2475 lines
92 KiB
Python
2475 lines
92 KiB
Python
# -*- coding: utf-8 -*-
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"""
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functions.py - Miscellaneous functions with no other home
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Copyright 2010 Luke Campagnola
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Distributed under MIT/X11 license. See license.txt for more infomation.
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"""
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from __future__ import division
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import warnings
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import numpy as np
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import decimal, re
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import ctypes
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import sys, struct
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from .python2_3 import asUnicode, basestring
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from .Qt import QtGui, QtCore, QT_LIB
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from . import getConfigOption, setConfigOptions
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from . import debug, reload
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from .reload import getPreviousVersion
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from .metaarray import MetaArray
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Colors = {
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'b': QtGui.QColor(0,0,255,255),
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'g': QtGui.QColor(0,255,0,255),
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'r': QtGui.QColor(255,0,0,255),
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'c': QtGui.QColor(0,255,255,255),
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'm': QtGui.QColor(255,0,255,255),
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'y': QtGui.QColor(255,255,0,255),
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'k': QtGui.QColor(0,0,0,255),
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'w': QtGui.QColor(255,255,255,255),
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'd': QtGui.QColor(150,150,150,255),
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'l': QtGui.QColor(200,200,200,255),
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's': QtGui.QColor(100,100,150,255),
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}
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SI_PREFIXES = asUnicode('yzafpnµm kMGTPEZY')
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SI_PREFIXES_ASCII = 'yzafpnum kMGTPEZY'
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SI_PREFIX_EXPONENTS = dict([(SI_PREFIXES[i], (i-8)*3) for i in range(len(SI_PREFIXES))])
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SI_PREFIX_EXPONENTS['u'] = -6
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FLOAT_REGEX = re.compile(r'(?P<number>[+-]?((\d+(\.\d*)?)|(\d*\.\d+))([eE][+-]?\d+)?)\s*((?P<siPrefix>[u' + SI_PREFIXES + r']?)(?P<suffix>\w.*))?$')
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INT_REGEX = re.compile(r'(?P<number>[+-]?\d+)\s*(?P<siPrefix>[u' + SI_PREFIXES + r']?)(?P<suffix>.*)$')
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def siScale(x, minVal=1e-25, allowUnicode=True):
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"""
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Return the recommended scale factor and SI prefix string for x.
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Example::
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siScale(0.0001) # returns (1e6, 'μ')
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# This indicates that the number 0.0001 is best represented as 0.0001 * 1e6 = 100 μUnits
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"""
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if isinstance(x, decimal.Decimal):
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x = float(x)
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try:
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if np.isnan(x) or np.isinf(x):
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return(1, '')
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except:
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print(x, type(x))
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raise
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if abs(x) < minVal:
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m = 0
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x = 0
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else:
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m = int(np.clip(np.floor(np.log(abs(x))/np.log(1000)), -9.0, 9.0))
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if m == 0:
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pref = ''
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elif m < -8 or m > 8:
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pref = 'e%d' % (m*3)
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else:
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if allowUnicode:
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pref = SI_PREFIXES[m+8]
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else:
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pref = SI_PREFIXES_ASCII[m+8]
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p = .001**m
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return (p, pref)
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def siFormat(x, precision=3, suffix='', space=True, error=None, minVal=1e-25, allowUnicode=True):
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"""
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Return the number x formatted in engineering notation with SI prefix.
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Example::
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siFormat(0.0001, suffix='V') # returns "100 μV"
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"""
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if space is True:
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space = ' '
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if space is False:
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space = ''
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(p, pref) = siScale(x, minVal, allowUnicode)
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if not (len(pref) > 0 and pref[0] == 'e'):
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pref = space + pref
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if error is None:
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fmt = "%." + str(precision) + "g%s%s"
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return fmt % (x*p, pref, suffix)
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else:
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if allowUnicode:
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plusminus = space + asUnicode("±") + space
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else:
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plusminus = " +/- "
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fmt = "%." + str(precision) + "g%s%s%s%s"
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return fmt % (x*p, pref, suffix, plusminus, siFormat(error, precision=precision, suffix=suffix, space=space, minVal=minVal))
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def siParse(s, regex=FLOAT_REGEX, suffix=None):
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"""Convert a value written in SI notation to a tuple (number, si_prefix, suffix).
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Example::
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siParse('100 μV") # returns ('100', 'μ', 'V')
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"""
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s = asUnicode(s)
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s = s.strip()
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if suffix is not None and len(suffix) > 0:
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if s[-len(suffix):] != suffix:
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raise ValueError("String '%s' does not have the expected suffix '%s'" % (s, suffix))
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s = s[:-len(suffix)] + 'X' # add a fake suffix so the regex still picks up the si prefix
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m = regex.match(s)
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if m is None:
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raise ValueError('Cannot parse number "%s"' % s)
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try:
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sip = m.group('siPrefix')
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except IndexError:
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sip = ''
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if suffix is None:
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try:
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suf = m.group('suffix')
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except IndexError:
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suf = ''
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else:
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suf = suffix
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return m.group('number'), '' if sip is None else sip, '' if suf is None else suf
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def siEval(s, typ=float, regex=FLOAT_REGEX, suffix=None):
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"""
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Convert a value written in SI notation to its equivalent prefixless value.
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Example::
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siEval("100 μV") # returns 0.0001
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"""
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val, siprefix, suffix = siParse(s, regex, suffix=suffix)
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v = typ(val)
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return siApply(v, siprefix)
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def siApply(val, siprefix):
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"""
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"""
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n = SI_PREFIX_EXPONENTS[siprefix] if siprefix != '' else 0
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if n > 0:
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return val * 10**n
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elif n < 0:
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# this case makes it possible to use Decimal objects here
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return val / 10**-n
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else:
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return val
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class Color(QtGui.QColor):
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def __init__(self, *args):
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QtGui.QColor.__init__(self, mkColor(*args))
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def glColor(self):
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"""Return (r,g,b,a) normalized for use in opengl"""
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return (self.red()/255., self.green()/255., self.blue()/255., self.alpha()/255.)
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def __getitem__(self, ind):
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return (self.red, self.green, self.blue, self.alpha)[ind]()
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def mkColor(*args):
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"""
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Convenience function for constructing QColor from a variety of argument types. Accepted arguments are:
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================ ================================================
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'c' one of: r, g, b, c, m, y, k, w
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R, G, B, [A] integers 0-255
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(R, G, B, [A]) tuple of integers 0-255
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float greyscale, 0.0-1.0
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int see :func:`intColor() <pyqtgraph.intColor>`
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(int, hues) see :func:`intColor() <pyqtgraph.intColor>`
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"RGB" hexadecimal strings; may begin with '#'
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"RGBA"
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"RRGGBB"
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"RRGGBBAA"
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QColor QColor instance; makes a copy.
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================ ================================================
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"""
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err = 'Not sure how to make a color from "%s"' % str(args)
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if len(args) == 1:
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if isinstance(args[0], basestring):
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c = args[0]
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if c[0] == '#':
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c = c[1:]
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if len(c) == 1:
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try:
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return Colors[c]
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except KeyError:
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raise ValueError('No color named "%s"' % c)
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if len(c) == 3:
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r = int(c[0]*2, 16)
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g = int(c[1]*2, 16)
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b = int(c[2]*2, 16)
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a = 255
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elif len(c) == 4:
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r = int(c[0]*2, 16)
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g = int(c[1]*2, 16)
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b = int(c[2]*2, 16)
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a = int(c[3]*2, 16)
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elif len(c) == 6:
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r = int(c[0:2], 16)
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g = int(c[2:4], 16)
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b = int(c[4:6], 16)
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a = 255
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elif len(c) == 8:
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r = int(c[0:2], 16)
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g = int(c[2:4], 16)
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b = int(c[4:6], 16)
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a = int(c[6:8], 16)
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elif isinstance(args[0], QtGui.QColor):
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return QtGui.QColor(args[0])
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elif isinstance(args[0], float):
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r = g = b = int(args[0] * 255)
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a = 255
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elif hasattr(args[0], '__len__'):
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if len(args[0]) == 3:
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(r, g, b) = args[0]
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a = 255
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elif len(args[0]) == 4:
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(r, g, b, a) = args[0]
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elif len(args[0]) == 2:
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return intColor(*args[0])
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else:
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raise TypeError(err)
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elif type(args[0]) == int:
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return intColor(args[0])
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else:
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raise TypeError(err)
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elif len(args) == 3:
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(r, g, b) = args
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a = 255
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elif len(args) == 4:
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(r, g, b, a) = args
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else:
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raise TypeError(err)
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args = [r,g,b,a]
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args = [0 if np.isnan(a) or np.isinf(a) else a for a in args]
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args = list(map(int, args))
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return QtGui.QColor(*args)
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def mkBrush(*args, **kwds):
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"""
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| Convenience function for constructing Brush.
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| This function always constructs a solid brush and accepts the same arguments as :func:`mkColor() <pyqtgraph.mkColor>`
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| Calling mkBrush(None) returns an invisible brush.
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"""
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if 'color' in kwds:
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color = kwds['color']
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elif len(args) == 1:
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arg = args[0]
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if arg is None:
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return QtGui.QBrush(QtCore.Qt.NoBrush)
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elif isinstance(arg, QtGui.QBrush):
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return QtGui.QBrush(arg)
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else:
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color = arg
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elif len(args) > 1:
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color = args
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return QtGui.QBrush(mkColor(color))
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def mkPen(*args, **kargs):
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"""
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Convenience function for constructing QPen.
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Examples::
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mkPen(color)
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mkPen(color, width=2)
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mkPen(cosmetic=False, width=4.5, color='r')
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mkPen({'color': "FF0", width: 2})
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mkPen(None) # (no pen)
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In these examples, *color* may be replaced with any arguments accepted by :func:`mkColor() <pyqtgraph.mkColor>` """
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color = kargs.get('color', None)
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width = kargs.get('width', 1)
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style = kargs.get('style', None)
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dash = kargs.get('dash', None)
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cosmetic = kargs.get('cosmetic', True)
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hsv = kargs.get('hsv', None)
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if len(args) == 1:
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arg = args[0]
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if isinstance(arg, dict):
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return mkPen(**arg)
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if isinstance(arg, QtGui.QPen):
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return QtGui.QPen(arg) ## return a copy of this pen
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elif arg is None:
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style = QtCore.Qt.NoPen
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else:
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color = arg
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if len(args) > 1:
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color = args
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if color is None:
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color = mkColor('l')
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if hsv is not None:
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color = hsvColor(*hsv)
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else:
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color = mkColor(color)
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pen = QtGui.QPen(QtGui.QBrush(color), width)
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pen.setCosmetic(cosmetic)
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if style is not None:
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pen.setStyle(style)
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if dash is not None:
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pen.setDashPattern(dash)
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return pen
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def hsvColor(hue, sat=1.0, val=1.0, alpha=1.0):
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"""Generate a QColor from HSVa values. (all arguments are float 0.0-1.0)"""
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c = QtGui.QColor()
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c.setHsvF(hue, sat, val, alpha)
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return c
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def colorTuple(c):
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"""Return a tuple (R,G,B,A) from a QColor"""
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return (c.red(), c.green(), c.blue(), c.alpha())
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def colorStr(c):
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"""Generate a hex string code from a QColor"""
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return ('%02x'*4) % colorTuple(c)
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def intColor(index, hues=9, values=1, maxValue=255, minValue=150, maxHue=360, minHue=0, sat=255, alpha=255):
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"""
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Creates a QColor from a single index. Useful for stepping through a predefined list of colors.
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The argument *index* determines which color from the set will be returned. All other arguments determine what the set of predefined colors will be
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Colors are chosen by cycling across hues while varying the value (brightness).
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By default, this selects from a list of 9 hues."""
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hues = int(hues)
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values = int(values)
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ind = int(index) % (hues * values)
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indh = ind % hues
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indv = ind // hues
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if values > 1:
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v = minValue + indv * ((maxValue-minValue) / (values-1))
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else:
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v = maxValue
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h = minHue + (indh * (maxHue-minHue)) / hues
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c = QtGui.QColor()
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c.setHsv(h, sat, v)
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c.setAlpha(alpha)
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return c
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def glColor(*args, **kargs):
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"""
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Convert a color to OpenGL color format (r,g,b,a) floats 0.0-1.0
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Accepts same arguments as :func:`mkColor <pyqtgraph.mkColor>`.
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"""
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c = mkColor(*args, **kargs)
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return (c.red()/255., c.green()/255., c.blue()/255., c.alpha()/255.)
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def makeArrowPath(headLen=20, tipAngle=20, tailLen=20, tailWidth=3, baseAngle=0):
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"""
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Construct a path outlining an arrow with the given dimensions.
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The arrow points in the -x direction with tip positioned at 0,0.
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If *tipAngle* is supplied (in degrees), it overrides *headWidth*.
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If *tailLen* is None, no tail will be drawn.
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"""
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headWidth = headLen * np.tan(tipAngle * 0.5 * np.pi/180.)
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path = QtGui.QPainterPath()
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path.moveTo(0,0)
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path.lineTo(headLen, -headWidth)
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if tailLen is None:
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innerY = headLen - headWidth * np.tan(baseAngle*np.pi/180.)
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path.lineTo(innerY, 0)
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else:
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tailWidth *= 0.5
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innerY = headLen - (headWidth-tailWidth) * np.tan(baseAngle*np.pi/180.)
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path.lineTo(innerY, -tailWidth)
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path.lineTo(headLen + tailLen, -tailWidth)
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path.lineTo(headLen + tailLen, tailWidth)
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path.lineTo(innerY, tailWidth)
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path.lineTo(headLen, headWidth)
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path.lineTo(0,0)
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return path
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def eq(a, b):
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"""The great missing equivalence function: Guaranteed evaluation to a single bool value.
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This function has some important differences from the == operator:
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1. Returns True if a IS b, even if a==b still evaluates to False, such as with nan values.
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2. Tests for equivalence using ==, but silently ignores some common exceptions that can occur
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(AtrtibuteError, ValueError).
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3. When comparing arrays, returns False if the array shapes are not the same.
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4. When comparing arrays of the same shape, returns True only if all elements are equal (whereas
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the == operator would return a boolean array).
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"""
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if a is b:
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return True
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# Avoid comparing large arrays against scalars; this is expensive and we know it should return False.
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aIsArr = isinstance(a, (np.ndarray, MetaArray))
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bIsArr = isinstance(b, (np.ndarray, MetaArray))
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if (aIsArr or bIsArr) and type(a) != type(b):
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return False
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# If both inputs are arrays, we can speeed up comparison if shapes / dtypes don't match
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# NOTE: arrays of dissimilar type should be considered unequal even if they are numerically
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# equal because they may behave differently when computed on.
