src/Mod/Draft/draftgeoutils/linear_algebra.py

# 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>                   *
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"""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


## @}