Inversion(...)

Objects derived from the _Point abstract class, with its position in space determined by its inversive relationship to a given geometric object


def Inversion

constructors:
returns:

A point determined by a inversive transformation with respect to a given geometric object

site ref:

http://mathworld.wolfram.com/InversiveGeometry.html

class CircleInversion

constructors:
  • Inversion(point,circle)
  • CircleInversion(point, circle)
returns:

the inverse point of a given point with respect to a given coplanar circle

conditions:

point and circle are coplanar; point not circle center

else returns:

None ; point at [MAX,MAX,MAX]

site ref:

http://mathworld.wolfram.com/InversePoints.html

class SphereInversion

constructors:
  • Inversion(point,sphere)
  • SphereInversion(point,sphere)
returns:

the point of inversion of a given point with respect to an inversive sphere

conditions:

point not sphere center

else returns:

point at [MAX,MAX,MAX]

site ref:

http://mathworld.wolfram.com/InversionSphere.html

class CirclePole

constructors:
  • Inversion(line,circle)
  • CirclePole(line,circle)
returns:

the pole of a given line with respect to a given coplanar circle

conditions:

line and circle are coplanar; line not on circle center

else returns:

None ; point at [MAX,MAX,MAX]

site ref:

http://mathworld.wolfram.com/InversionPole.html

class SpherePole

constructors:
  • Inversion(plane,sphere)
  • SpherePole(plane,sphere)
returns:

the pole of a given plane with respect to a given sphere

conditions:

line not on sphere center

else returns:

point at [MAX,MAX,MAX]

site ref:

http://mathworld.wolfram.com/InversionPole.html

class ConicPole

constructors:
  • Inversion(line,conic)
  • ConicPole(line,conic)
returns:

the pole of a given line with respect to a given coplanar conic

conditions:

line and conic are coplanar

else returns:

None

site ref:

http://mathworld.wolfram.com/InversionPole.html