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if aIsArr and bIsArr and (a.shape != b.shape or a.dtype != b.dtype):
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return False
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# Test for equivalence.
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# If the test raises a recognized exception, then return Falase
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try:
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try:
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# Sometimes running catch_warnings(module=np) generates AttributeError ???
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catcher = warnings.catch_warnings(module=np) # ignore numpy futurewarning (numpy v. 1.10)
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catcher.__enter__()
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except Exception:
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catcher = None
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e = a==b
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except (ValueError, AttributeError):
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return False
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except:
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print('failed to evaluate equivalence for:')
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print(" a:", str(type(a)), str(a))
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print(" b:", str(type(b)), str(b))
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raise
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finally:
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if catcher is not None:
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catcher.__exit__(None, None, None)
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t = type(e)
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if t is bool:
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return e
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elif t is np.bool_:
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return bool(e)
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elif isinstance(e, np.ndarray) or (hasattr(e, 'implements') and e.implements('MetaArray')):
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try: ## disaster: if a is an empty array and b is not, then e.all() is True
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if a.shape != b.shape:
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return False
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except:
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return False
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if (hasattr(e, 'implements') and e.implements('MetaArray')):
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return e.asarray().all()
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else:
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return e.all()
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else:
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raise Exception("== operator returned type %s" % str(type(e)))
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|
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def affineSliceCoords(shape, origin, vectors, axes):
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"""Return the array of coordinates used to sample data arrays in affineSlice().
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"""
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# sanity check
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if len(shape) != len(vectors):
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raise Exception("shape and vectors must have same length.")
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if len(origin) != len(axes):
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raise Exception("origin and axes must have same length.")
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for v in vectors:
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if len(v) != len(axes):
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raise Exception("each vector must be same length as axes.")
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|
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shape = list(map(np.ceil, shape))
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|
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## make sure vectors are arrays
|
|
if not isinstance(vectors, np.ndarray):
|
|
vectors = np.array(vectors)
|
|
if not isinstance(origin, np.ndarray):
|
|
origin = np.array(origin)
|
|
origin.shape = (len(axes),) + (1,)*len(shape)
|
|
|
|
## Build array of sample locations.
|
|
grid = np.mgrid[tuple([slice(0,x) for x in shape])] ## mesh grid of indexes
|
|
x = (grid[np.newaxis,...] * vectors.transpose()[(Ellipsis,) + (np.newaxis,)*len(shape)]).sum(axis=1) ## magic
|
|
x += origin
|
|
|
|
return x
|
|
|
|
|
|
def affineSlice(data, shape, origin, vectors, axes, order=1, returnCoords=False, **kargs):
|
|
"""
|
|
Take a slice of any orientation through an array. This is useful for extracting sections of multi-dimensional arrays
|
|
such as MRI images for viewing as 1D or 2D data.
|
|
|
|
The slicing axes are aribtrary; they do not need to be orthogonal to the original data or even to each other. It is
|
|
possible to use this function to extract arbitrary linear, rectangular, or parallelepiped shapes from within larger
|
|
datasets. The original data is interpolated onto a new array of coordinates using either interpolateArray if order<2
|
|
or scipy.ndimage.map_coordinates otherwise.
|
|
|
|
For a graphical interface to this function, see :func:`ROI.getArrayRegion <pyqtgraph.ROI.getArrayRegion>`
|
|
|
|
============== ====================================================================================================
|
|
**Arguments:**
|
|
*data* (ndarray) the original dataset
|
|
*shape* the shape of the slice to take (Note the return value may have more dimensions than len(shape))
|
|
*origin* the location in the original dataset that will become the origin of the sliced data.
|
|
*vectors* list of unit vectors which point in the direction of the slice axes. Each vector must have the same
|
|
length as *axes*. If the vectors are not unit length, the result will be scaled relative to the
|
|
original data. If the vectors are not orthogonal, the result will be sheared relative to the
|
|
original data.
|
|
*axes* The axes in the original dataset which correspond to the slice *vectors*
|
|
*order* The order of spline interpolation. Default is 1 (linear). See scipy.ndimage.map_coordinates
|
|
for more information.
|
|
*returnCoords* If True, return a tuple (result, coords) where coords is the array of coordinates used to select
|
|
values from the original dataset.
|
|
*All extra keyword arguments are passed to scipy.ndimage.map_coordinates.*
|
|
--------------------------------------------------------------------------------------------------------------------
|
|
============== ====================================================================================================
|
|
|
|
Note the following must be true:
|
|
|
|
| len(shape) == len(vectors)
|
|
| len(origin) == len(axes) == len(vectors[i])
|
|
|
|
Example: start with a 4D fMRI data set, take a diagonal-planar slice out of the last 3 axes
|
|
|
|
* data = array with dims (time, x, y, z) = (100, 40, 40, 40)
|
|
* The plane to pull out is perpendicular to the vector (x,y,z) = (1,1,1)
|
|
* The origin of the slice will be at (x,y,z) = (40, 0, 0)
|
|
* We will slice a 20x20 plane from each timepoint, giving a final shape (100, 20, 20)
|
|
|
|
The call for this example would look like::
|
|
|
|
affineSlice(data, shape=(20,20), origin=(40,0,0), vectors=((-1, 1, 0), (-1, 0, 1)), axes=(1,2,3))
|
|
|
|
"""
|
|
x = affineSliceCoords(shape, origin, vectors, axes)
|
|
|
|
## transpose data so slice axes come first
|
|
trAx = list(range(data.ndim))
|
|
for ax in axes:
|
|
trAx.remove(ax)
|
|
tr1 = tuple(axes) + tuple(trAx)
|
|
data = data.transpose(tr1)
|
|
#print "tr1:", tr1
|
|
## dims are now [(slice axes), (other axes)]
|
|
|
|
if order > 1:
|
|
try:
|
|
import scipy.ndimage
|
|
except ImportError:
|
|
raise ImportError("Interpolating with order > 1 requires the scipy.ndimage module, but it could not be imported.")
|
|
|
|
# iterate manually over unused axes since map_coordinates won't do it for us
|
|
extraShape = data.shape[len(axes):]
|
|
output = np.empty(tuple(shape) + extraShape, dtype=data.dtype)
|
|
for inds in np.ndindex(*extraShape):
|
|
ind = (Ellipsis,) + inds
|
|
output[ind] = scipy.ndimage.map_coordinates(data[ind], x, order=order, **kargs)
|
|
else:
|
|
# map_coordinates expects the indexes as the first axis, whereas
|
|
# interpolateArray expects indexes at the last axis.
|
|
tr = tuple(range(1, x.ndim)) + (0,)
|
|
output = interpolateArray(data, x.transpose(tr), order=order)
|
|
|
|
tr = list(range(output.ndim))
|
|
trb = []
|
|
for i in range(min(axes)):
|
|
ind = tr1.index(i) + (len(shape)-len(axes))
|
|
tr.remove(ind)
|
|
trb.append(ind)
|
|
tr2 = tuple(trb+tr)
|
|
|
|
## Untranspose array before returning
|
|
output = output.transpose(tr2)
|
|
if returnCoords:
|
|
return (output, x)
|
|
else:
|
|
return output
|
|
|
|
|
|
def interpolateArray(data, x, default=0.0, order=1):
|
|
"""
|
|
N-dimensional interpolation similar to scipy.ndimage.map_coordinates.
|
|
|
|
This function returns linearly-interpolated values sampled from a regular
|
|
grid of data. It differs from `ndimage.map_coordinates` by allowing broadcasting
|
|
within the input array.
|
|
|
|
============== ===========================================================================================
|
|
**Arguments:**
|
|
*data* Array of any shape containing the values to be interpolated.
|
|
*x* Array with (shape[-1] <= data.ndim) containing the locations within *data* to interpolate.
|
|
(note: the axes for this argument are transposed relative to the same argument for
|
|
`ndimage.map_coordinates`).
|
|
*default* Value to return for locations in *x* that are outside the bounds of *data*.
|
|
*order* Order of interpolation: 0=nearest, 1=linear.
|
|
============== ===========================================================================================
|
|
|
|
Returns array of shape (x.shape[:-1] + data.shape[x.shape[-1]:])
|
|
|
|
For example, assume we have the following 2D image data::
|
|
|
|
>>> data = np.array([[1, 2, 4 ],
|
|
[10, 20, 40 ],
|
|
[100, 200, 400]])
|
|
|
|
To compute a single interpolated point from this data::
|
|
|
|
>>> x = np.array([(0.5, 0.5)])
|
|
>>> interpolateArray(data, x)
|
|
array([ 8.25])
|
|
|
|
To compute a 1D list of interpolated locations::
|
|
|
|
>>> x = np.array([(0.5, 0.5),
|
|
(1.0, 1.0),
|
|
(1.0, 2.0),
|
|
(1.5, 0.0)])
|
|
>>> interpolateArray(data, x)
|
|
array([ 8.25, 20. , 40. , 55. ])
|
|
|
|
To compute a 2D array of interpolated locations::
|
|
|
|
>>> x = np.array([[(0.5, 0.5), (1.0, 2.0)],
|
|
[(1.0, 1.0), (1.5, 0.0)]])
|
|
>>> interpolateArray(data, x)
|
|
array([[ 8.25, 40. ],
|
|
[ 20. , 55. ]])
|
|
|
|
..and so on. The *x* argument may have any shape as long as
|
|
```x.shape[-1] <= data.ndim```. In the case that
|
|
```x.shape[-1] < data.ndim```, then the remaining axes are simply
|
|
broadcasted as usual. For example, we can interpolate one location
|
|
from an entire row of the data::
|
|
|
|
>>> x = np.array([[0.5]])
|
|
>>> interpolateArray(data, x)
|
|
array([[ 5.5, 11. , 22. ]])
|
|
|
|
This is useful for interpolating from arrays of colors, vertexes, etc.
|
|
"""
|
|
if order not in (0, 1):
|
|
raise ValueError("interpolateArray requires order=0 or 1 (got %s)" % order)
|
|
|
|
prof = debug.Profiler()
|
|
|
|
nd = data.ndim
|
|
md = x.shape[-1]
|
|
if md > nd:
|
|
raise TypeError("x.shape[-1] must be less than or equal to data.ndim")
|
|
|
|
totalMask = np.ones(x.shape[:-1], dtype=bool) # keep track of out-of-bound indexes
|
|
if order == 0:
|
|
xinds = np.round(x).astype(int) # NOTE: for 0.5 this rounds to the nearest *even* number
|
|
for ax in range(md):
|
|
mask = (xinds[...,ax] >= 0) & (xinds[...,ax] <= data.shape[ax]-1)
|
|
xinds[...,ax][~mask] = 0
|
|
# keep track of points that need to be set to default
|
|
totalMask &= mask
|
|
result = data[tuple([xinds[...,i] for i in range(xinds.shape[-1])])]
|
|
|
|
elif order == 1:
|
|
# First we generate arrays of indexes that are needed to
|
|
# extract the data surrounding each point
|
|
fields = np.mgrid[(slice(0,order+1),) * md]
|
|
xmin = np.floor(x).astype(int)
|
|
xmax = xmin + 1
|
|
indexes = np.concatenate([xmin[np.newaxis, ...], xmax[np.newaxis, ...]])
|
|
fieldInds = []
|
|
for ax in range(md):
|
|
mask = (xmin[...,ax] >= 0) & (x[...,ax] <= data.shape[ax]-1)
|
|
# keep track of points that need to be set to default
|
|
totalMask &= mask
|
|
|
|
# ..and keep track of indexes that are out of bounds
|
|
# (note that when x[...,ax] == data.shape[ax], then xmax[...,ax] will be out
|
|
# of bounds, but the interpolation will work anyway)
|
|
mask &= (xmax[...,ax] < data.shape[ax])
|
|
axisIndex = indexes[...,ax][fields[ax]]
|
|
axisIndex[axisIndex < 0] = 0
|
|
axisIndex[axisIndex >= data.shape[ax]] = 0
|
|
fieldInds.append(axisIndex)
|
|
prof()
|
|
|
|
# Get data values surrounding each requested point
|
|
fieldData = data[tuple(fieldInds)]
|
|
prof()
|
|
|
|
## Interpolate
|
|
s = np.empty((md,) + fieldData.shape, dtype=float)
|
|
dx = x - xmin
|
|
# reshape fields for arithmetic against dx
|
|
for ax in range(md):
|
|
f1 = fields[ax].reshape(fields[ax].shape + (1,)*(dx.ndim-1))
|
|
sax = f1 * dx[...,ax] + (1-f1) * (1-dx[...,ax])
|
|
sax = sax.reshape(sax.shape + (1,) * (s.ndim-1-sax.ndim))
|
|
s[ax] = sax
|
|
s = np.product(s, axis=0)
|
|
result = fieldData * s
|
|
for i in range(md):
|
|
result = result.sum(axis=0)
|
|
|
|
prof()
|
|
|
|
if totalMask.ndim > 0:
|
|
result[~totalMask] = default
|
|
else:
|
|
if totalMask is False:
|
|
result[:] = default
|
|
|
|
prof()
|
|
return result
|
|
|
|
|
|
def subArray(data, offset, shape, stride):
|
|
"""
|
|
Unpack a sub-array from *data* using the specified offset, shape, and stride.
|
|
|
|
Note that *stride* is specified in array elements, not bytes.
|
|
For example, we have a 2x3 array packed in a 1D array as follows::
|
|
|
|
data = [_, _, 00, 01, 02, _, 10, 11, 12, _]
|
|
|
|
Then we can unpack the sub-array with this call::
|
|
|
|
subArray(data, offset=2, shape=(2, 3), stride=(4, 1))
|
|
|
|
..which returns::
|
|
|
|
[[00, 01, 02],
|
|
[10, 11, 12]]
|
|
|
|
This function operates only on the first axis of *data*. So changing
|
|
the input in the example above to have shape (10, 7) would cause the
|
|
output to have shape (2, 3, 7).
|
|
"""
|
|
data = np.ascontiguousarray(data)[offset:]
|
|
shape = tuple(shape)
|
|
extraShape = data.shape[1:]
|
|
|
|
strides = list(data.strides[::-1])
|
|
itemsize = strides[-1]
|
|
for s in stride[1::-1]:
|
|
strides.append(itemsize * s)
|
|
strides = tuple(strides[::-1])
|
|
|
|
return np.ndarray(buffer=data, shape=shape+extraShape, strides=strides, dtype=data.dtype)
|
|
|
|
|
|
def transformToArray(tr):
|
|
"""
|
|
Given a QTransform, return a 3x3 numpy array.
