mightyscape-1.2/extensions/fablabchemnitz/spirograph/spirograph.py

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#!/usr/bin/python
import math
import os
import numpy as np
import scipy.signal as scipySignal
import inkscapeMadeEasy.inkscapeMadeEasy_Base as inkBase
import inkscapeMadeEasy.inkscapeMadeEasy_Draw as inkDraw
import inkscapeMadeEasy.inkscapeMadeEasy_Plot as inkPlot
# least common multiplier
def myLcm(x, y):
return x * y / math.gcd(int(x), int(y))
# ---------------------------------------------
# noinspection PyAttributeOutsideInit
class Spirograph(inkBase.inkscapeMadeEasy):
def __init__(self):
inkBase.inkscapeMadeEasy.__init__(self)
self.arg_parser.add_argument("--curveType", type=str, dest="curveType", default='resistor')
self.arg_parser.add_argument("--radius_R", type=float, dest="radius_R", default=10.0)
self.arg_parser.add_argument("--radius_r", type=float, dest="radius_r", default=5.0)
self.arg_parser.add_argument("--detailLevel", type=float, dest="detailLevel", default=1.0)
self.arg_parser.add_argument("--adaptiveTheta", type=self.bool, dest="adaptiveTheta", default=False)
self.arg_parser.add_argument("--pencil_distance", type=float, dest="pencil_distance", default=1.0)
self.arg_parser.add_argument("--drawBaseCircles", type=self.bool, dest="drawBaseCircles", default=False)
self.arg_parser.add_argument("--animate", type=self.bool, dest="animate", default=False)
self.arg_parser.add_argument("--directory", type=str, dest="directory", default='./')
def effect(self):
so = self.options
# sets the position to the viewport center, round to next 10.
position = [self.svg.namedview.center[0], self.svg.namedview.center[1]]
position[0] = int(math.ceil(position[0] / 10.0)) * 10
position[1] = int(math.ceil(position[1] / 10.0)) * 10
root_layer = self.document.getroot()
group = self.createGroup(root_layer, 'Spiro')
# curve parameters
R = so.radius_R
r = so.radius_r
d = so.pencil_distance
finalTheta = 2 * np.pi * myLcm(abs(r), R) / R
if 'hypo' in so.curveType.lower():
typeCurve = 'hypo'
if 'epi' in so.curveType.lower():
typeCurve = 'epi'
# markers and linestyles
Lgray = inkDraw.color.gray(0.8)
Dgray = inkDraw.color.gray(0.3)
# wheel
markerCenterDisk = inkDraw.marker.createDotMarker(self, nameID='diskCenter', scale=0.3, RenameMode=1, strokeColor=Dgray,
fillColor=inkDraw.color.defined('white'))
markerPen = inkDraw.marker.createDotMarker(self, nameID='diskPen', scale=0.3, RenameMode=1, strokeColor=Dgray,
fillColor=inkDraw.color.defined('white'))
[startArrowMarker, endArrowMarker] = inkDraw.marker.createArrow1Marker(self, nameID='arrowRot', RenameMode=1, scale=0.3, strokeColor=Dgray,
fillColor=Dgray)
if typeCurve == 'hypo':
self.lineStyleArrow = inkDraw.lineStyle.set(lineWidth=r / 40, lineColor=Dgray, markerStart=startArrowMarker, markerEnd=None)
else:
self.lineStyleArrow = inkDraw.lineStyle.set(lineWidth=r / 40, lineColor=Dgray, markerStart=None, markerEnd=endArrowMarker)
self.lineStyleARM = inkDraw.lineStyle.set(lineWidth=r / 40, lineColor=Dgray, markerStart=markerCenterDisk, markerEnd=markerPen)
self.lineStyleDisk = inkDraw.lineStyle.set(lineWidth=r / 40, lineColor=None, fillColor=Lgray)
# curve
self.lineStyleCurve = inkDraw.lineStyle.set(lineWidth=0.8, lineColor=inkDraw.color.defined('red'), markerStart=None, markerEnd=None,
markerMid=None)
self.lineStyleCurve2 = inkDraw.lineStyle.set(lineWidth=0.8, lineColor=inkDraw.color.defined('Dgreen'), markerStart=None, markerEnd=None,
markerMid=None)
self.lineStyleCurve3 = inkDraw.lineStyle.set(lineWidth=0.8, lineColor=inkDraw.color.defined('blue'), markerStart=None, markerEnd=None,
markerMid=None)
self.lineStylePre = inkDraw.lineStyle.set(lineWidth=1, lineColor=inkDraw.color.defined('red'))
self.constructionLine = inkDraw.lineStyle.set(lineWidth=0.5, lineColor=Dgray)
# draft Points
if so.adaptiveTheta:
nPrePoints = 10 * so.detailLevel # number of pre points per turn
thetasDraft = np.linspace(0, finalTheta, int(nPrePoints * finalTheta / (2 * np.pi)))
[pointsDraft, _, curvatureDraft] = self.calcCurve__trochoid(typeCurve, R, r, d, thetasDraft)
# find sampling points based on local curvature
nSamples = np.ones(curvatureDraft.shape)*min(2,so.detailLevel)
detailFactor=5
# treshold normalized curvatures
nSamples[curvatureDraft>0.8] *=detailFactor
detailFactor = 2.5
# check if vector changed direction abuptly
for i,p in enumerate(pointsDraft):
if i==0:
v1=pointsDraft[i+1]-pointsDraft[i]
v2=pointsDraft[i]-pointsDraft[-1]
elif i < len(pointsDraft)-1:
v1=pointsDraft[i+1]-pointsDraft[i]
v2=pointsDraft[i]-pointsDraft[i-1]
else:
v1=pointsDraft[0]-pointsDraft[i]
v2=pointsDraft[i]-pointsDraft[i-1]
v1=v1/np.linalg.norm(v1)
v2=v2/np.linalg.norm(v2)
if np.dot(v1,v2)<0.5:
nSamples[i] *=detailFactor
thetasFinal = np.array([])
for i in range(len(nSamples) - 1):
thetasFinal = np.append(thetasFinal, np.linspace(thetasDraft[i], thetasDraft[i + 1], int(nSamples[i]), endpoint=False))
thetasFinal = np.append(thetasFinal, finalTheta)
