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