|
|
Given a QMatrix4x4, return a 4x4 numpy array.
|
|
|
|
Example: map an array of x,y coordinates through a transform::
|
|
|
|
## coordinates to map are (1,5), (2,6), (3,7), and (4,8)
|
|
coords = np.array([[1,2,3,4], [5,6,7,8], [1,1,1,1]]) # the extra '1' coordinate is needed for translation to work
|
|
|
|
## Make an example transform
|
|
tr = QtGui.QTransform()
|
|
tr.translate(3,4)
|
|
tr.scale(2, 0.1)
|
|
|
|
## convert to array
|
|
m = pg.transformToArray()[:2] # ignore the perspective portion of the transformation
|
|
|
|
## map coordinates through transform
|
|
mapped = np.dot(m, coords)
|
|
"""
|
|
#return np.array([[tr.m11(), tr.m12(), tr.m13()],[tr.m21(), tr.m22(), tr.m23()],[tr.m31(), tr.m32(), tr.m33()]])
|
|
## The order of elements given by the method names m11..m33 is misleading--
|
|
## It is most common for x,y translation to occupy the positions 1,3 and 2,3 in
|
|
## a transformation matrix. However, with QTransform these values appear at m31 and m32.
|
|
## So the correct interpretation is transposed:
|
|
if isinstance(tr, QtGui.QTransform):
|
|
return np.array([[tr.m11(), tr.m21(), tr.m31()], [tr.m12(), tr.m22(), tr.m32()], [tr.m13(), tr.m23(), tr.m33()]])
|
|
elif isinstance(tr, QtGui.QMatrix4x4):
|
|
return np.array(tr.copyDataTo()).reshape(4,4)
|
|
else:
|
|
raise Exception("Transform argument must be either QTransform or QMatrix4x4.")
|
|
|
|
def transformCoordinates(tr, coords, transpose=False):
|
|
"""
|
|
Map a set of 2D or 3D coordinates through a QTransform or QMatrix4x4.
|
|
The shape of coords must be (2,...) or (3,...)
|
|
The mapping will _ignore_ any perspective transformations.
|
|
|
|
For coordinate arrays with ndim=2, this is basically equivalent to matrix multiplication.
|
|
Most arrays, however, prefer to put the coordinate axis at the end (eg. shape=(...,3)). To
|
|
allow this, use transpose=True.
|
|
|
|
"""
|
|
|
|
if transpose:
|
|
## move last axis to beginning. This transposition will be reversed before returning the mapped coordinates.
|
|
coords = coords.transpose((coords.ndim-1,) + tuple(range(0,coords.ndim-1)))
|
|
|
|
nd = coords.shape[0]
|
|
if isinstance(tr, np.ndarray):
|
|
m = tr
|
|
else:
|
|
m = transformToArray(tr)
|
|
m = m[:m.shape[0]-1] # remove perspective
|
|
|
|
## If coords are 3D and tr is 2D, assume no change for Z axis
|
|
if m.shape == (2,3) and nd == 3:
|
|
m2 = np.zeros((3,4))
|
|
m2[:2, :2] = m[:2,:2]
|
|
m2[:2, 3] = m[:2,2]
|
|
m2[2,2] = 1
|
|
m = m2
|
|
|
|
## if coords are 2D and tr is 3D, ignore Z axis
|
|
if m.shape == (3,4) and nd == 2:
|
|
m2 = np.empty((2,3))
|
|
m2[:,:2] = m[:2,:2]
|
|
m2[:,2] = m[:2,3]
|
|
m = m2
|
|
|
|
## reshape tr and coords to prepare for multiplication
|
|
m = m.reshape(m.shape + (1,)*(coords.ndim-1))
|
|
coords = coords[np.newaxis, ...]
|
|
|
|
# separate scale/rotate and translation
|
|
translate = m[:,-1]
|
|
m = m[:, :-1]
|
|
|
|
## map coordinates and return
|
|
mapped = (m*coords).sum(axis=1) ## apply scale/rotate
|
|
mapped += translate
|
|
|
|
if transpose:
|
|
## move first axis to end.
|
|
mapped = mapped.transpose(tuple(range(1,mapped.ndim)) + (0,))
|
|
return mapped
|
|
|
|
|
|
|
|
|
|
def solve3DTransform(points1, points2):
|
|
"""
|
|
Find a 3D transformation matrix that maps points1 onto points2.
|
|
Points must be specified as either lists of 4 Vectors or
|
|
(4, 3) arrays.
|
|
"""
|
|
import numpy.linalg
|
|
pts = []
|
|
for inp in (points1, points2):
|
|
if isinstance(inp, np.ndarray):
|
|
A = np.empty((4,4), dtype=float)
|
|
A[:,:3] = inp[:,:3]
|
|
A[:,3] = 1.0
|
|
else:
|
|
A = np.array([[inp[i].x(), inp[i].y(), inp[i].z(), 1] for i in range(4)])
|
|
pts.append(A)
|
|
|
|
## solve 3 sets of linear equations to determine transformation matrix elements
|
|
matrix = np.zeros((4,4))
|
|
for i in range(3):
|
|
## solve Ax = B; x is one row of the desired transformation matrix
|
|
matrix[i] = numpy.linalg.solve(pts[0], pts[1][:,i])
|
|
|
|
return matrix
|
|
|
|
def solveBilinearTransform(points1, points2):
|
|
"""
|
|
Find a bilinear transformation matrix (2x4) that maps points1 onto points2.
|
|
Points must be specified as a list of 4 Vector, Point, QPointF, etc.
|
|
|
|
To use this matrix to map a point [x,y]::
|
|
|
|
mapped = np.dot(matrix, [x*y, x, y, 1])
|
|
"""
|
|
import numpy.linalg
|
|
## A is 4 rows (points) x 4 columns (xy, x, y, 1)
|
|
## B is 4 rows (points) x 2 columns (x, y)
|
|
A = np.array([[points1[i].x()*points1[i].y(), points1[i].x(), points1[i].y(), 1] for i in range(4)])
|
|
B = np.array([[points2[i].x(), points2[i].y()] for i in range(4)])
|
|
|
|
## solve 2 sets of linear equations to determine transformation matrix elements
|
|
matrix = np.zeros((2,4))
|
|
for i in range(2):
|
|
matrix[i] = numpy.linalg.solve(A, B[:,i]) ## solve Ax = B; x is one row of the desired transformation matrix
|
|
|
|
return matrix
|
|
|
|
def rescaleData(data, scale, offset, dtype=None, clip=None):
|
|
"""Return data rescaled and optionally cast to a new dtype::
|
|
|
|
data => (data-offset) * scale
|
|
|
|
"""
|
|
if dtype is None:
|
|
dtype = data.dtype
|
|
else:
|
|
dtype = np.dtype(dtype)
|
|
|
|
try:
|
|
if not getConfigOption('useWeave'):
|
|
raise Exception('Weave is disabled; falling back to slower version.')
|
|
try:
|
|
import scipy.weave
|
|
except ImportError:
|
|
raise Exception('scipy.weave is not importable; falling back to slower version.')
|
|
|
|
## require native dtype when using weave
|
|
if not data.dtype.isnative:
|
|
data = data.astype(data.dtype.newbyteorder('='))
|
|
if not dtype.isnative:
|
|
weaveDtype = dtype.newbyteorder('=')
|
|
else:
|
|
weaveDtype = dtype
|
|
|
|
newData = np.empty((data.size,), dtype=weaveDtype)
|
|
flat = np.ascontiguousarray(data).reshape(data.size)
|
|
size = data.size
|
|
|
|
code = """
|
|
double sc = (double)scale;
|
|
double off = (double)offset;
|
|
for( int i=0; i<size; i++ ) {
|
|
newData[i] = ((double)flat[i] - off) * sc;
|
|
}
|
|
"""
|
|
scipy.weave.inline(code, ['flat', 'newData', 'size', 'offset', 'scale'], compiler='gcc')
|
|
if dtype != weaveDtype:
|
|
newData = newData.astype(dtype)
|
|
data = newData.reshape(data.shape)
|
|
except:
|
|
if getConfigOption('useWeave'):
|
|
if getConfigOption('weaveDebug'):
|
|
debug.printExc("Error; disabling weave.")
|
|
setConfigOptions(useWeave=False)
|
|
|
|
#p = np.poly1d([scale, -offset*scale])
|
|
#d2 = p(data)
|
|
d2 = data - float(offset)
|
|
d2 *= scale
|
|
|
|
# Clip before converting dtype to avoid overflow
|
|
if dtype.kind in 'ui':
|
|
lim = np.iinfo(dtype)
|
|
if clip is None:
|
|
# don't let rescale cause integer overflow
|
|
d2 = np.clip(d2, lim.min, lim.max)
|
|
else:
|
|
d2 = np.clip(d2, max(clip[0], lim.min), min(clip[1], lim.max))
|
|
else:
|
|
if clip is not None:
|
|
d2 = np.clip(d2, *clip)
|
|
data = d2.astype(dtype)
|
|
return data
|
|
|
|
def applyLookupTable(data, lut):
|
|
"""
|
|
Uses values in *data* as indexes to select values from *lut*.
|
|
The returned data has shape data.shape + lut.shape[1:]
|
|
|
|
Note: color gradient lookup tables can be generated using GradientWidget.
|
|
"""
|
|
if data.dtype.kind not in ('i', 'u'):
|
|
data = data.astype(int)
|
|
|
|
return np.take(lut, data, axis=0, mode='clip')
|
|
|
|
|
|
def makeRGBA(*args, **kwds):
|
|
"""Equivalent to makeARGB(..., useRGBA=True)"""
|
|
kwds['useRGBA'] = True
|
|
return makeARGB(*args, **kwds)
|
|
|
|
|
|
def makeARGB(data, lut=None, levels=None, scale=None, useRGBA=False):
|
|
"""
|
|
Convert an array of values into an ARGB array suitable for building QImages,
|
|
OpenGL textures, etc.
|
|
|
|
Returns the ARGB array (unsigned byte) and a boolean indicating whether
|
|
there is alpha channel data. This is a two stage process:
|
|
|
|
1) Rescale the data based on the values in the *levels* argument (min, max).
|
|
2) Determine the final output by passing the rescaled values through a
|
|
lookup table.
|
|
|
|
Both stages are optional.
|
|
|
|
============== ==================================================================================
|
|
**Arguments:**
|
|
data numpy array of int/float types. If
|
|
levels List [min, max]; optionally rescale data before converting through the
|
|
lookup table. The data is rescaled such that min->0 and max->*scale*::
|
|
|
|
rescaled = (clip(data, min, max) - min) * (*scale* / (max - min))
|
|
|
|
It is also possible to use a 2D (N,2) array of values for levels. In this case,
|
|
it is assumed that each pair of min,max values in the levels array should be
|
|
applied to a different subset of the input data (for example, the input data may
|
|
already have RGB values and the levels are used to independently scale each
|
|
channel). The use of this feature requires that levels.shape[0] == data.shape[-1].
|
|
scale The maximum value to which data will be rescaled before being passed through the
|
|
lookup table (or returned if there is no lookup table). By default this will
|
|
be set to the length of the lookup table, or 255 if no lookup table is provided.
|
|
lut Optional lookup table (array with dtype=ubyte).
|
|
Values in data will be converted to color by indexing directly from lut.
|
|
The output data shape will be input.shape + lut.shape[1:].
|
|
Lookup tables can be built using ColorMap or GradientWidget.
|
|
useRGBA If True, the data is returned in RGBA order (useful for building OpenGL textures).
|
|
The default is False, which returns in ARGB order for use with QImage
|
|
(Note that 'ARGB' is a term used by the Qt documentation; the *actual* order
|
|
is BGRA).
|
|
============== ==================================================================================
|
|
"""
|
|
profile = debug.Profiler()
|
|
|
|
if data.ndim not in (2, 3):
|
|
raise TypeError("data must be 2D or 3D")
|
|
if data.ndim == 3 and data.shape[2] > 4:
|
|
raise TypeError("data.shape[2] must be <= 4")
|
|
|
|
if lut is not None and not isinstance(lut, np.ndarray):
|
|
lut = np.array(lut)
|
|
|
|
if levels is None:
|
|
# automatically decide levels based on data dtype
|
|
if data.dtype.kind == 'u':
|
|
levels = np.array([0, 2**(data.itemsize*8)-1])
|
|
elif data.dtype.kind == 'i':
|
|
s = 2**(data.itemsize*8 - 1)
|
|
levels = np.array([-s, s-1])
|
|
elif data.dtype.kind == 'b':
|
|
levels = np.array([0,1])
|
|
else:
|
|
raise Exception('levels argument is required for float input types')
|
|
if not isinstance(levels, np.ndarray):
|
|
levels = np.array(levels)
|
|
levels = levels.astype(np.float)
|
|
if levels.ndim == 1:
|
|
if levels.shape[0] != 2:
|
|
raise Exception('levels argument must have length 2')
|
|
elif levels.ndim == 2:
|
|
if lut is not None and lut.ndim > 1:
|
|
raise Exception('Cannot make ARGB data when both levels and lut have ndim > 2')
|
|
if levels.shape != (data.shape[-1], 2):
|
|
raise Exception('levels must have shape (data.shape[-1], 2)')
|
|
else:
|
|
raise Exception("levels argument must be 1D or 2D (got shape=%s)." % repr(levels.shape))
|
|
|
|
profile()
|
|
|
|
# Decide on maximum scaled value
|
|
if scale is None:
|
|
if lut is not None:
|
|
scale = lut.shape[0] - 1
|
|
else:
|
|
scale = 255.
