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snowflake.py
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snowflake.py
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from dxfwrite import DXFEngine as dxf
import math
import random
import copy
import matplotlib.pyplot as plt
from matplotlib.path import Path
import matplotlib.patches as patches
def create3dPrintFile(points, filename):
"""
Generates a starter file for creating a 3d print
"""
drawing = dxf.drawing(filename + '.dxf')
for x in points:
polyline= dxf.polyline()
polyline.add_vertices(x)
polyline.close()
drawing.add(polyline)
drawing.save()
def plotPoints(points):
"""
Plots coordinates on a graph and connects them
takes in a list of points (tuples), or a list of lists of tuples
- ex: [(x1,y1), (x2,y2), ...]
- ex: [ [(x1,y1), (x2,y2), ...], [(x1,y1), (x2,y2), ...] ...]
"""
fig = plt.figure()
ax = fig.add_subplot(111)
ax.grid(linestyle='-', linewidth=1)
ax.set_axisbelow(True)
if type(points[0]) is not list:
path = Path(points)
patch = patches.PathPatch(path, facecolor='orange', lw=2)
patch.set_alpha(0.4)
ax.add_patch(patch)
# TODO: remove code dupe
else:
for x in points:
path = Path(x)
randomColor = [random.random() for x in range(0, 3)]
patch = patches.PathPatch(path, facecolor=randomColor, lw=2)
patch.set_alpha(0.4)
ax.add_patch(patch)
plt.axis('equal')
plt.xlabel('x coordinate')
plt.ylabel('y coordinate')
ax.autoscale_view()
plt.show()
def rotate(origin, point, angle):
"""
Rotate a point counterclockwise by a given angle around a given origin.
The angle should be given in degrees.
"""
angle = math.radians(angle)
ox, oy = origin
px, py = point
cosA = math.cos(angle)
sinA = math.sin(angle)
qx = ox + cosA * (px - ox) - sinA * (py - oy)
qy = oy + sinA * (px - ox) + cosA * (py - oy)
return (qx, qy)
def rotateList(l, pivot, angle):
return [rotate(pivot, x, angle) for x in l]
def rotatePetal(l, angle=15, pivot=(0,0)):
"""
Rotates a set of coordinates around a pivot point, for a given angle
- Optional:
angle: angle in degrees, default=15
pivot: a tuple that represents (x,y) pivot point, default=(0,0)
"""
total = []
for x in l:
total.append(rotateList(x, pivot, angle))
return total
import PointsAlongPolygon as pp
def getChildrenCoordinates(coords, numChildren, yCutoff):
"""
Figures out points along the polygon (defined by coords) that children can be put at
"""
pointsAbovePerim = []
numPointsOnPerim = 0
# TODO: super innefficient, but it works
# Because PointsAlongPolygon.PerimeterPnts calculates evenly across the total permin,
# we want to get the number of children, but only above a certain cutoff on the y axis
# So Keep increasing the points pp.PerimeterPnts calculates until there are numChildren points above the cutoff
while len(pointsAbovePerim) < numChildren:
numPointsOnPerim += 1
pointsAbovePerim = []
perimeterPoints = pp.PerimeterPnts([coords], numPointsOnPerim)
for p in perimeterPoints:
if p[1] >= yCutoff:
tmp = {'coords': p, 'lineSegment': perimeterPoints[p]}
pointsAbovePerim.append(tmp)
return pointsAbovePerim
# TODO: optimize list so that a straight line isn't split into multiple segments (by user)
def min(coords):
# returns min y coordniate pair, or midpoint of min line
# sort list by y value
sortedCoords = sorted(coords, key=lambda x: x[1])
p1, p2 = sortedCoords[:2]
if p1[1] == p2[1]:
return ((p2[0] + p1[0]) / 2, p2[1])
else:
return p1
def transformey(coords, scalars, offsets, localScale=True, origin=None):
"""
Applies a transformation to coordinate set
coords: list of tuples [(x1,y1), (x2,y2), ...],
scalars: tuple (x scalar, y scalar)
offsets tuple (x offset, y offset)
"""
# NOTE: maybe break up in to translate and scaling functions
newCoords = []
for p in coords:
x, y = p
if localScale is True and origin:
x = x - origin[0]