# filter the sampled angles to have a smooth transition.
Ntaps = 5
gaussWindow = scipySignal.gaussian(Ntaps, std=5)
gaussWindow = gaussWindow / np.sum(gaussWindow)
# inkPlot.plot.cartesian(self, root_layer, np.arange(thetasFinal.shape[0]), thetasFinal * 180 / np.pi, position, xTicks=False, yTicks=True, xTickStep=thetasFinal.shape[0]/10, yTickStep=120.0, xScale=10, yScale=10,xGrid=True, yGrid=True, forceXlim=None, forceYlim=None)
thetasFinal = scipySignal.filtfilt(gaussWindow, np.array([1]), thetasFinal)
# inkPlot.plot.cartesian(self, root_layer, np.arange(thetasFinal.shape[0]), thetasFinal * 180 / np.pi, position, xTicks=False, yTicks=True,xTickStep=thetasFinal.shape[0]/10, yTickStep=120.0, xScale=10, yScale=10, xGrid=True, yGrid=True, forceXlim=None, forceYlim=None,drawAxis=False)
else:
nPrePoints = 20 * so.detailLevel # number of pre points per turn
thetasFinal = np.linspace(0, finalTheta, int(nPrePoints * finalTheta / (2 * np.pi)))
# final shape
[PointsFinal, CentersFinal, curvatureFinal] = self.calcCurve__trochoid(typeCurve, R, r, d, thetasFinal)
[PointsFinal2, CentersFinal2, curvatureFinal2] = self.calcCurve__trochoid(typeCurve, R, r, -d, thetasFinal)
[PointsFinal3, CentersFinal3, curvatureFinal3] = self.calcCurve__trochoid(typeCurve, R, r, r, thetasFinal)
if so.animate:
animGroup = self.createGroup(group, 'Anim')
circle_R = inkDraw.circle.centerRadius(parent=animGroup, centerPoint=[0, 0], radius=R, offset=position, lineStyle=self.constructionLine)
# draw planetary wheel
wheelGroup = self.createGroup(animGroup, 'Anim')
circle_r = inkDraw.circle.centerRadius(wheelGroup, centerPoint=CentersFinal[0], radius=r, offset=position, lineStyle=self.lineStyleDisk)
arms1 = inkDraw.line.absCoords(wheelGroup, coordsList=[CentersFinal[0], PointsFinal[0]], offset=position, lineStyle=self.lineStyleARM)
arms2 = inkDraw.line.absCoords(wheelGroup, coordsList=[CentersFinal2[0], PointsFinal2[0]], offset=position, lineStyle=self.lineStyleARM)
arms3 = inkDraw.line.absCoords(wheelGroup, coordsList=[CentersFinal3[0], PointsFinal3[0]], offset=position, lineStyle=self.lineStyleARM)
arc1 = inkDraw.arc.centerAngStartAngEnd(wheelGroup, centerPoint=CentersFinal[0], radius=r * 0.6, angStart=40, angEnd=80, offset=position,
lineStyle=self.lineStyleArrow)
arc2 = inkDraw.arc.centerAngStartAngEnd(wheelGroup, centerPoint=CentersFinal[0], radius=r * 0.6, angStart=160, angEnd=200,
offset=position, lineStyle=self.lineStyleArrow)
arc3 = inkDraw.arc.centerAngStartAngEnd(wheelGroup, centerPoint=CentersFinal[0], radius=r * 0.6, angStart=280, angEnd=320,
offset=position, lineStyle=self.lineStyleArrow)
self.exportSVG(animGroup, os.path.join(so.directory,'outSVG_%1.5d.svg' % 0))
for i in range(1, len(thetasFinal)):
self.moveElement(wheelGroup, [CentersFinal[i][0] - CentersFinal[i - 1][0], CentersFinal[i][1] - CentersFinal[i - 1][1]])
if typeCurve == 'hypo':
self.rotateElement(wheelGroup, [position[0] + CentersFinal[i][0], position[1] + CentersFinal[i][1]],
(thetasFinal[i] - thetasFinal[i - 1]) * (R - r) / r * 180 / np.pi)
else:
self.rotateElement(wheelGroup, [position[0] + CentersFinal[i][0], position[1] + CentersFinal[i][1]],
- (thetasFinal[i] - thetasFinal[i - 1]) * (R + r) / r * 180 / np.pi)
curve1 = inkDraw.line.absCoords(parent=animGroup, coordsList=PointsFinal[:i + 1], offset=position, lineStyle=self.lineStyleCurve,