|
|
|
|
# Decide on the dtype we want after scaling
|
|
if lut is None:
|
|
dtype = np.ubyte
|
|
else:
|
|
dtype = np.min_scalar_type(lut.shape[0]-1)
|
|
|
|
# Apply levels if given
|
|
if levels is not None:
|
|
if isinstance(levels, np.ndarray) and levels.ndim == 2:
|
|
# we are going to rescale each channel independently
|
|
if levels.shape[0] != data.shape[-1]:
|
|
raise Exception("When rescaling multi-channel data, there must be the same number of levels as channels (data.shape[-1] == levels.shape[0])")
|
|
newData = np.empty(data.shape, dtype=int)
|
|
for i in range(data.shape[-1]):
|
|
minVal, maxVal = levels[i]
|
|
if minVal == maxVal:
|
|
maxVal += 1e-16
|
|
rng = maxVal-minVal
|
|
rng = 1 if rng == 0 else rng
|
|
newData[...,i] = rescaleData(data[...,i], scale / rng, minVal, dtype=dtype)
|
|
data = newData
|
|
else:
|
|
# Apply level scaling unless it would have no effect on the data
|
|
minVal, maxVal = levels
|
|
if minVal != 0 or maxVal != scale:
|
|
if minVal == maxVal:
|
|
maxVal += 1e-16
|
|
data = rescaleData(data, scale/(maxVal-minVal), minVal, dtype=dtype)
|
|
|
|
|
|
profile()
|
|
|
|
# apply LUT if given
|
|
if lut is not None:
|
|
data = applyLookupTable(data, lut)
|
|
else:
|
|
if data.dtype is not np.ubyte:
|
|
data = np.clip(data, 0, 255).astype(np.ubyte)
|
|
|
|
profile()
|
|
|
|
# this will be the final image array
|
|
imgData = np.empty(data.shape[:2]+(4,), dtype=np.ubyte)
|
|
|
|
profile()
|
|
|
|
# decide channel order
|
|
if useRGBA:
|
|
order = [0,1,2,3] # array comes out RGBA
|
|
else:
|
|
order = [2,1,0,3] # for some reason, the colors line up as BGR in the final image.
|
|
|
|
# copy data into image array
|
|
if data.ndim == 2:
|
|
# This is tempting:
|
|
# imgData[..., :3] = data[..., np.newaxis]
|
|
# ..but it turns out this is faster:
|
|
for i in range(3):
|
|
imgData[..., i] = data
|
|
elif data.shape[2] == 1:
|
|
for i in range(3):
|
|
imgData[..., i] = data[..., 0]
|
|
else:
|
|
for i in range(0, data.shape[2]):
|
|
imgData[..., i] = data[..., order[i]]
|
|
|
|
profile()
|
|
|
|
# add opaque alpha channel if needed
|
|
if data.ndim == 2 or data.shape[2] == 3:
|
|
alpha = False
|
|
imgData[..., 3] = 255
|
|
else:
|
|
alpha = True
|
|
|
|
profile()
|
|
return imgData, alpha
|
|
|
|
|
|
def makeQImage(imgData, alpha=None, copy=True, transpose=True):
|
|
"""
|
|
Turn an ARGB array into QImage.
|
|
By default, the data is copied; changes to the array will not
|
|
be reflected in the image. The image will be given a 'data' attribute
|
|
pointing to the array which shares its data to prevent python
|
|
freeing that memory while the image is in use.
|
|
|
|
============== ===================================================================
|
|
**Arguments:**
|
|
imgData Array of data to convert. Must have shape (width, height, 3 or 4)
|
|
and dtype=ubyte. The order of values in the 3rd axis must be
|
|
(b, g, r, a).
|
|
alpha If True, the QImage returned will have format ARGB32. If False,
|
|
the format will be RGB32. By default, _alpha_ is True if
|
|
array.shape[2] == 4.
|
|
copy If True, the data is copied before converting to QImage.
|
|
If False, the new QImage points directly to the data in the array.
|
|
Note that the array must be contiguous for this to work
|
|
(see numpy.ascontiguousarray).
|
|
transpose If True (the default), the array x/y axes are transposed before
|
|
creating the image. Note that Qt expects the axes to be in
|
|
(height, width) order whereas pyqtgraph usually prefers the
|
|
opposite.
|
|
============== ===================================================================
|
|
"""
|
|
## create QImage from buffer
|
|
profile = debug.Profiler()
|
|
|
|
## If we didn't explicitly specify alpha, check the array shape.
|
|
if alpha is None:
|
|
alpha = (imgData.shape[2] == 4)
|
|
|
|
copied = False
|
|
if imgData.shape[2] == 3: ## need to make alpha channel (even if alpha==False; QImage requires 32 bpp)
|
|
if copy is True:
|
|
d2 = np.empty(imgData.shape[:2] + (4,), dtype=imgData.dtype)
|
|
d2[:,:,:3] = imgData
|
|
d2[:,:,3] = 255
|
|
imgData = d2
|
|
copied = True
|
|
else:
|
|
raise Exception('Array has only 3 channels; cannot make QImage without copying.')
|
|
|
|
if alpha:
|
|
imgFormat = QtGui.QImage.Format_ARGB32
|
|
else:
|
|
imgFormat = QtGui.QImage.Format_RGB32
|
|
|
|
if transpose:
|
|
imgData = imgData.transpose((1, 0, 2)) ## QImage expects the row/column order to be opposite
|
|
|
|
profile()
|
|
|
|
if not imgData.flags['C_CONTIGUOUS']:
|
|
if copy is False:
|
|
extra = ' (try setting transpose=False)' if transpose else ''
|
|
raise Exception('Array is not contiguous; cannot make QImage without copying.'+extra)
|
|
imgData = np.ascontiguousarray(imgData)
|
|
copied = True
|
|
|
|
if copy is True and copied is False:
|
|
imgData = imgData.copy()
|
|
|
|
if QT_LIB in ['PySide', 'PySide2']:
|
|
ch = ctypes.c_char.from_buffer(imgData, 0)
|
|
|
|
# Bug in PySide + Python 3 causes refcount for image data to be improperly
|
|
# incremented, which leads to leaked memory. As a workaround, we manually
|
|
# reset the reference count after creating the QImage.
|
|
# See: https://bugreports.qt.io/browse/PYSIDE-140
|
|
|
|
# Get initial reference count (PyObject struct has ob_refcnt as first element)
|
|
rcount = ctypes.c_long.from_address(id(ch)).value
|
|
img = QtGui.QImage(ch, imgData.shape[1], imgData.shape[0], imgFormat)
|
|
if sys.version[0] == '3':
|
|
# Reset refcount only on python 3. Technically this would have no effect
|
|
# on python 2, but this is a nasty hack, and checking for version here
|
|
# helps to mitigate possible unforseen consequences.
|
|
ctypes.c_long.from_address(id(ch)).value = rcount
|
|
else:
|
|
#addr = ctypes.addressof(ctypes.c_char.from_buffer(imgData, 0))
|
|
## PyQt API for QImage changed between 4.9.3 and 4.9.6 (I don't know exactly which version it was)
|
|
## So we first attempt the 4.9.6 API, then fall back to 4.9.3
|
|
#addr = ctypes.c_char.from_buffer(imgData, 0)
|
|
#try:
|
|
#img = QtGui.QImage(addr, imgData.shape[1], imgData.shape[0], imgFormat)
|
|
#except TypeError:
|
|
#addr = ctypes.addressof(addr)
|
|
#img = QtGui.QImage(addr, imgData.shape[1], imgData.shape[0], imgFormat)
|
|
try:
|
|
img = QtGui.QImage(imgData.ctypes.data, imgData.shape[1], imgData.shape[0], imgFormat)
|
|
except:
|
|
if copy:
|
|
# does not leak memory, is not mutable
|
|
img = QtGui.QImage(buffer(imgData), imgData.shape[1], imgData.shape[0], imgFormat)
|
|
else:
|
|
# mutable, but leaks memory
|
|
img = QtGui.QImage(memoryview(imgData), imgData.shape[1], imgData.shape[0], imgFormat)
|
|
|
|
img.data = imgData
|
|
return img
|
|
#try:
|
|
#buf = imgData.data
|
|
#except AttributeError: ## happens when image data is non-contiguous
|
|
#buf = imgData.data
|
|
|
|
#profiler()
|
|
#qimage = QtGui.QImage(buf, imgData.shape[1], imgData.shape[0], imgFormat)
|
|
#profiler()
|
|
#qimage.data = imgData
|
|
#return qimage
|
|
|
|
def imageToArray(img, copy=False, transpose=True):
|
|
"""
|
|
Convert a QImage into numpy array. The image must have format RGB32, ARGB32, or ARGB32_Premultiplied.
|
|
By default, the image is not copied; changes made to the array will appear in the QImage as well (beware: if
|
|
the QImage is collected before the array, there may be trouble).
|
|
The array will have shape (width, height, (b,g,r,a)).
|
|
"""
|
|
fmt = img.format()
|
|
ptr = img.bits()
|
|
if QT_LIB in ['PySide', 'PySide2']:
|
|
arr = np.frombuffer(ptr, dtype=np.ubyte)
|
|
else:
|
|
ptr.setsize(img.byteCount())
|
|
arr = np.asarray(ptr)
|
|
if img.byteCount() != arr.size * arr.itemsize:
|
|
# Required for Python 2.6, PyQt 4.10
|
|
# If this works on all platforms, then there is no need to use np.asarray..
|
|
arr = np.frombuffer(ptr, np.ubyte, img.byteCount())
|
|
|
|
arr = arr.reshape(img.height(), img.width(), 4)
|
|
if fmt == img.Format_RGB32:
|
|
arr[...,3] = 255
|
|
|
|
if copy:
|
|
arr = arr.copy()
|
|
|
|
if transpose:
|
|
return arr.transpose((1,0,2))
|
|
else:
|
|
return arr
|
|
|
|
def colorToAlpha(data, color):
|
|
"""
|
|
Given an RGBA image in *data*, convert *color* to be transparent.
|
|
*data* must be an array (w, h, 3 or 4) of ubyte values and *color* must be
|
|
an array (3) of ubyte values.
|
|
This is particularly useful for use with images that have a black or white background.
|
|
|
|
Algorithm is taken from Gimp's color-to-alpha function in plug-ins/common/colortoalpha.c
|
|
Credit:
|
|
/*
|
|
* Color To Alpha plug-in v1.0 by Seth Burgess, sjburges@gimp.org 1999/05/14
|
|
* with algorithm by clahey
|
|
*/
|
|
|
|
"""
|
|
data = data.astype(float)
|
|
if data.shape[-1] == 3: ## add alpha channel if needed
|
|
d2 = np.empty(data.shape[:2]+(4,), dtype=data.dtype)
|
|
d2[...,:3] = data
|
|
d2[...,3] = 255
|
|
data = d2
|
|
|
|
color = color.astype(float)
|
|
alpha = np.zeros(data.shape[:2]+(3,), dtype=float)
|
|
output = data.copy()
|
|
|
|
for i in [0,1,2]:
|
|
d = data[...,i]
|
|
c = color[i]
|
|
mask = d > c
|
|
alpha[...,i][mask] = (d[mask] - c) / (255. - c)
|
|
imask = d < c
|
|
alpha[...,i][imask] = (c - d[imask]) / c
|
|
|
|
output[...,3] = alpha.max(axis=2) * 255.
|
|
|
|
mask = output[...,3] >= 1.0 ## avoid zero division while processing alpha channel
|
|
correction = 255. / output[...,3][mask] ## increase value to compensate for decreased alpha
|
|
for i in [0,1,2]:
|
|
output[...,i][mask] = ((output[...,i][mask]-color[i]) * correction) + color[i]
|
|
output[...,3][mask] *= data[...,3][mask] / 255. ## combine computed and previous alpha values
|
|
|
|
#raise Exception()
|
|
return np.clip(output, 0, 255).astype(np.ubyte)
|
|
|
|
def gaussianFilter(data, sigma):
|
|
"""
|
|
Drop-in replacement for scipy.ndimage.gaussian_filter.
|
|
|
|
(note: results are only approximately equal to the output of
|
|
gaussian_filter)
|
|
"""
|
|
if np.isscalar(sigma):
|
|
sigma = (sigma,) * data.ndim
|
|
|
|
baseline = data.mean()
|
|
filtered = data - baseline
|
|
for ax in range(data.ndim):
|
|
s = sigma[ax]
|
|
if s == 0:
|
|
continue
|
|
|
|
# generate 1D gaussian kernel
|
|
ksize = int(s * 6)
|
|
x = np.arange(-ksize, ksize)
|
|
kernel = np.exp(-x**2 / (2*s**2))
|
|
kshape = [1,] * data.ndim
|
|
kshape[ax] = len(kernel)
|
|
kernel = kernel.reshape(kshape)
|
|
|
|
# convolve as product of FFTs
|
|
shape = data.shape[ax] + ksize
|
|
scale = 1.0 / (abs(s) * (2*np.pi)**0.5)
|
|
filtered = scale * np.fft.irfft(np.fft.rfft(filtered, shape, axis=ax) *
|
|
np.fft.rfft(kernel, shape, axis=ax),
|
|
axis=ax)
|
|
|
|
# clip off extra data
|
|
sl = [slice(None)] * data.ndim
|
|
sl[ax] = slice(filtered.shape[ax]-data.shape[ax],None,None)
|
|
filtered = filtered[tuple(sl)]
|
|
return filtered + baseline
|
|
|
|
|
|
def downsample(data, n, axis=0, xvals='subsample'):
|
|
"""Downsample by averaging points together across axis.
|
|
If multiple axes are specified, runs once per axis.
|
|
If a metaArray is given, then the axis values can be either subsampled
|
|
or downsampled to match.
|
|
"""
|
|
ma = None
|
|
if (hasattr(data, 'implements') and data.implements('MetaArray')):
|
|
ma = data
|
|
data = data.view(np.ndarray)
|
|
|
|
|
|
if hasattr(axis, '__len__'):
|
|
if not hasattr(n, '__len__'):
|
|
n = [n]*len(axis)
|
|
for i in range(len(axis)):
|
|
data = downsample(data, n[i], axis[i])
|
|
return data
|
|
|
|
if n <= 1:
|
|
return data
|
|
nPts = int(data.shape[axis] / n)
|
|
s = list(data.shape)
|
|
s[axis] = nPts
|
|
s.insert(axis+1, n)
|
|
sl = [slice(None)] * data.ndim
|
|
sl[axis] = slice(0, nPts*n)
|
|
d1 = data[tuple(sl)]
|
|
#print d1.shape, s
|
|
d1.shape = tuple(s)
|
|
d2 = d1.mean(axis+1)
|
|
|
|
if ma is None:
|
|
return d2
|
|
else:
|
|
info = ma.infoCopy()
|
|
if 'values' in info[axis]:
|
|
if xvals == 'subsample':
|
|
info[axis]['values'] = info[axis]['values'][::n][:nPts]
|
|
elif xvals == 'downsample':
|
|
info[axis]['values'] = downsample(info[axis]['values'], n)
|
|
return MetaArray(d2, info=info)
|
|
|
|
|
|
def arrayToQPath(x, y, connect='all'):
|
|
"""Convert an array of x,y coordinats to QPainterPath as efficiently as possible.
|
|
The *connect* argument may be 'all', indicating that each point should be
|
|
connected to the next; 'pairs', indicating that each pair of points
|
|
should be connected, or an array of int32 values (0 or 1) indicating
|
|
connections.
