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985c397 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 | # SPDX-License-Identifier: LGPL-2.1-or-later
# ***************************************************************************
# * Copyright (c) 2009, 2010 Yorik van Havre <yorik@uncreated.net> *
# * Copyright (c) 2009, 2010 Ken Cline <cline@frii.com> *
# * *
# * This file is part of the FreeCAD CAx development system. *
# * *
# * This program is free software; you can redistribute it and/or modify *
# * it under the terms of the GNU Lesser General Public License (LGPL) *
# * as published by the Free Software Foundation; either version 2 of *
# * the License, or (at your option) any later version. *
# * for detail see the LICENCE text file. *
# * *
# * FreeCAD 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 Library General Public License for more details. *
# * *
# * You should have received a copy of the GNU Library General Public *
# * License along with FreeCAD; if not, write to the Free Software *
# * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 *
# * USA *
# * *
# ***************************************************************************
"""Provides various functions for linear algebra.
This includes calculating linear equation parameters, and matrix determinants.
"""
## @package linear_algebra
# \ingroup draftgeoutils
# \brief Provides various functions for linear algebra.
## \addtogroup draftgeoutils
# @{
import FreeCAD as App
def linearFromPoints(p1, p2):
"""Calculate linear equation from points.
Calculate the slope and offset parameters of the linear equation
of a line defined by two points.
Linear equation:
y = m * x + b
m = dy / dx
m ... Slope
b ... Offset (point where the line intersects the y axis)
dx/dy ... Delta x and y. Using both as a vector results
in a non-offset direction vector.
"""
if not isinstance(p1, App.Vector) and not isinstance(p2, App.Vector):
return None
line = {}
line["dx"] = p2.x - p1.x
line["dy"] = p2.y - p1.y
line["slope"] = line["dy"] / line["dx"]
line["offset"] = p1.y - line["slope"] * p1.x
return line
def determinant(mat, n):
"""Return the determinant of an N-matrix.
It recursively expands the minors.
"""
matTemp = [[0.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]]
if n > 1:
if n == 2:
d = mat[0][0] * mat[1][1] - mat[1][0] * mat[0][1]
else:
d = 0.0
for j1 in range(n):
# Create minor
for i in range(1, n):
j2 = 0
for j in range(n):
if j == j1:
continue
matTemp[i - 1][j2] = mat[i][j]
j2 += 1
d += (-1.0) ** (1.0 + j1 + 1.0) * mat[0][j1] * determinant(matTemp, n - 1)
return d
else:
return 0
## @}
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