src/Mod/Draft/draftgeoutils/circle_inversion.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 inversive operations using a circle.

http://en.wikipedia.org/wiki/Inversive_geometry
"""
## @package circle_inversion
# \ingroup draftgeoutils
# \brief Provides various functions for inversive geometry operations.

import lazy_loader.lazy_loader as lz

import FreeCAD as App
import DraftVecUtils

from draftgeoutils.general import NORM, geomType
from draftgeoutils.geometry import findDistance

# Delay import of module until first use because it is heavy
Part = lz.LazyLoader("Part", globals(), "Part")

## \addtogroup draftgeoutils
# @{


def pointInversion(circle, point):
    """Return the circle inversion of a point.

    It will return `None` if the given point is equal to the center
    of the circle.
    """
    if geomType(circle) != "Circle" or isinstance(point, App.Vector):
        print("debug: pointInversion bad parameters!")
        return None

    cen = circle.Curve.Center
    rad = circle.Curve.Radius

    if DraftVecUtils.equals(cen, point):
        return None

    # Inverse the distance of the point
    # dist(cen -> P) = r^2 / dist(cen -> invP)

    dist = DraftVecUtils.dist(point, cen)
    invDist = rad**2 / dist

    invPoint = App.Vector(0, 0, point.z)
    invPoint.x = cen.x + (point.x - cen.x) * invDist / dist
    invPoint.y = cen.y + (point.y - cen.y) * invDist / dist

    return invPoint


def polarInversion(circle, edge):
    """Return the inversion pole of a line. The edge is the polar.

    The nearest point on the line is inversed.

    http://mathworld.wolfram.com/InversionPole.html
    """
    if geomType(circle) != "Circle" or geomType(edge) != "Line":
        print("debug: circleInversionPole bad parameters! Must be a circle.")
        return None

    nearest = circle.Curve.Center.add(findDistance(circle.Curve.Center, edge, False))
    if nearest:
        inversionPole = pointInversion(circle, nearest)
        if inversionPole:
            return inversionPole

    return None


def circleInversion(circle, circle2):
    """Circle inversion of a circle, inverting the center point.

    Returns the new circle created from the inverted center of circle2.
    """
    if geomType(circle) != "Circle" or geomType(circle2) != "Circle":
        print("debug: circleInversion bad parameters! Must be circles.")
        return None

    cen1 = circle.Curve.Center

    cen2 = circle2.Curve.Center
    rad2 = circle2.Curve.Radius

    if DraftVecUtils.equals(cen1, cen2):
        return None

    invCen2 = pointInversion(circle, cen2)

    pointOnCircle2 = App.Vector.add(cen2, App.Vector(rad2, 0, 0))
    invPointOnCircle2 = pointInversion(circle, pointOnCircle2)

    return Part.Circle(invCen2, NORM, DraftVecUtils.dist(invCen2, invPointOnCircle2))


## @}