|
|
"""
|
|
|
|
## Create all vertices in path. The method used below creates a binary format so that all
|
|
## vertices can be read in at once. This binary format may change in future versions of Qt,
|
|
## so the original (slower) method is left here for emergencies:
|
|
#path.moveTo(x[0], y[0])
|
|
#if connect == 'all':
|
|
#for i in range(1, y.shape[0]):
|
|
#path.lineTo(x[i], y[i])
|
|
#elif connect == 'pairs':
|
|
#for i in range(1, y.shape[0]):
|
|
#if i%2 == 0:
|
|
#path.lineTo(x[i], y[i])
|
|
#else:
|
|
#path.moveTo(x[i], y[i])
|
|
#elif isinstance(connect, np.ndarray):
|
|
#for i in range(1, y.shape[0]):
|
|
#if connect[i] == 1:
|
|
#path.lineTo(x[i], y[i])
|
|
#else:
|
|
#path.moveTo(x[i], y[i])
|
|
#else:
|
|
#raise Exception('connect argument must be "all", "pairs", or array')
|
|
|
|
## Speed this up using >> operator
|
|
## Format is:
|
|
## numVerts(i4) 0(i4)
|
|
## x(f8) y(f8) 0(i4) <-- 0 means this vertex does not connect
|
|
## x(f8) y(f8) 1(i4) <-- 1 means this vertex connects to the previous vertex
|
|
## ...
|
|
## 0(i4)
|
|
##
|
|
## All values are big endian--pack using struct.pack('>d') or struct.pack('>i')
|
|
|
|
path = QtGui.QPainterPath()
|
|
|
|
#profiler = debug.Profiler()
|
|
n = x.shape[0]
|
|
# create empty array, pad with extra space on either end
|
|
arr = np.empty(n+2, dtype=[('x', '>f8'), ('y', '>f8'), ('c', '>i4')])
|
|
# write first two integers
|
|
#profiler('allocate empty')
|
|
byteview = arr.view(dtype=np.ubyte)
|
|
byteview[:12] = 0
|
|
byteview.data[12:20] = struct.pack('>ii', n, 0)
|
|
#profiler('pack header')
|
|
# Fill array with vertex values
|
|
arr[1:-1]['x'] = x
|
|
arr[1:-1]['y'] = y
|
|
|
|
# decide which points are connected by lines
|
|
if eq(connect, 'all'):
|
|
arr[1:-1]['c'] = 1
|
|
elif eq(connect, 'pairs'):
|
|
arr[1:-1]['c'][::2] = 1
|
|
arr[1:-1]['c'][1::2] = 0
|
|
elif eq(connect, 'finite'):
|
|
arr[1:-1]['c'] = np.isfinite(x) & np.isfinite(y)
|
|
elif isinstance(connect, np.ndarray):
|
|
arr[1:-1]['c'] = connect
|
|
else:
|
|
raise Exception('connect argument must be "all", "pairs", "finite", or array')
|
|
|
|
#profiler('fill array')
|
|
# write last 0
|
|
lastInd = 20*(n+1)
|
|
byteview.data[lastInd:lastInd+4] = struct.pack('>i', 0)
|
|
#profiler('footer')
|
|
# create datastream object and stream into path
|
|
|
|
## Avoiding this method because QByteArray(str) leaks memory in PySide
|
|
#buf = QtCore.QByteArray(arr.data[12:lastInd+4]) # I think one unnecessary copy happens here
|
|
|
|
path.strn = byteview.data[12:lastInd+4] # make sure data doesn't run away
|
|
try:
|
|
buf = QtCore.QByteArray.fromRawData(path.strn)
|
|
except TypeError:
|
|
buf = QtCore.QByteArray(bytes(path.strn))
|
|
#profiler('create buffer')
|
|
ds = QtCore.QDataStream(buf)
|
|
|
|
ds >> path
|
|
#profiler('load')
|
|
|
|
return path
|
|
|
|
#def isosurface(data, level):
|
|
#"""
|
|
#Generate isosurface from volumetric data using marching tetrahedra algorithm.
|
|
#See Paul Bourke, "Polygonising a Scalar Field Using Tetrahedrons" (http://local.wasp.uwa.edu.au/~pbourke/geometry/polygonise/)
|
|
|
|
#*data* 3D numpy array of scalar values
|
|
#*level* The level at which to generate an isosurface
|
|
#"""
|
|
|
|
#facets = []
|
|
|
|
### mark everything below the isosurface level
|
|
#mask = data < level
|
|
|
|
#### make eight sub-fields
|
|
#fields = np.empty((2,2,2), dtype=object)
|
|
#slices = [slice(0,-1), slice(1,None)]
|
|
#for i in [0,1]:
|
|
#for j in [0,1]:
|
|
#for k in [0,1]:
|
|
#fields[i,j,k] = mask[slices[i], slices[j], slices[k]]
|
|
|
|
|
|
|
|
### split each cell into 6 tetrahedra
|
|
### these all have the same 'orienation'; points 1,2,3 circle
|
|
### clockwise around point 0
|
|
#tetrahedra = [
|
|
#[(0,1,0), (1,1,1), (0,1,1), (1,0,1)],
|
|
#[(0,1,0), (0,1,1), (0,0,1), (1,0,1)],
|
|
#[(0,1,0), (0,0,1), (0,0,0), (1,0,1)],
|
|
#[(0,1,0), (0,0,0), (1,0,0), (1,0,1)],
|
|
#[(0,1,0), (1,0,0), (1,1,0), (1,0,1)],
|
|
#[(0,1,0), (1,1,0), (1,1,1), (1,0,1)]
|
|
#]
|
|
|
|
### each tetrahedron will be assigned an index
|
|
### which determines how to generate its facets.
|
|
### this structure is:
|
|
### facets[index][facet1, facet2, ...]
|
|
### where each facet is triangular and its points are each
|
|
### interpolated between two points on the tetrahedron
|
|
### facet = [(p1a, p1b), (p2a, p2b), (p3a, p3b)]
|
|
### facet points always circle clockwise if you are looking
|
|
### at them from below the isosurface.
|
|
#indexFacets = [
|
|
#[], ## all above
|
|
#[[(0,1), (0,2), (0,3)]], # 0 below
|
|
#[[(1,0), (1,3), (1,2)]], # 1 below
|
|
#[[(0,2), (1,3), (1,2)], [(0,2), (0,3), (1,3)]], # 0,1 below
|
|
#[[(2,0), (2,1), (2,3)]], # 2 below
|
|
#[[(0,3), (1,2), (2,3)], [(0,3), (0,1), (1,2)]], # 0,2 below
|
|
#[[(1,0), (2,3), (2,0)], [(1,0), (1,3), (2,3)]], # 1,2 below
|
|
#[[(3,0), (3,1), (3,2)]], # 3 above
|
|
#[[(3,0), (3,2), (3,1)]], # 3 below
|
|
#[[(1,0), (2,0), (2,3)], [(1,0), (2,3), (1,3)]], # 0,3 below
|
|
#[[(0,3), (2,3), (1,2)], [(0,3), (1,2), (0,1)]], # 1,3 below
|
|
#[[(2,0), (2,3), (2,1)]], # 0,1,3 below
|
|
#[[(0,2), (1,2), (1,3)], [(0,2), (1,3), (0,3)]], # 2,3 below
|
|
#[[(1,0), (1,2), (1,3)]], # 0,2,3 below
|
|
#[[(0,1), (0,3), (0,2)]], # 1,2,3 below
|
|
#[] ## all below
|
|
#]
|
|
|
|
#for tet in tetrahedra:
|
|
|
|
### get the 4 fields for this tetrahedron
|
|
#tetFields = [fields[c] for c in tet]
|
|
|
|
### generate an index for each grid cell
|
|
#index = tetFields[0] + tetFields[1]*2 + tetFields[2]*4 + tetFields[3]*8
|
|
|
|
### add facets
|
|
#for i in xrange(index.shape[0]): # data x-axis
|
|
#for j in xrange(index.shape[1]): # data y-axis
|
|
#for k in xrange(index.shape[2]): # data z-axis
|
|
#for f in indexFacets[index[i,j,k]]: # faces to generate for this tet
|
|
#pts = []
|
|
#for l in [0,1,2]: # points in this face
|
|
#p1 = tet[f[l][0]] # tet corner 1
|
|
#p2 = tet[f[l][1]] # tet corner 2
|
|
#pts.append([(p1[x]+p2[x])*0.5+[i,j,k][x]+0.5 for x in [0,1,2]]) ## interpolate between tet corners
|
|
#facets.append(pts)
|
|
|
|
#return facets
|
|
|
|
|
|
def isocurve(data, level, connected=False, extendToEdge=False, path=False):
|
|
"""
|
|
Generate isocurve from 2D data using marching squares algorithm.
|
|
|
|
============== =========================================================
|
|
**Arguments:**
|
|
data 2D numpy array of scalar values
|
|
level The level at which to generate an isosurface
|
|
connected If False, return a single long list of point pairs
|
|
If True, return multiple long lists of connected point
|
|
locations. (This is slower but better for drawing
|
|
continuous lines)
|
|
extendToEdge If True, extend the curves to reach the exact edges of
|
|
the data.
|
|
path if True, return a QPainterPath rather than a list of
|
|
vertex coordinates. This forces connected=True.
|
|
============== =========================================================
|
|
|
|
This function is SLOW; plenty of room for optimization here.
|
|
"""
|
|
|
|
if path is True:
|
|
connected = True
|
|
|
|
if extendToEdge:
|
|
d2 = np.empty((data.shape[0]+2, data.shape[1]+2), dtype=data.dtype)
|
|
d2[1:-1, 1:-1] = data
|
|
d2[0, 1:-1] = data[0]
|
|
d2[-1, 1:-1] = data[-1]
|
|
d2[1:-1, 0] = data[:, 0]
|
|
d2[1:-1, -1] = data[:, -1]
|
|
d2[0,0] = d2[0,1]
|
|
d2[0,-1] = d2[1,-1]
|
|
d2[-1,0] = d2[-1,1]
|
|
d2[-1,-1] = d2[-1,-2]
|
|
data = d2
|
|
|
|
sideTable = [
|
|
[],
|
|
[0,1],
|
|
[1,2],
|
|
[0,2],
|
|
[0,3],
|
|
[1,3],
|
|
[0,1,2,3],
|
|
[2,3],
|
|
[2,3],
|
|
[0,1,2,3],
|
|
[1,3],
|
|
[0,3],
|
|
[0,2],
|
|
[1,2],
|
|
[0,1],
|
|
[]
|
|
]
|
|
|
|
edgeKey=[
|
|
[(0,1), (0,0)],
|
|
[(0,0), (1,0)],
|
|
[(1,0), (1,1)],
|
|
[(1,1), (0,1)]
|
|
]
|
|
|
|
|
|
lines = []
|
|
|
|
## mark everything below the isosurface level
|
|
mask = data < level
|
|
|
|
### make four sub-fields and compute indexes for grid cells
|
|
index = np.zeros([x-1 for x in data.shape], dtype=np.ubyte)
|
|
fields = np.empty((2,2), dtype=object)
|
|
slices = [slice(0,-1), slice(1,None)]
|
|
for i in [0,1]:
|
|
for j in [0,1]:
|
|
fields[i,j] = mask[slices[i], slices[j]]
|
|
#vertIndex = i - 2*j*i + 3*j + 4*k ## this is just to match Bourk's vertex numbering scheme
|
|
vertIndex = i+2*j
|
|
#print i,j,k," : ", fields[i,j,k], 2**vertIndex
|
|
np.add(index, fields[i,j] * 2**vertIndex, out=index, casting='unsafe')
|
|
#print index
|
|
#print index
|
|
|
|
## add lines
|
|
for i in range(index.shape[0]): # data x-axis
|
|
for j in range(index.shape[1]): # data y-axis
|
|
sides = sideTable[index[i,j]]
|
|
for l in range(0, len(sides), 2): ## faces for this grid cell
|
|
edges = sides[l:l+2]
|
|
pts = []
|
|
for m in [0,1]: # points in this face
|
|
p1 = edgeKey[edges[m]][0] # p1, p2 are points at either side of an edge
|
|
p2 = edgeKey[edges[m]][1]
|
|
v1 = data[i+p1[0], j+p1[1]] # v1 and v2 are the values at p1 and p2
|
|
v2 = data[i+p2[0], j+p2[1]]
|
|
f = (level-v1) / (v2-v1)
|
|
fi = 1.0 - f
|
|
p = ( ## interpolate between corners
|
|
p1[0]*fi + p2[0]*f + i + 0.5,
|
|
p1[1]*fi + p2[1]*f + j + 0.5
|
|
)
|
|
if extendToEdge:
|
|
## check bounds
|
|
p = (
|
|
min(data.shape[0]-2, max(0, p[0]-1)),
|
|
min(data.shape[1]-2, max(0, p[1]-1)),
|
|
)
|
|
if connected:
|
|
gridKey = i + (1 if edges[m]==2 else 0), j + (1 if edges[m]==3 else 0), edges[m]%2
|
|
pts.append((p, gridKey)) ## give the actual position and a key identifying the grid location (for connecting segments)
|
|
else:
|
|
pts.append(p)
|
|
|
|
lines.append(pts)
|
|
|
|
if not connected:
|
|
return lines
|
|
|
|
## turn disjoint list of segments into continuous lines
|
|
|
|
#lines = [[2,5], [5,4], [3,4], [1,3], [6,7], [7,8], [8,6], [11,12], [12,15], [11,13], [13,14]]
|
|
#lines = [[(float(a), a), (float(b), b)] for a,b in lines]
|
|
points = {} ## maps each point to its connections
|
|
for a,b in lines:
|
|
if a[1] not in points:
|
|
points[a[1]] = []
|
|
points[a[1]].append([a,b])
|
|
if b[1] not in points:
|
|
points[b[1]] = []
|
|
points[b[1]].append([b,a])
|
|
|
|
## rearrange into chains
|
|
for k in list(points.keys()):
|
|
try:
|
|
chains = points[k]
|
|
except KeyError: ## already used this point elsewhere
|
|
continue
|
|
#print "===========", k
|
|
for chain in chains:
|
|
#print " chain:", chain
|
|
x = None
|
|
while True:
|
|
if x == chain[-1][1]:
|
|
break ## nothing left to do on this chain
|
|
|
|
x = chain[-1][1]
|
|
if x == k:
|
|
break ## chain has looped; we're done and can ignore the opposite chain
|
|
y = chain[-2][1]
|
|
connects = points[x]
|
|
for conn in connects[:]:
|
|
if conn[1][1] != y:
|
|
#print " ext:", conn
|
|
chain.extend(conn[1:])
|
|
#print " del:", x
|
|
del points[x]
|
|
if chain[0][1] == chain[-1][1]: # looped chain; no need to continue the other direction
|
|
chains.pop()
|
|
break
|
|
|
|
|
|
## extract point locations
|
|
lines = []
|
|
for chain in points.values():
|
|
if len(chain) == 2:
|
|
chain = chain[1][1:][::-1] + chain[0] # join together ends of chain
|
|
else:
|
|
chain = chain[0]
|
|
lines.append([p[0] for p in chain])
|
|
|
|
if not path:
|
|
return lines ## a list of pairs of points
|
|
|
|
path = QtGui.QPainterPath()
|
|
for line in lines:
|
|
path.moveTo(*line[0])
|
|
for p in line[1:]:
|
|
path.lineTo(*p)
|
|
|
|
return path
|
|
|
|
|
|
def traceImage(image, values, smooth=0.5):
|
|
"""
|
|
Convert an image to a set of QPainterPath curves.