y = y - origin[1]
x = x * scalars[0] + offsets[0] # TODO: priority option
y = y * scalars[1] + offsets[1]
if localScale is True and origin:
x = x + origin[0]
y = y + origin[1]
newCoords.append((x,y))
return newCoords
def length(coords, axis):
"""
Returns the max distance between the points on the given axis
axis=0 is x
axis=1 is y, etc
"""
s = sorted(coords, key=lambda x: x[axis])
minn = s[0]
maxx = s[-1]
return maxx[axis] - minn[axis]
def getRotation(endPoints):
"""
Figures out the angle of rotation wanted for a child. That is angle of the line segment the child falls on
endPoints: two coordinates on linear line [(x1,y1), (x2,y2)]
"""
p1, p2 = endPoints
xDiff = p2[0] - p1[0]
yDiff = p2[1] - p1[1]
angleOfInclination = math.atan2(yDiff, xDiff)
angleOfInclination = math.degrees(angleOfInclination)
return angleOfInclination + 180
def grow(coords, numChildren=4, yCutoff=None, origin=None, scalar=0.33):
"""
Returns all of the transformations for the first iteration of children for coords
aka makes numChildren kids of coords, that are scaled and evenly spaced around coords
coords: [(x1,y1), (x2,y2)....]
yCutoff: The y value that children will appear above
origin: pivot point for coords
scalar: size of child relative to coords
"""
finalCoords = [ ]
if yCutoff is None:
yCutoff = length(coords, 1) / 2
if origin is None:
origin = min(coords)
scaledCoords = transformey(coords, [scalar, scalar], [0,0], localScale=True, origin=origin) # siblings are the same scale
childTranslations = getChildrenCoordinates(coords, numChildren, yCutoff)
for i in range(numChildren):
translateX, translateY = childTranslations[i]['coords']
translateX -= origin[0]
translateY -= origin[1]
angle = getRotation(childTranslations[i]['lineSegment'])
rotatedCoords = rotateList(scaledCoords, origin, angle)
translatedCoords = transformey(rotatedCoords, [1,1], [translateX,translateY], localScale=False)
info = {
'coords': translatedCoords,
'translation': (translateX, translateY),
'rotation': angle,
'origin': (translateX + origin[0], translateY + origin[1]),
'depth': 1
}
finalCoords.append(info)
return finalCoords
# then for one child, we take all the children in finalCoords, scale it, rotate and translate it by the amount that that child was
def genChild(template, parent, scalar):
"""
parent is the shape that the child will be placed along. the template is the one of the originally generated versions of the shape (1 of numChildren original children)
"""
#scalar = scalar ** parent['depth']
coords = template['coords']
x, y = parent['translation']
parentOrign = (parent['origin'][0] - x, parent['origin'][1] - y)
for i in range(parent['depth']):
coords = transformey(coords, [scalar, scalar], [0,0], origin=parentOrign)
coords = transformey(coords, [1,1], parent['translation'] )
coords = rotateList(coords, parent['origin'], parent['rotation'])
kid = {
'coords': coords, 'translation': (x,y),
'rotation': parent['rotation'],
'origin': (x + parentOrign[0], y + parentOrign[1]),
'depth': parent['depth'] + 1
}
return kid
def growFlake(startCoords, depth=3, numChildren=3, scalar=0.4):
final = []
totalNumShapes = depth**numChildren + numChildren + 1
base = grow(startCoords, numChildren=numChildren, yCutoff=1, scalar=scalar) # minus startCoords
baseCopy = [x for x in base]
if depth == 1:
return [startCoords] + [x['coords'] for x in base]
grandKidCoords = []
while len(baseCopy) > 0:
# if len(baseCopy) > totalNumShapes:
# break
parent = baseCopy.pop()
if parent['depth'] >= depth:
continue
more = []
for template in base: # this makes all the necessary children for a given polygon
grandKid = genChild(template, parent, scalar)
grandKidCoords.append(grandKid['coords'])
baseCopy.append(grandKid)
final = [startCoords] + [x['coords'] for x in base] + grandKidCoords
return final