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Diffstat (limited to 'src/python/mathutil.py')
-rw-r--r-- | src/python/mathutil.py | 168 |
1 files changed, 168 insertions, 0 deletions
diff --git a/src/python/mathutil.py b/src/python/mathutil.py new file mode 100644 index 0000000..b27758e --- /dev/null +++ b/src/python/mathutil.py @@ -0,0 +1,168 @@ +# libavg - Media Playback Engine. +# Copyright (C) 2003-2014 Ulrich von Zadow +# +# This library is free software; you can redistribute it and/or +# modify it under the terms of the GNU Lesser General Public +# License as published by the Free Software Foundation; either +# version 2 of the License, or (at your option) any later version. +# +# This library is distributed in the hope that it will be useful, +# but WITHOUT ANY WARRANTY; without even the implied warranty of +# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +# Lesser General Public License for more details. +# +# You should have received a copy of the GNU Lesser General Public +# License along with this library; if not, write to the Free Software +# Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA +# +# Current versions can be found at www.libavg.de +# +# Original author of this file is Martin Heistermann <mh at sponc dot de> +# + +# TODO: Some of this stuff is duplicated - either in Point2D or in MathHelper.h/.cpp. +# Clean that up. + +import math +from libavg import Point2D + +def getAngle(p1, p2): + vec = p2 - p1 + res = math.atan2(vec.y, vec.x) + if res < 0: + res += math.pi * 2 + return res + +def getDistance (p, q): + return math.sqrt((p.x-q.x)**2 + (p.y-q.y)**2) + +def getDistSquared (p, q): + return (p.x-q.x)**2 + (p.y-q.y)**2 + +def getScaleToSize ((width, height), (max_width, max_height)): + if width < max_width: + height = height * (float(max_width) / width) + width = max_width + elif height > max_height: + width = width * (float(max_height) / height) + height = max_height + return getScaledDim((width, height), (max_width, max_height)) + +def getScaledDim (size, max = None, min = None): + width, height = size + if width == 0 or height == 0: + return size + + if max: + max = Point2D(max) + assert (max.x > 0 and max.y > 0) + if width > max.x: + height = height * (max.x / width) + width = max.x + if height > max.y: + width = width * (max.y / height) + height = max.y + + if min: + min = Point2D(min) + assert (min.x > 0 and min.y > 0) + if width < min.x: + height = height * (min.x / width) + width = min.x + if height < min.y: + width = width * (min.y / height) + height = min.y + + return Point2D(width, height) + + +class EquationNotSolvable (Exception): + pass +class EquationSingular (Exception): + pass + +def gauss_jordan(m, eps = 1.0/(10**10)): + """Puts given matrix (2D array) into the Reduced Row Echelon Form. + Returns True if successful, False if 'm' is singular. + NOTE: make sure all the matrix items support fractions! Int matrix will NOT work! + Written by Jarno Elonen in April 2005, released into Public Domain + http://elonen.iki.fi/code/misc-notes/affine-fit/index.html""" + (h, w) = (len(m), len(m[0])) + for y in range(0,h): + maxrow = y + for y2 in range(y+1, h): # Find max pivot + if abs(m[y2][y]) > abs(m[maxrow][y]): + maxrow = y2 + (m[y], m[maxrow]) = (m[maxrow], m[y]) + if abs(m[y][y]) <= eps: # Singular? + raise EquationSingular + for y2 in range(y+1, h): # Eliminate column y + c = m[y2][y] / m[y][y] + for x in range(y, w): + m[y2][x] -= m[y][x] * c + for y in range(h-1, 0-1, -1): # Backsubstitute + c = m[y][y] + for y2 in range(0,y): + for x in range(w-1, y-1, -1): + m[y2][x] -= m[y][x] * m[y2][y] / c + m[y][y] /= c + for x in range(h, w): # Normalize row y + m[y][x] /= c + return m + + +def solveEquationMatrix(_matrix, eps = 1.0/(10**10)): + matrix=[] + for coefficients, res in _matrix: + newrow = map(float, coefficients + (res,)) + matrix.append(newrow) + matrix = gauss_jordan (matrix) + res=[] + for col in xrange(len(matrix[0])-1): + rows = filter(lambda row: row[col] >= eps, matrix) + if len(rows)!=1: + raise EquationNotSolvable + res.append (rows[0][-1]) + + return res + + +def getOffsetForMovedPivot(oldPivot, newPivot, angle): + oldPos = Point2D(0,0).getRotated(angle, oldPivot) + newPos = Point2D(0,0).getRotated(angle, newPivot) + return oldPos - newPos + +def isNaN(x): + return (not(x<=0) and not(x>=0)) + +def sgn (x): + if x<0: + return -1 + elif x==0: + return 0 + else: + return 1 + +class MovingAverage: + """ + Moving average implementation. + Example: + ma = MovingAverage(20) + print ma(2) + print ma(3) + print ma(10) + """ + def __init__(self, points): + self.__points = points + self.__values = [] + + def __appendValue(self, value): + self.__values = (self.__values + [value])[-self.__points:] + + def __getAverage(self): + sum = reduce(lambda a,b:a+b, self.__values) + return float(sum) / len(self.__values) + + def __call__(self, value): + self.__appendValue(value) + return self.__getAverage() |