|
|
One curve will be generated for each item in *values*; each curve outlines the area
|
|
of the image that is closer to its value than to any others.
|
|
|
|
If image is RGB or RGBA, then the shape of values should be (nvals, 3/4)
|
|
The parameter *smooth* is expressed in pixels.
|
|
"""
|
|
try:
|
|
import scipy.ndimage as ndi
|
|
except ImportError:
|
|
raise Exception("traceImage() requires the package scipy.ndimage, but it is not importable.")
|
|
|
|
if values.ndim == 2:
|
|
values = values.T
|
|
values = values[np.newaxis, np.newaxis, ...].astype(float)
|
|
image = image[..., np.newaxis].astype(float)
|
|
diff = np.abs(image-values)
|
|
if values.ndim == 4:
|
|
diff = diff.sum(axis=2)
|
|
|
|
labels = np.argmin(diff, axis=2)
|
|
|
|
paths = []
|
|
for i in range(diff.shape[-1]):
|
|
d = (labels==i).astype(float)
|
|
d = gaussianFilter(d, (smooth, smooth))
|
|
lines = isocurve(d, 0.5, connected=True, extendToEdge=True)
|
|
path = QtGui.QPainterPath()
|
|
for line in lines:
|
|
path.moveTo(*line[0])
|
|
for p in line[1:]:
|
|
path.lineTo(*p)
|
|
|
|
paths.append(path)
|
|
return paths
|
|
|
|
|
|
|
|
IsosurfaceDataCache = None
|
|
def isosurface(data, level):
|
|
"""
|
|
Generate isosurface from volumetric data using marching cubes algorithm.
|
|
See Paul Bourke, "Polygonising a Scalar Field"
|
|
(http://paulbourke.net/geometry/polygonise/)
|
|
|
|
*data* 3D numpy array of scalar values. Must be contiguous.
|
|
*level* The level at which to generate an isosurface
|
|
|
|
Returns an array of vertex coordinates (Nv, 3) and an array of
|
|
per-face vertex indexes (Nf, 3)
|
|
"""
|
|
## For improvement, see:
|
|
##
|
|
## Efficient implementation of Marching Cubes' cases with topological guarantees.
|
|
## Thomas Lewiner, Helio Lopes, Antonio Wilson Vieira and Geovan Tavares.
|
|
## Journal of Graphics Tools 8(2): pp. 1-15 (december 2003)
|
|
|
|
## Precompute lookup tables on the first run
|
|
global IsosurfaceDataCache
|
|
if IsosurfaceDataCache is None:
|
|
## map from grid cell index to edge index.
|
|
## grid cell index tells us which corners are below the isosurface,
|
|
## edge index tells us which edges are cut by the isosurface.
|
|
## (Data stolen from Bourk; see above.)
|
|
edgeTable = np.array([
|
|
0x0 , 0x109, 0x203, 0x30a, 0x406, 0x50f, 0x605, 0x70c,
|
|
0x80c, 0x905, 0xa0f, 0xb06, 0xc0a, 0xd03, 0xe09, 0xf00,
|
|
0x190, 0x99 , 0x393, 0x29a, 0x596, 0x49f, 0x795, 0x69c,
|
|
0x99c, 0x895, 0xb9f, 0xa96, 0xd9a, 0xc93, 0xf99, 0xe90,
|
|
0x230, 0x339, 0x33 , 0x13a, 0x636, 0x73f, 0x435, 0x53c,
|
|
0xa3c, 0xb35, 0x83f, 0x936, 0xe3a, 0xf33, 0xc39, 0xd30,
|
|
0x3a0, 0x2a9, 0x1a3, 0xaa , 0x7a6, 0x6af, 0x5a5, 0x4ac,
|
|
0xbac, 0xaa5, 0x9af, 0x8a6, 0xfaa, 0xea3, 0xda9, 0xca0,
|
|
0x460, 0x569, 0x663, 0x76a, 0x66 , 0x16f, 0x265, 0x36c,
|
|
0xc6c, 0xd65, 0xe6f, 0xf66, 0x86a, 0x963, 0xa69, 0xb60,
|
|
0x5f0, 0x4f9, 0x7f3, 0x6fa, 0x1f6, 0xff , 0x3f5, 0x2fc,
|
|
0xdfc, 0xcf5, 0xfff, 0xef6, 0x9fa, 0x8f3, 0xbf9, 0xaf0,
|
|
0x650, 0x759, 0x453, 0x55a, 0x256, 0x35f, 0x55 , 0x15c,
|
|
0xe5c, 0xf55, 0xc5f, 0xd56, 0xa5a, 0xb53, 0x859, 0x950,
|
|
0x7c0, 0x6c9, 0x5c3, 0x4ca, 0x3c6, 0x2cf, 0x1c5, 0xcc ,
|
|
0xfcc, 0xec5, 0xdcf, 0xcc6, 0xbca, 0xac3, 0x9c9, 0x8c0,
|
|
0x8c0, 0x9c9, 0xac3, 0xbca, 0xcc6, 0xdcf, 0xec5, 0xfcc,
|
|
0xcc , 0x1c5, 0x2cf, 0x3c6, 0x4ca, 0x5c3, 0x6c9, 0x7c0,
|
|
0x950, 0x859, 0xb53, 0xa5a, 0xd56, 0xc5f, 0xf55, 0xe5c,
|
|
0x15c, 0x55 , 0x35f, 0x256, 0x55a, 0x453, 0x759, 0x650,
|
|
0xaf0, 0xbf9, 0x8f3, 0x9fa, 0xef6, 0xfff, 0xcf5, 0xdfc,
|
|
0x2fc, 0x3f5, 0xff , 0x1f6, 0x6fa, 0x7f3, 0x4f9, 0x5f0,
|
|
0xb60, 0xa69, 0x963, 0x86a, 0xf66, 0xe6f, 0xd65, 0xc6c,
|
|
0x36c, 0x265, 0x16f, 0x66 , 0x76a, 0x663, 0x569, 0x460,
|
|
0xca0, 0xda9, 0xea3, 0xfaa, 0x8a6, 0x9af, 0xaa5, 0xbac,
|
|
0x4ac, 0x5a5, 0x6af, 0x7a6, 0xaa , 0x1a3, 0x2a9, 0x3a0,
|
|
0xd30, 0xc39, 0xf33, 0xe3a, 0x936, 0x83f, 0xb35, 0xa3c,
|
|
0x53c, 0x435, 0x73f, 0x636, 0x13a, 0x33 , 0x339, 0x230,
|
|
0xe90, 0xf99, 0xc93, 0xd9a, 0xa96, 0xb9f, 0x895, 0x99c,
|
|
0x69c, 0x795, 0x49f, 0x596, 0x29a, 0x393, 0x99 , 0x190,
|
|
0xf00, 0xe09, 0xd03, 0xc0a, 0xb06, 0xa0f, 0x905, 0x80c,
|
|
0x70c, 0x605, 0x50f, 0x406, 0x30a, 0x203, 0x109, 0x0
|
|
], dtype=np.uint16)
|
|
|
|
## Table of triangles to use for filling each grid cell.
|
|
## Each set of three integers tells us which three edges to
|
|
## draw a triangle between.
|
|
## (Data stolen from Bourk; see above.)
|
|
triTable = [
|
|
[],
|
|
[0, 8, 3],
|
|
[0, 1, 9],
|
|
[1, 8, 3, 9, 8, 1],
|
|
[1, 2, 10],
|
|
[0, 8, 3, 1, 2, 10],
|
|
[9, 2, 10, 0, 2, 9],
|
|
[2, 8, 3, 2, 10, 8, 10, 9, 8],
|
|
[3, 11, 2],
|
|
[0, 11, 2, 8, 11, 0],
|
|
[1, 9, 0, 2, 3, 11],
|
|
[1, 11, 2, 1, 9, 11, 9, 8, 11],
|
|
[3, 10, 1, 11, 10, 3],
|
|
[0, 10, 1, 0, 8, 10, 8, 11, 10],
|
|
[3, 9, 0, 3, 11, 9, 11, 10, 9],
|
|
[9, 8, 10, 10, 8, 11],
|
|
[4, 7, 8],
|
|
[4, 3, 0, 7, 3, 4],
|
|
[0, 1, 9, 8, 4, 7],
|
|
[4, 1, 9, 4, 7, 1, 7, 3, 1],
|
|
[1, 2, 10, 8, 4, 7],
|
|
[3, 4, 7, 3, 0, 4, 1, 2, 10],
|
|
[9, 2, 10, 9, 0, 2, 8, 4, 7],
|
|
[2, 10, 9, 2, 9, 7, 2, 7, 3, 7, 9, 4],
|
|
[8, 4, 7, 3, 11, 2],
|
|
[11, 4, 7, 11, 2, 4, 2, 0, 4],
|
|
[9, 0, 1, 8, 4, 7, 2, 3, 11],
|
|
[4, 7, 11, 9, 4, 11, 9, 11, 2, 9, 2, 1],
|
|
[3, 10, 1, 3, 11, 10, 7, 8, 4],
|
|
[1, 11, 10, 1, 4, 11, 1, 0, 4, 7, 11, 4],
|
|
[4, 7, 8, 9, 0, 11, 9, 11, 10, 11, 0, 3],
|
|
[4, 7, 11, 4, 11, 9, 9, 11, 10],
|
|
[9, 5, 4],
|
|
[9, 5, 4, 0, 8, 3],
|
|
[0, 5, 4, 1, 5, 0],
|
|
[8, 5, 4, 8, 3, 5, 3, 1, 5],
|
|
[1, 2, 10, 9, 5, 4],
|
|
[3, 0, 8, 1, 2, 10, 4, 9, 5],
|
|
[5, 2, 10, 5, 4, 2, 4, 0, 2],
|
|
[2, 10, 5, 3, 2, 5, 3, 5, 4, 3, 4, 8],
|
|
[9, 5, 4, 2, 3, 11],
|
|
[0, 11, 2, 0, 8, 11, 4, 9, 5],
|
|
[0, 5, 4, 0, 1, 5, 2, 3, 11],
|
|
[2, 1, 5, 2, 5, 8, 2, 8, 11, 4, 8, 5],
|
|
[10, 3, 11, 10, 1, 3, 9, 5, 4],
|
|
[4, 9, 5, 0, 8, 1, 8, 10, 1, 8, 11, 10],
|
|
[5, 4, 0, 5, 0, 11, 5, 11, 10, 11, 0, 3],
|
|
[5, 4, 8, 5, 8, 10, 10, 8, 11],
|
|
[9, 7, 8, 5, 7, 9],
|
|
[9, 3, 0, 9, 5, 3, 5, 7, 3],
|
|
[0, 7, 8, 0, 1, 7, 1, 5, 7],
|
|
[1, 5, 3, 3, 5, 7],
|
|
[9, 7, 8, 9, 5, 7, 10, 1, 2],
|
|
[10, 1, 2, 9, 5, 0, 5, 3, 0, 5, 7, 3],
|
|
[8, 0, 2, 8, 2, 5, 8, 5, 7, 10, 5, 2],
|
|
[2, 10, 5, 2, 5, 3, 3, 5, 7],
|
|
[7, 9, 5, 7, 8, 9, 3, 11, 2],
|
|
[9, 5, 7, 9, 7, 2, 9, 2, 0, 2, 7, 11],
|
|
[2, 3, 11, 0, 1, 8, 1, 7, 8, 1, 5, 7],
|
|
[11, 2, 1, 11, 1, 7, 7, 1, 5],
|
|
[9, 5, 8, 8, 5, 7, 10, 1, 3, 10, 3, 11],
|
|
[5, 7, 0, 5, 0, 9, 7, 11, 0, 1, 0, 10, 11, 10, 0],
|
|
[11, 10, 0, 11, 0, 3, 10, 5, 0, 8, 0, 7, 5, 7, 0],
|
|
[11, 10, 5, 7, 11, 5],
|
|
[10, 6, 5],
|
|
[0, 8, 3, 5, 10, 6],
|
|
[9, 0, 1, 5, 10, 6],
|
|
[1, 8, 3, 1, 9, 8, 5, 10, 6],
|
|
[1, 6, 5, 2, 6, 1],
|
|
[1, 6, 5, 1, 2, 6, 3, 0, 8],
|
|
[9, 6, 5, 9, 0, 6, 0, 2, 6],
|
|
[5, 9, 8, 5, 8, 2, 5, 2, 6, 3, 2, 8],
|
|
[2, 3, 11, 10, 6, 5],
|
|
[11, 0, 8, 11, 2, 0, 10, 6, 5],
|
|
[0, 1, 9, 2, 3, 11, 5, 10, 6],
|
|
[5, 10, 6, 1, 9, 2, 9, 11, 2, 9, 8, 11],
|
|
[6, 3, 11, 6, 5, 3, 5, 1, 3],
|
|
[0, 8, 11, 0, 11, 5, 0, 5, 1, 5, 11, 6],
|
|
[3, 11, 6, 0, 3, 6, 0, 6, 5, 0, 5, 9],
|
|
[6, 5, 9, 6, 9, 11, 11, 9, 8],
|
|
[5, 10, 6, 4, 7, 8],
|
|
[4, 3, 0, 4, 7, 3, 6, 5, 10],
|
|
[1, 9, 0, 5, 10, 6, 8, 4, 7],
