mobTransform(....)

Contents

Objects derived from the _zTransformation abstract class represented a defined linear fractional transformation of a given list of geometric objects of the complex plane

def mobTransform

constructors:
returns:

a defined transformation of a given list of objects

class mobPointSets

constructors:
  • mobTransform([z1,z2,z3],[z1a,z2a,z3a],[list of objects])
  • mobPointSets([z1,z2,z3],[z1a,z2a,z3a],[list of objects])
returns:

the Mobius transformation which maps the 3 (ordered) points of the first point set to the 3 (ordered) points of the second point set, applied to the given list of objects of the complex plane.
site ref:

http://en.wikipedia.org/wiki/Mobius_group#Specifying_a_transformation_by_three_points

class mobUnitCircle

constructors:
  • mobTransform(zcircle,[list of objects])
  • mobUnitCircle(zcircle,[list of objects])
returns:

a Mobius transformation which maps the given circle to the unit circle, applied to the given list of objects of the complex plane.
site ref:

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

class mobMultiply

constructors:
  • mobTransform(zpoint,[list of objects])
  • mobMultiply(zpoint,[list of objects])
returns:

a normal form elliptical Mobius transformation with the given complex point as multiplier, applied to the given list of objects of the complex plane.

:site ref:http://en.wikipedia.org/wiki/Mobius_group#Elliptic_transformations

class mobTranslate

constructors:
  • mobTransform(zpoint,[list of objects],alt=TRANSLATE)
  • mobTranslate(zpoint,[list of objects])
returns:

a normal form parabolic Mobius transformation translating the given given list of objects in the direction of the given point of the complex plane/

:site ref:http://en.wikipedia.org/wiki/Mobius_group#Hyperbolic_transformations

class mobReciprocate

constructors:
  • mobTransform([list of objects])
  • mobReciprocate([list of objects])
returns:

a normal form Mobius transformation reciprocating the given given list of objects of the complex plane/

:site ref:http://mathworld.wolfram.com/Reciprocal.html

class mobRotate

constructors:
  • mobTransform(zpoint,numeric,[list of objects])
  • mobRotate(zpoint,numeric,[list of objects])
returns:

the Mobius transformation induced by the rotation of the Riemann sphere, with the stereographic projection of the given complex point as axis, by an the given numeric angle (in radians), and applied to the given list of geometric objects.

:site ref:http://en.wikipedia.org/wiki/Mobius_group#Hyperbolic_transformations

class mobMapCircles

constructors:
  • mobTransform(zcircle1,zcircle2,[list of objects])
  • mobMapCircles(zcircle1,zcircle2,[list of objects])
returns:

a Mobius transformation mapping the interior of the first given circle to the exterior of the second given circle, applied to the given list of geometric objects

:site ref:http://www.americanscientist.org/template/BookReviewTypeDetail/assetid/17185;jsessionid=aaa6s5lwY8zkwS

class mobInverse

constructors:
  • mobTransform(mobTransform,[list of objects])
  • mobInverse(mobTransform,[list of objects])
returns:

a Mobius transformation defined by the matrix inverse of matrix represetning the given Mobius transformation.

:site ref:http://www.americanscientist.org/template/BookReviewTypeDetail/assetid/17185;jsessionid=aaa6s5lwY8zkwS