the correct rotation
and offset. This is used to connect the multiple curves correctly.
"""
if iteration > 1:
firstExtension = z_orderCurve(iteration - 1, 0 + xOffset, math.pow(2, iteration - 1) + yOffset)
secondExtension = z_orderCurve(iteration - 1, math.pow(2, iteration - 1) + xOffset, math.pow(2, iteration - 1) + yOffset)
thirdExtension = z_orderCurve(iteration - 1, 0 + xOffset, 0 + yOffset)
fourthExtension = z_orderCurve(iteration - 1, math.pow(2, iteration - 1) + xOffset, 0 + yOffset)
return firstExtension + secondExtension + thirdExtension + fourthExtension
else:
return [(0 + xOffset, 1 + yOffset),
(1 + xOffset, 1 + yOffset),
(0 + xOffset, 0 + yOffset),
(1 + xOffset, 0 + yOffset)]