|
|
[10, 6, 5, 1, 9, 7, 1, 7, 3, 7, 9, 4],
|
|
[6, 1, 2, 6, 5, 1, 4, 7, 8],
|
|
[1, 2, 5, 5, 2, 6, 3, 0, 4, 3, 4, 7],
|
|
[8, 4, 7, 9, 0, 5, 0, 6, 5, 0, 2, 6],
|
|
[7, 3, 9, 7, 9, 4, 3, 2, 9, 5, 9, 6, 2, 6, 9],
|
|
[3, 11, 2, 7, 8, 4, 10, 6, 5],
|
|
[5, 10, 6, 4, 7, 2, 4, 2, 0, 2, 7, 11],
|
|
[0, 1, 9, 4, 7, 8, 2, 3, 11, 5, 10, 6],
|
|
[9, 2, 1, 9, 11, 2, 9, 4, 11, 7, 11, 4, 5, 10, 6],
|
|
[8, 4, 7, 3, 11, 5, 3, 5, 1, 5, 11, 6],
|
|
[5, 1, 11, 5, 11, 6, 1, 0, 11, 7, 11, 4, 0, 4, 11],
|
|
[0, 5, 9, 0, 6, 5, 0, 3, 6, 11, 6, 3, 8, 4, 7],
|
|
[6, 5, 9, 6, 9, 11, 4, 7, 9, 7, 11, 9],
|
|
[10, 4, 9, 6, 4, 10],
|
|
[4, 10, 6, 4, 9, 10, 0, 8, 3],
|
|
[10, 0, 1, 10, 6, 0, 6, 4, 0],
|
|
[8, 3, 1, 8, 1, 6, 8, 6, 4, 6, 1, 10],
|
|
[1, 4, 9, 1, 2, 4, 2, 6, 4],
|
|
[3, 0, 8, 1, 2, 9, 2, 4, 9, 2, 6, 4],
|
|
[0, 2, 4, 4, 2, 6],
|
|
[8, 3, 2, 8, 2, 4, 4, 2, 6],
|
|
[10, 4, 9, 10, 6, 4, 11, 2, 3],
|
|
[0, 8, 2, 2, 8, 11, 4, 9, 10, 4, 10, 6],
|
|
[3, 11, 2, 0, 1, 6, 0, 6, 4, 6, 1, 10],
|
|
[6, 4, 1, 6, 1, 10, 4, 8, 1, 2, 1, 11, 8, 11, 1],
|
|
[9, 6, 4, 9, 3, 6, 9, 1, 3, 11, 6, 3],
|
|
[8, 11, 1, 8, 1, 0, 11, 6, 1, 9, 1, 4, 6, 4, 1],
|
|
[3, 11, 6, 3, 6, 0, 0, 6, 4],
|
|
[6, 4, 8, 11, 6, 8],
|
|
[7, 10, 6, 7, 8, 10, 8, 9, 10],
|
|
[0, 7, 3, 0, 10, 7, 0, 9, 10, 6, 7, 10],
|
|
[10, 6, 7, 1, 10, 7, 1, 7, 8, 1, 8, 0],
|
|
[10, 6, 7, 10, 7, 1, 1, 7, 3],
|
|
[1, 2, 6, 1, 6, 8, 1, 8, 9, 8, 6, 7],
|
|
[2, 6, 9, 2, 9, 1, 6, 7, 9, 0, 9, 3, 7, 3, 9],
|
|
[7, 8, 0, 7, 0, 6, 6, 0, 2],
|
|
[7, 3, 2, 6, 7, 2],
|
|
[2, 3, 11, 10, 6, 8, 10, 8, 9, 8, 6, 7],
|
|
[2, 0, 7, 2, 7, 11, 0, 9, 7, 6, 7, 10, 9, 10, 7],
|
|
[1, 8, 0, 1, 7, 8, 1, 10, 7, 6, 7, 10, 2, 3, 11],
|
|
[11, 2, 1, 11, 1, 7, 10, 6, 1, 6, 7, 1],
|
|
[8, 9, 6, 8, 6, 7, 9, 1, 6, 11, 6, 3, 1, 3, 6],
|
|
[0, 9, 1, 11, 6, 7],
|
|
[7, 8, 0, 7, 0, 6, 3, 11, 0, 11, 6, 0],
|
|
[7, 11, 6],
|
|
[7, 6, 11],
|
|
[3, 0, 8, 11, 7, 6],
|
|
[0, 1, 9, 11, 7, 6],
|
|
[8, 1, 9, 8, 3, 1, 11, 7, 6],
|
|
[10, 1, 2, 6, 11, 7],
|
|
[1, 2, 10, 3, 0, 8, 6, 11, 7],
|
|
[2, 9, 0, 2, 10, 9, 6, 11, 7],
|
|
[6, 11, 7, 2, 10, 3, 10, 8, 3, 10, 9, 8],
|
|
[7, 2, 3, 6, 2, 7],
|
|
[7, 0, 8, 7, 6, 0, 6, 2, 0],
|
|
[2, 7, 6, 2, 3, 7, 0, 1, 9],
|
|
[1, 6, 2, 1, 8, 6, 1, 9, 8, 8, 7, 6],
|
|
[10, 7, 6, 10, 1, 7, 1, 3, 7],
|
|
[10, 7, 6, 1, 7, 10, 1, 8, 7, 1, 0, 8],
|
|
[0, 3, 7, 0, 7, 10, 0, 10, 9, 6, 10, 7],
|
|
[7, 6, 10, 7, 10, 8, 8, 10, 9],
|
|
[6, 8, 4, 11, 8, 6],
|
|
[3, 6, 11, 3, 0, 6, 0, 4, 6],
|
|
[8, 6, 11, 8, 4, 6, 9, 0, 1],
|
|
[9, 4, 6, 9, 6, 3, 9, 3, 1, 11, 3, 6],
|
|
[6, 8, 4, 6, 11, 8, 2, 10, 1],
|
|
[1, 2, 10, 3, 0, 11, 0, 6, 11, 0, 4, 6],
|
|
[4, 11, 8, 4, 6, 11, 0, 2, 9, 2, 10, 9],
|
|
[10, 9, 3, 10, 3, 2, 9, 4, 3, 11, 3, 6, 4, 6, 3],
|
|
[8, 2, 3, 8, 4, 2, 4, 6, 2],
|
|
[0, 4, 2, 4, 6, 2],
|
|
[1, 9, 0, 2, 3, 4, 2, 4, 6, 4, 3, 8],
|
|
[1, 9, 4, 1, 4, 2, 2, 4, 6],
|
|
[8, 1, 3, 8, 6, 1, 8, 4, 6, 6, 10, 1],
|
|
[10, 1, 0, 10, 0, 6, 6, 0, 4],
|
|
[4, 6, 3, 4, 3, 8, 6, 10, 3, 0, 3, 9, 10, 9, 3],
|
|
[10, 9, 4, 6, 10, 4],
|
|
[4, 9, 5, 7, 6, 11],
|
|
[0, 8, 3, 4, 9, 5, 11, 7, 6],
|
|
[5, 0, 1, 5, 4, 0, 7, 6, 11],
|
|
[11, 7, 6, 8, 3, 4, 3, 5, 4, 3, 1, 5],
|
|
[9, 5, 4, 10, 1, 2, 7, 6, 11],
|
|
[6, 11, 7, 1, 2, 10, 0, 8, 3, 4, 9, 5],
|
|
[7, 6, 11, 5, 4, 10, 4, 2, 10, 4, 0, 2],
|
|
[3, 4, 8, 3, 5, 4, 3, 2, 5, 10, 5, 2, 11, 7, 6],
|
|
[7, 2, 3, 7, 6, 2, 5, 4, 9],
|
|
[9, 5, 4, 0, 8, 6, 0, 6, 2, 6, 8, 7],
|
|
[3, 6, 2, 3, 7, 6, 1, 5, 0, 5, 4, 0],
|
|
[6, 2, 8, 6, 8, 7, 2, 1, 8, 4, 8, 5, 1, 5, 8],
|
|
[9, 5, 4, 10, 1, 6, 1, 7, 6, 1, 3, 7],
|
|
[1, 6, 10, 1, 7, 6, 1, 0, 7, 8, 7, 0, 9, 5, 4],
|
|
[4, 0, 10, 4, 10, 5, 0, 3, 10, 6, 10, 7, 3, 7, 10],
|
|
[7, 6, 10, 7, 10, 8, 5, 4, 10, 4, 8, 10],
|
|
[6, 9, 5, 6, 11, 9, 11, 8, 9],
|
|
[3, 6, 11, 0, 6, 3, 0, 5, 6, 0, 9, 5],
|
|
[0, 11, 8, 0, 5, 11, 0, 1, 5, 5, 6, 11],
|
|
[6, 11, 3, 6, 3, 5, 5, 3, 1],
|
|
[1, 2, 10, 9, 5, 11, 9, 11, 8, 11, 5, 6],
|
|
[0, 11, 3, 0, 6, 11, 0, 9, 6, 5, 6, 9, 1, 2, 10],
|
|
[11, 8, 5, 11, 5, 6, 8, 0, 5, 10, 5, 2, 0, 2, 5],
|
|
[6, 11, 3, 6, 3, 5, 2, 10, 3, 10, 5, 3],
|
|
[5, 8, 9, 5, 2, 8, 5, 6, 2, 3, 8, 2],
|
|
[9, 5, 6, 9, 6, 0, 0, 6, 2],
|
|
[1, 5, 8, 1, 8, 0, 5, 6, 8, 3, 8, 2, 6, 2, 8],
|
|
[1, 5, 6, 2, 1, 6],
|
|
[1, 3, 6, 1, 6, 10, 3, 8, 6, 5, 6, 9, 8, 9, 6],
|
|
[10, 1, 0, 10, 0, 6, 9, 5, 0, 5, 6, 0],
|
|
[0, 3, 8, 5, 6, 10],
|
|
[10, 5, 6],
|
|
[11, 5, 10, 7, 5, 11],
|
|
[11, 5, 10, 11, 7, 5, 8, 3, 0],
|
|
[5, 11, 7, 5, 10, 11, 1, 9, 0],
|
|
[10, 7, 5, 10, 11, 7, 9, 8, 1, 8, 3, 1],
|
|
[11, 1, 2, 11, 7, 1, 7, 5, 1],
|
|
[0, 8, 3, 1, 2, 7, 1, 7, 5, 7, 2, 11],
|
|
[9, 7, 5, 9, 2, 7, 9, 0, 2, 2, 11, 7],
|
|
[7, 5, 2, 7, 2, 11, 5, 9, 2, 3, 2, 8, 9, 8, 2],
|
|
[2, 5, 10, 2, 3, 5, 3, 7, 5],
|
|
[8, 2, 0, 8, 5, 2, 8, 7, 5, 10, 2, 5],
|
|
[9, 0, 1, 5, 10, 3, 5, 3, 7, 3, 10, 2],
|
|
[9, 8, 2, 9, 2, 1, 8, 7, 2, 10, 2, 5, 7, 5, 2],
|
|
[1, 3, 5, 3, 7, 5],
|
|
[0, 8, 7, 0, 7, 1, 1, 7, 5],
|
|
[9, 0, 3, 9, 3, 5, 5, 3, 7],
|
|
[9, 8, 7, 5, 9, 7],
|
|
[5, 8, 4, 5, 10, 8, 10, 11, 8],
|
|
[5, 0, 4, 5, 11, 0, 5, 10, 11, 11, 3, 0],
|
|
[0, 1, 9, 8, 4, 10, 8, 10, 11, 10, 4, 5],
|
|
[10, 11, 4, 10, 4, 5, 11, 3, 4, 9, 4, 1, 3, 1, 4],
|
|
[2, 5, 1, 2, 8, 5, 2, 11, 8, 4, 5, 8],
|
|
[0, 4, 11, 0, 11, 3, 4, 5, 11, 2, 11, 1, 5, 1, 11],
|
|
[0, 2, 5, 0, 5, 9, 2, 11, 5, 4, 5, 8, 11, 8, 5],
|
|
[9, 4, 5, 2, 11, 3],
|
|
[2, 5, 10, 3, 5, 2, 3, 4, 5, 3, 8, 4],
|
|
[5, 10, 2, 5, 2, 4, 4, 2, 0],
|
|
[3, 10, 2, 3, 5, 10, 3, 8, 5, 4, 5, 8, 0, 1, 9],
|
|
[5, 10, 2, 5, 2, 4, 1, 9, 2, 9, 4, 2],
|
|
[8, 4, 5, 8, 5, 3, 3, 5, 1],
|
|
[0, 4, 5, 1, 0, 5],
|
|
[8, 4, 5, 8, 5, 3, 9, 0, 5, 0, 3, 5],
|
|
[9, 4, 5],
|
|
[4, 11, 7, 4, 9, 11, 9, 10, 11],
|
|
[0, 8, 3, 4, 9, 7, 9, 11, 7, 9, 10, 11],
|
|
[1, 10, 11, 1, 11, 4, 1, 4, 0, 7, 4, 11],
|
|
[3, 1, 4, 3, 4, 8, 1, 10, 4, 7, 4, 11, 10, 11, 4],
|
|
[4, 11, 7, 9, 11, 4, 9, 2, 11, 9, 1, 2],
|
|
[9, 7, 4, 9, 11, 7, 9, 1, 11, 2, 11, 1, 0, 8, 3],
|
|
[11, 7, 4, 11, 4, 2, 2, 4, 0],
|
|
[11, 7, 4, 11, 4, 2, 8, 3, 4, 3, 2, 4],
|
|
[2, 9, 10, 2, 7, 9, 2, 3, 7, 7, 4, 9],
|
|
[9, 10, 7, 9, 7, 4, 10, 2, 7, 8, 7, 0, 2, 0, 7],
|
|
[3, 7, 10, 3, 10, 2, 7, 4, 10, 1, 10, 0, 4, 0, 10],
|
|
[1, 10, 2, 8, 7, 4],
|
|
[4, 9, 1, 4, 1, 7, 7, 1, 3],
|
|
[4, 9, 1, 4, 1, 7, 0, 8, 1, 8, 7, 1],
|
|
[4, 0, 3, 7, 4, 3],
|
|
[4, 8, 7],
|
|
[9, 10, 8, 10, 11, 8],
|
|
[3, 0, 9, 3, 9, 11, 11, 9, 10],
|
|
[0, 1, 10, 0, 10, 8, 8, 10, 11],
|
|
[3, 1, 10, 11, 3, 10],
|
|
[1, 2, 11, 1, 11, 9, 9, 11, 8],
|
|
[3, 0, 9, 3, 9, 11, 1, 2, 9, 2, 11, 9],
|
|
[0, 2, 11, 8, 0, 11],
|
|
[3, 2, 11],
|
|
[2, 3, 8, 2, 8, 10, 10, 8, 9],
|
|
[9, 10, 2, 0, 9, 2],
|
|
[2, 3, 8, 2, 8, 10, 0, 1, 8, 1, 10, 8],
|
|
[1, 10, 2],
|
|
[1, 3, 8, 9, 1, 8],
|
|
[0, 9, 1],
|
|
[0, 3, 8],
|
|
[]
|
|
]
|
|
edgeShifts = np.array([ ## maps edge ID (0-11) to (x,y,z) cell offset and edge ID (0-2)
|
|
[0, 0, 0, 0],
|
|
[1, 0, 0, 1],
|
|
[0, 1, 0, 0],
|
|
[0, 0, 0, 1],
|
|
[0, 0, 1, 0],
|
|
[1, 0, 1, 1],
|
|
[0, 1, 1, 0],
|
|
[0, 0, 1, 1],
|
|
[0, 0, 0, 2],
|
|
[1, 0, 0, 2],
|
|
[1, 1, 0, 2],
|
|
[0, 1, 0, 2],
|
|
#[9, 9, 9, 9] ## fake
|
|
], dtype=np.uint16) # don't use ubyte here! This value gets added to cell index later; will need the extra precision.
