89 lines
3.5 KiB
Python
89 lines
3.5 KiB
Python
# ***************************************************************************
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# * Copyright (c) 2009, 2010 Yorik van Havre <yorik@uncreated.net> *
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# * Copyright (c) 2009, 2010 Ken Cline <cline@frii.com> *
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# * *
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# * This file is part of the FreeCAD CAx development system. *
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# * *
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# * This program is free software; you can redistribute it and/or modify *
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# * it under the terms of the GNU Lesser General Public License (LGPL) *
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# * as published by the Free Software Foundation; either version 2 of *
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# * the License, or (at your option) any later version. *
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# * for detail see the LICENCE text file. *
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# * *
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# * FreeCAD is distributed in the hope that it will be useful, *
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# * but WITHOUT ANY WARRANTY; without even the implied warranty of *
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# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
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# * GNU Library General Public License for more details. *
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# * *
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# * You should have received a copy of the GNU Library General Public *
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# * License along with FreeCAD; if not, write to the Free Software *
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# * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 *
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# * USA *
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# * *
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# ***************************************************************************
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"""Provides various functions for linear algebra.
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This includes calculating linear equation parameters, and matrix determinants.
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"""
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## @package linear_algebra
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# \ingroup draftgeoutils
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# \brief Provides various functions for linear algebra.
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## \addtogroup draftgeoutils
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# @{
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import FreeCAD as App
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def linearFromPoints(p1, p2):
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"""Calculate linear equation from points.
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Calculate the slope and offset parameters of the linear equation
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of a line defined by two points.
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Linear equation:
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y = m * x + b
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m = dy / dx
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m ... Slope
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b ... Offset (point where the line intersects the y axis)
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dx/dy ... Delta x and y. Using both as a vector results
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in a non-offset direction vector.
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"""
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if not isinstance(p1, App.Vector) and not isinstance(p2, App.Vector):
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return None
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line = {}
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line['dx'] = (p2.x - p1.x)
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line['dy'] = (p2.y - p1.y)
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line['slope'] = line['dy'] / line['dx']
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line['offset'] = p1.y - line['slope'] * p1.x
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return line
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def determinant(mat, n):
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"""Return the determinant of an N-matrix.
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It recursively expands the minors.
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"""
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matTemp = [[0.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]]
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if (n > 1):
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if n == 2:
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d = mat[0][0] * mat[1][1] - mat[1][0] * mat[0][1]
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else:
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d = 0.0
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for j1 in range(n):
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# Create minor
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for i in range(1, n):
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j2 = 0
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for j in range(n):
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if j == j1:
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continue
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matTemp[i-1][j2] = mat[i][j]
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j2 += 1
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d += ((-1.0)**(1.0 + j1 + 1.0)
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* mat[0][j1] * determinant(matTemp, n-1))
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return d
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else:
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return 0
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## @}
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