closePath=False)
curve2 = inkDraw.line.absCoords(parent=animGroup, coordsList=PointsFinal2[:i + 1], offset=position, lineStyle=self.lineStyleCurve2,
closePath=False)
curve3 = inkDraw.line.absCoords(parent=animGroup, coordsList=PointsFinal3[:i + 1], offset=position, lineStyle=self.lineStyleCurve3,
closePath=False)
self.exportSVG(animGroup, os.path.join(so.directory , 'outSVG_%1.5d.svg' % i))
self.removeElement(curve1)
self.removeElement(curve2)
self.removeElement(curve3)
self.removeElement(animGroup)
else:
if so.drawBaseCircles:
inkDraw.circle.centerRadius(parent=group, centerPoint=position, radius=R, offset=[0, 0], lineStyle=self.constructionLine)
if typeCurve == 'hypo':
inkDraw.circle.centerRadius(parent=group, centerPoint=position, radius=r, offset=[R - r, 0], lineStyle=self.constructionLine)
if typeCurve == 'epi':
inkDraw.circle.centerRadius(parent=group, centerPoint=position, radius=r, offset=[R + r, 0], lineStyle=self.constructionLine)
inkDraw.line.absCoords(group, PointsFinal, position, 'spiro', self.lineStyleCurve, closePath=True)
# plot curvatures
if False:
inkPlot.plot.polar(self, group, curvatureFinal, thetasFinal * 180 / np.pi, [position[0] + 3 * R, position[1]], rTicks=False,
tTicks=False, rTickStep=0.2, tTickStep=45.0, rScale=20, rGrid=True, tGrid=True, lineStylePlot=self.lineStyleCurve,
forceRlim=[0.0, 1.0])
return
# typeCurve: 'hypo', 'epi'
def calcCurve__trochoid(self, typeCurve, R, r, d, thetas):
j = complex(0, 1)
if typeCurve.lower() == 'hypo':
# https://www.mathcurve.com/courbes2d.gb/hypotrochoid/hypotrochoid.shtml
P_complex = (R - r) * np.exp(j * thetas) + d * np.exp(-j * thetas * (R - r) / r)
dP_complex = (R - r) * j * np.exp(j * thetas) + d * (-j) * (R - r) / r * np.exp(-j * thetas * (R - r) / r)
ddP_complex = (R - r) * (-1) * np.exp(j * thetas) + d * (-1) * ((R - r) / r) ** 2 * np.exp(-j * thetas * (R - r) / r)
centerGear = (R - r) * np.exp(j * thetas)
if typeCurve.lower() == 'epi':
# https://www.mathcurve.com/courbes2d.gb/epitrochoid/epitrochoid.shtml
P_complex = (R + r) * np.exp(j * thetas) - d * np.exp(j * thetas * (R + r) / r)
dP_complex = (R + r) * j * np.exp(j * thetas) - d * j * (R + r) / r * np.exp(j * thetas * (R + r) / r)
ddP_complex = (R + r) * (-1) * np.exp(j * thetas) - d * (-1) * ((R + r) / r) ** 2 * np.exp(j * thetas * (R + r) / r)
centerGear = (R + r) * np.exp(j * thetas)
with np.errstate(divide='ignore', invalid='ignore'):
curvature = np.divide(abs(dP_complex.real * ddP_complex.imag - dP_complex.imag * ddP_complex.real),
(dP_complex.real ** 2 + dP_complex.imag ** 2) ** (2 / 3))
# remove Nan=0/0
np.nan_to_num(curvature, copy=False)
# remove values too large
curvature[curvature > 10 * np.mean(curvature)] = 0.0
# self.Dump(curvature, '/home/fernando/lixo.txt', 'w')
# normalize curvature
curvature = self._normalizeCurvatures(curvature, 0.0, 1.0)
Points = np.column_stack((P_complex.real, P_complex.imag))
Centers = np.column_stack((centerGear.real, centerGear.imag))
return [Points, Centers, curvature]
def _normalizeCurvatures(self, curvatures, normMin=0.0, normMax=1.0):
y1 = normMin
y2 = normMax
x1 = np.min(curvatures)
x2 = np.max(curvatures)
alpha = (y2 - y1) / (x2 - x1)
return alpha * (curvatures - x1) + y1
if __name__ == '__main__':
sp = Spirograph()
sp.run()