|
|
nTableFaces = np.array([len(f)/3 for f in triTable], dtype=np.ubyte)
|
|
faceShiftTables = [None]
|
|
for i in range(1,6):
|
|
## compute lookup table of index: vertexes mapping
|
|
faceTableI = np.zeros((len(triTable), i*3), dtype=np.ubyte)
|
|
faceTableInds = np.argwhere(nTableFaces == i)
|
|
faceTableI[faceTableInds[:,0]] = np.array([triTable[j[0]] for j in faceTableInds])
|
|
faceTableI = faceTableI.reshape((len(triTable), i, 3))
|
|
faceShiftTables.append(edgeShifts[faceTableI])
|
|
|
|
## Let's try something different:
|
|
#faceTable = np.empty((256, 5, 3, 4), dtype=np.ubyte) # (grid cell index, faces, vertexes, edge lookup)
|
|
#for i,f in enumerate(triTable):
|
|
#f = np.array(f + [12] * (15-len(f))).reshape(5,3)
|
|
#faceTable[i] = edgeShifts[f]
|
|
|
|
|
|
IsosurfaceDataCache = (faceShiftTables, edgeShifts, edgeTable, nTableFaces)
|
|
else:
|
|
faceShiftTables, edgeShifts, edgeTable, nTableFaces = IsosurfaceDataCache
|
|
|
|
# We use strides below, which means we need contiguous array input.
|
|
# Ideally we can fix this just by removing the dependency on strides.
|
|
if not data.flags['C_CONTIGUOUS']:
|
|
raise TypeError("isosurface input data must be c-contiguous.")
|
|
|
|
## mark everything below the isosurface level
|
|
mask = data < level
|
|
|
|
### make eight sub-fields and compute indexes for grid cells
|
|
index = np.zeros([x-1 for x in data.shape], dtype=np.ubyte)
|
|
fields = np.empty((2,2,2), dtype=object)
|
|
slices = [slice(0,-1), slice(1,None)]
|
|
for i in [0,1]:
|
|
for j in [0,1]:
|
|
for k in [0,1]:
|
|
fields[i,j,k] = mask[slices[i], slices[j], slices[k]]
|
|
vertIndex = i - 2*j*i + 3*j + 4*k ## this is just to match Bourk's vertex numbering scheme
|
|
np.add(index, fields[i,j,k] * 2**vertIndex, out=index, casting='unsafe')
|
|
|
|
### Generate table of edges that have been cut
|
|
cutEdges = np.zeros([x+1 for x in index.shape]+[3], dtype=np.uint32)
|
|
edges = edgeTable[index]
|
|
for i, shift in enumerate(edgeShifts[:12]):
|
|
slices = [slice(shift[j],cutEdges.shape[j]+(shift[j]-1)) for j in range(3)]
|
|
cutEdges[slices[0], slices[1], slices[2], shift[3]] += edges & 2**i
|
|
|
|
## for each cut edge, interpolate to see where exactly the edge is cut and generate vertex positions
|
|
m = cutEdges > 0
|
|
vertexInds = np.argwhere(m) ## argwhere is slow!
|
|
vertexes = vertexInds[:,:3].astype(np.float32)
|
|
dataFlat = data.reshape(data.shape[0]*data.shape[1]*data.shape[2])
|
|
|
|
## re-use the cutEdges array as a lookup table for vertex IDs
|
|
cutEdges[vertexInds[:,0], vertexInds[:,1], vertexInds[:,2], vertexInds[:,3]] = np.arange(vertexInds.shape[0])
|
|
|
|
for i in [0,1,2]:
|
|
vim = vertexInds[:,3] == i
|
|
vi = vertexInds[vim, :3]
|
|
viFlat = (vi * (np.array(data.strides[:3]) // data.itemsize)[np.newaxis,:]).sum(axis=1)
|
|
v1 = dataFlat[viFlat]
|
|
v2 = dataFlat[viFlat + data.strides[i]//data.itemsize]
|
|
vertexes[vim,i] += (level-v1) / (v2-v1)
|
|
|
|
### compute the set of vertex indexes for each face.
|
|
|
|
## This works, but runs a bit slower.
|
|
#cells = np.argwhere((index != 0) & (index != 255)) ## all cells with at least one face
|
|
#cellInds = index[cells[:,0], cells[:,1], cells[:,2]]
|
|
#verts = faceTable[cellInds]
|
|
#mask = verts[...,0,0] != 9
|
|
#verts[...,:3] += cells[:,np.newaxis,np.newaxis,:] ## we now have indexes into cutEdges
|
|
#verts = verts[mask]
|
|
#faces = cutEdges[verts[...,0], verts[...,1], verts[...,2], verts[...,3]] ## and these are the vertex indexes we want.
|
|
|
|
|
|
## To allow this to be vectorized efficiently, we count the number of faces in each
|
|
## grid cell and handle each group of cells with the same number together.
|
|
## determine how many faces to assign to each grid cell
|
|
nFaces = nTableFaces[index]
|
|
totFaces = nFaces.sum()
|
|
faces = np.empty((totFaces, 3), dtype=np.uint32)
|
|
ptr = 0
|
|
#import debug
|
|
#p = debug.Profiler()
|
|
|
|
## this helps speed up an indexing operation later on
|
|
cs = np.array(cutEdges.strides)//cutEdges.itemsize
|
|
cutEdges = cutEdges.flatten()
|
|
|
|
## this, strangely, does not seem to help.
|
|
#ins = np.array(index.strides)/index.itemsize
|
|
#index = index.flatten()
|
|
|
|
for i in range(1,6):
|
|
### expensive:
|
|
#profiler()
|
|
cells = np.argwhere(nFaces == i) ## all cells which require i faces (argwhere is expensive)
|
|
#profiler()
|
|
if cells.shape[0] == 0:
|
|
continue
|
|
cellInds = index[cells[:,0], cells[:,1], cells[:,2]] ## index values of cells to process for this round
|
|
#profiler()
|
|
|
|
### expensive:
|
|
verts = faceShiftTables[i][cellInds]
|
|
#profiler()
|
|
np.add(verts[...,:3], cells[:,np.newaxis,np.newaxis,:], out=verts[...,:3], casting='unsafe') ## we now have indexes into cutEdges
|
|
verts = verts.reshape((verts.shape[0]*i,)+verts.shape[2:])
|
|
#profiler()
|
|
|
|
### expensive:
|
|
verts = (verts * cs[np.newaxis, np.newaxis, :]).sum(axis=2)
|
|
vertInds = cutEdges[verts]
|
|
#profiler()
|
|
nv = vertInds.shape[0]
|
|
#profiler()
|
|
faces[ptr:ptr+nv] = vertInds #.reshape((nv, 3))
|
|
#profiler()
|
|
ptr += nv
|
|
|
|
return vertexes, faces
|
|
|
|
|
|
|
|
def invertQTransform(tr):
|
|
"""Return a QTransform that is the inverse of *tr*.
|
|
Rasises an exception if tr is not invertible.
|
|
|
|
Note that this function is preferred over QTransform.inverted() due to
|
|
bugs in that method. (specifically, Qt has floating-point precision issues
|
|
when determining whether a matrix is invertible)
|
|
"""
|
|
try:
|
|
import numpy.linalg
|
|
arr = np.array([[tr.m11(), tr.m12(), tr.m13()], [tr.m21(), tr.m22(), tr.m23()], [tr.m31(), tr.m32(), tr.m33()]])
|
|
inv = numpy.linalg.inv(arr)
|
|
return QtGui.QTransform(inv[0,0], inv[0,1], inv[0,2], inv[1,0], inv[1,1], inv[1,2], inv[2,0], inv[2,1])
|
|
except ImportError:
|
|
inv = tr.inverted()
|
|
if inv[1] is False:
|
|
raise Exception("Transform is not invertible.")
|
|
return inv[0]
|
|
|
|
|
|
def pseudoScatter(data, spacing=None, shuffle=True, bidir=False):
|
|
"""
|
|
Used for examining the distribution of values in a set. Produces scattering as in beeswarm or column scatter plots.
|
|
|
|
Given a list of x-values, construct a set of y-values such that an x,y scatter-plot
|
|
will not have overlapping points (it will look similar to a histogram).
|
|
"""
|
|
inds = np.arange(len(data))
|
|
if shuffle:
|
|
np.random.shuffle(inds)
|
|
|
|
data = data[inds]
|
|
|
|
if spacing is None:
|
|
spacing = 2.*np.std(data)/len(data)**0.5
|
|
s2 = spacing**2
|
|
|
|
yvals = np.empty(len(data))
|
|
if len(data) == 0:
|
|
return yvals
|
|
yvals[0] = 0
|
|
for i in range(1,len(data)):
|
|
x = data[i] # current x value to be placed
|
|
x0 = data[:i] # all x values already placed
|
|
y0 = yvals[:i] # all y values already placed
|
|
y = 0
|
|
|
|
dx = (x0-x)**2 # x-distance to each previous point
|
|
xmask = dx < s2 # exclude anything too far away
|
|
|
|
if xmask.sum() > 0:
|
|
if bidir:
|
|
dirs = [-1, 1]
|
|
else:
|
|
dirs = [1]
|
|
yopts = []
|
|
for direction in dirs:
|
|
y = 0
|
|
dx2 = dx[xmask]
|
|
dy = (s2 - dx2)**0.5
|
|
limits = np.empty((2,len(dy))) # ranges of y-values to exclude
|
|
limits[0] = y0[xmask] - dy
|
|
limits[1] = y0[xmask] + dy
|
|
while True:
|
|
# ignore anything below this y-value
|
|
if direction > 0:
|
|
mask = limits[1] >= y
|
|
else:
|
|
mask = limits[0] <= y
|
|
|
|
limits2 = limits[:,mask]
|
|
|
|
# are we inside an excluded region?
|
|
mask = (limits2[0] < y) & (limits2[1] > y)
|
|
if mask.sum() == 0:
|
|
break
|
|
|
|
if direction > 0:
|
|
y = limits2[:,mask].max()
|
|
else:
|
|
y = limits2[:,mask].min()
|
|
yopts.append(y)
|
|
if bidir:
|
|
y = yopts[0] if -yopts[0] < yopts[1] else yopts[1]
|
|
else:
|
|
y = yopts[0]
|
|
yvals[i] = y
|
|
|
|
return yvals[np.argsort(inds)] ## un-shuffle values before returning
|
|
|
|
|
|
|
|
def toposort(deps, nodes=None, seen=None, stack=None, depth=0):
|
|
"""Topological sort. Arguments are:
|
|
deps dictionary describing dependencies where a:[b,c] means "a depends on b and c"
|
|
nodes optional, specifies list of starting nodes (these should be the nodes
|
|
which are not depended on by any other nodes). Other candidate starting
|
|
nodes will be ignored.
|
|
|
|
Example::
|
|
|
|
# Sort the following graph:
|
|
#
|
|
# B ──┬─────> C <── D
|
|
# │ │
|
|
# E <─┴─> A <─┘
|
|
#
|
|
deps = {'a': ['b', 'c'], 'c': ['b', 'd'], 'e': ['b']}
|
|
toposort(deps)
|
|
=> ['b', 'd', 'c', 'a', 'e']
|
|
"""
|
|
# fill in empty dep lists
|
|
deps = deps.copy()
|
|
for k,v in list(deps.items()):
|
|
for k in v:
|
|
if k not in deps:
|
|
deps[k] = []
|
|
|
|
if nodes is None:
|
|
## run through deps to find nodes that are not depended upon
|
|
rem = set()
|
|
for dep in deps.values():
|
|
rem |= set(dep)
|
|
nodes = set(deps.keys()) - rem
|
|
if seen is None:
|
|
seen = set()
|
|
stack = []
|
|
sorted = []
|
|
for n in nodes:
|
|
if n in stack:
|
|
raise Exception("Cyclic dependency detected", stack + [n])
|
|
if n in seen:
|
|
continue
|
|
seen.add(n)
|
|
sorted.extend( toposort(deps, deps[n], seen, stack+[n], depth=depth+1))
|
|
sorted.append(n)
|
|
return sorted
|
|
|
|
|
|
def disconnect(signal, slot):
|
|
"""Disconnect a Qt signal from a slot.
|
|
|
|
This method augments Qt's Signal.disconnect():
|
|
|
|
* Return bool indicating whether disconnection was successful, rather than
|
|
raising an exception
|
|
* Attempt to disconnect prior versions of the slot when using pg.reload
|
|
"""
|
|
while True:
|
|
try:
|
|
signal.disconnect(slot)
|
|
return True
|
|
except (TypeError, RuntimeError):
|
|
slot = reload.getPreviousVersion(slot)
|
|
if slot is None:
|
|
return False
|
|
|
|
|
|
class SignalBlock(object):
|
|
"""Class used to temporarily block a Qt signal connection::
|
|
|
|
with SignalBlock(signal, slot):
|
|
# do something that emits a signal; it will
|
|
# not be delivered to slot
|
|
"""
|
|
def __init__(self, signal, slot):
|
|
self.signal = signal
|
|
self.slot = slot
|
|
|
|
def __enter__(self):
|
|
self.reconnect = disconnect(self.signal, self.slot)
|
|
return self
|
|
|
|
def __exit__(self, *args):
|
|
if self.reconnect:
|
|
self.signal.connect(self.slot)
|
|
|
|
|
|
|