111 lines
3.3 KiB
Python
111 lines
3.3 KiB
Python
# -*- coding: utf-8 -*-
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"""
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Displays an interactive Koch fractal
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"""
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import initExample ## Add path to library (just for examples; you do not need this)
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from functools import reduce
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import pyqtgraph as pg
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from pyqtgraph.Qt import QtCore, QtGui
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import numpy as np
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app = pg.mkQApp("Fractal Example")
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# Set up UI widgets
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win = pg.QtGui.QWidget()
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win.setWindowTitle('pyqtgraph example: fractal demo')
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layout = pg.QtGui.QGridLayout()
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win.setLayout(layout)
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layout.setContentsMargins(0, 0, 0, 0)
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depthLabel = pg.QtGui.QLabel('fractal depth:')
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layout.addWidget(depthLabel, 0, 0)
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depthSpin = pg.SpinBox(value=5, step=1, bounds=[1, 10], delay=0, int=True)
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depthSpin.resize(100, 20)
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layout.addWidget(depthSpin, 0, 1)
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w = pg.GraphicsLayoutWidget()
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layout.addWidget(w, 1, 0, 1, 2)
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win.show()
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# Set up graphics
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v = w.addViewBox()
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v.setAspectLocked()
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baseLine = pg.PolyLineROI([[0, 0], [1, 0], [1.5, 1], [2, 0], [3, 0]], pen=(0, 255, 0, 100), movable=False)
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v.addItem(baseLine)
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fc = pg.PlotCurveItem(pen=(255, 255, 255, 200), antialias=True)
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v.addItem(fc)
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v.autoRange()
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transformMap = [0, 0, None]
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def update():
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# recalculate and redraw the fractal curve
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depth = depthSpin.value()
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pts = baseLine.getState()['points']
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nbseg = len(pts) - 1
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nseg = nbseg**depth
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# Get a transformation matrix for each base segment
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trs = []
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v1 = pts[-1] - pts[0]
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l1 = v1.length()
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for i in range(len(pts)-1):
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p1 = pts[i]
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p2 = pts[i+1]
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v2 = p2 - p1
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t = p1 - pts[0]
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r = v2.angle(v1)
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s = v2.length() / l1
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trs.append(pg.SRTTransform({'pos': t, 'scale': (s, s), 'angle': r}))
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basePts = [np.array(list(pt) + [1]) for pt in baseLine.getState()['points']]
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baseMats = np.dstack([tr.matrix().T for tr in trs]).transpose(2, 0, 1)
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# Generate an array of matrices to transform base points
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global transformMap
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if transformMap[:2] != [depth, nbseg]:
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# we can cache the transform index to save a little time..
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nseg = nbseg**depth
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matInds = np.empty((depth, nseg), dtype=int)
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for i in range(depth):
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matInds[i] = np.tile(np.repeat(np.arange(nbseg), nbseg**(depth-1-i)), nbseg**i)
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transformMap = [depth, nbseg, matInds]
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# Each column in matInds contains the indices referring to the base transform
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# matrices that must be multiplied together to generate the final transform
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# for each segment of the fractal
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matInds = transformMap[2]
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# Collect all matrices needed for generating fractal curve
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mats = baseMats[matInds]
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# Magic-multiply stacks of matrices together
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def matmul(a, b):
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return np.sum(np.transpose(a,(0,2,1))[..., None] * b[..., None, :], axis=-3)
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mats = reduce(matmul, mats)
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# Transform base points through matrix array
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pts = np.empty((nseg * nbseg + 1, 2))
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for l in range(len(trs)):
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bp = basePts[l]
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pts[l:-1:len(trs)] = np.dot(mats, bp)[:, :2]
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# Finish the curve with the last base point
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pts[-1] = basePts[-1][:2]
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# update fractal curve with new points
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fc.setData(pts[:,0], pts[:,1])
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# Update the fractal whenever the base shape or depth has changed
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baseLine.sigRegionChanged.connect(update)
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depthSpin.valueChanged.connect(update)
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# Initialize
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update()
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if __name__ == '__main__':
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pg.exec()
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