zPoint(...)

Object derived from the _zPoint abstract class, representing a point of the complex plane, with its position determined with respect to its numeric, geometric, and/or constant arguments

def zPoint

constructors:
returns:

A point of the origin centered 'unit sphere'_, as determined by its arguments

site ref:

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

class zFixedPoint

constructors:
  • zPoint(<float>,<float>)
  • zPoint(complex)
  • zFixedPoint(<float>,<float>)
  • zFixedPoint(complex)
returns:

a point on the complex plane. With 2 float arguments, the 1st is the real, the second the imaginary element. Also accepts a complex number argument.

site ref:

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

class zPolarPoint

constructors:
  • zPoint(angle=<float>,dist=<float>)
  • zPolarPoint(angle=<float>,dist=<float>)
returns:

a point on the complex plane expressed in polar coordinates , with the angle keyword argument defaulting to PI and the dist keyword argument defaulting to 1.

site ref:

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

class zConjugate

constructors:
  • zPoint(zPoint)
  • zPoint(zPoint,alt=CONJUGATE)
  • zConjugate(zPoint)
returns:

the complex conjugate of the given complex point.

site ref:

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

class zOrthoPoint

constructors:
  • zPoint(zPoint,alt=ORTHO)
  • zOrthoPoint(zPoint)
returns:

the point of the complex plane orthogonal to the given complex point, i.e. the point antipodal to it's stereographic projection onto the 'unit sphere`_.

site ref:

http://www.bbc.co.uk/dna/h2g2/A974397

class zInversePoint

constructors:
  • zPoint(zpoint,zcircle)
  • zInversePoint(plane, line)
returns:

the point of complex 'inverse point'_ to the given complex point with respect to the given circle

site ref:

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

class zPowerPoint

constructors:
  • zPoint(zcircle1,zcircle2)
  • zPowerPoint(zcircle1,zcircle2)
returns:

the point of intersection of the radical axis of the given circles and the line of the circles' centers

site ref:

http://mathworld.wolfram.com/Circle-CircleIntersection.html

class zRotation

constructors:
  • zPoint(zpoint,zpoint,<angle=PI>)
  • zRotation(zpoint,zpoint,<angle=PI>)
returns:

the rotation of the second point argument induced by the rotation of the unit sphere , with the stereographic projection of the first point argument as axis of rotation .

site ref:

http://www.math.union.edu/~dpvc/math/4D/stereo-projection/welcome.html

class z_uRotation

constructors:
  • zPoint(upoint,zpoint,<angle=PI>)
  • z_uRotation(Upoint,zpoint,<angle=PI>)
returns:

the rotation of the second point argument induced by the rotation of the unit sphere , with the upoint argument as axis of rotation .

site ref:

http://www.math.union.edu/~dpvc/math/4D/stereo-projection/welcome.html

class zCircumPoint

constructors:
  • zPoint(zcircle,<angle=PI>)
  • zCircumPoint(zcircle,<angle=PI>)
returns:

the point on the given circle rotated by the given angle (in radians)

site ref:

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

class zHarmonic

constructors:
  • zPoint(zpoint1,zpoint2,zpoint3)
  • zHarmonic(zpoint1,zpoint2,zpoint3)
returns:

the harmonic conjugate of the 3rd argument with the respect to the first 2 arguments

site ref:

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

class zCrossPoint

constructors:
  • zPoint([zpoint1,zpoint2,zpoint3,zpoint4],[zpoint1a,zpoint2a,zpoint3a])
  • zCrossPoint([zpoint1,zpoint2,zpoint3,zpoint4],[zpoint1a,zpoint2a,zpoint3a],zpoint4)
returns:

the Mobius transformation of the 4th point of the first point set, defined by the ordered correspondance of the first 3 points in the first point set to the 3 points in the second point set

site ref:

http://s13a.math.aca.mmu.ac.uk/Geometry/M23Geom/XRatio/xratio.html