zCircle(...)

Objects derived from the _zCircle abstract class representing the set of points of the complex plane that are equidistant from a given point

def zCircle

constructors:
returns:

an instance of an object derived from the _zCircle abstract class, determined uniquely by reference to its arguments

Keyword arguments: see _zCircle

class zUnitCircle

constructors:
  • zCircle()
  • zUnitCircle()
returns:

the origin center complex circle_ of radius 1

site ref:

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

class zCircleFromPoints

constructors:
  • zCircle(zpoint1,zpoint2)
  • zCircleFromPoints(zpoint1,zpoint2)
returns:

the complex circle that with the first zpoint as center and the second zpoint on the circumference and determining the radius

condition:

points distinct

else returns:

None

site ref:

http://www.ies.co.jp/math/java/comp/cplcircle/cplcircle.html

class zCircumCircle

constructors:
  • zCircle(zpoint1,zpoint2,zpoint3)
  • zCircumCircle(zpoint1,zpoint2,zpoint3)
returns:

the complex circle through the 3 point arguments

condition:

points distinct

else returns:

None

site ref:

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

class zOrthoCircle

constructors:
  • zCircle(zcircle,zpoint)
  • zOrthoCircle(zcircle,zpoint)
returns:

the complex circle orthogonal to the given complex circle , with given zpoint as center

site ref:

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

class zOrthoCircle_Circum

constructors:
  • zCircle(zcircle,zpoint1,zpoint2)
  • zOrthoCircle_Circum(zcircle,zpoint1,zpoint2)
returns:

the complex circle orthogonal to the given complex circle , and through the given zpoint arguments.

condition:

points distinct

else returns:

None

site ref:

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

class zInverseCircle

constructors:
  • zCircle(zcircle1,zcircle2)
  • zCircle(zcircle1,zcircle2,alt=INVERSE)
  • zInverseCircle(zcircle1,zcircle2)
returns:

the complex circle inverse to the second zcircle argument with respect to the first zcircle argument, optional 'alt=INVERSE' keyword to disambiguate the argument signature from class zFundamentalCircle

site ref:

http://whistleralley.com/inversion/inversion.htm

class u_to_zCircle

constructors:
  • zCircle(ucircle);
  • u_to_zCircle(ucircle);
returns:

the stereographic projection of the given spheric section of the Riemann sphere to the complex plane

site ref:

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

class zFundamentalCircle

constructors:
  • zCircle(zcircle1,zcircle2,alt=FUNDAMENTAL)
  • zFundamentalCircle(zcircle1,zcircle2)
returns:

the complex circle in by which the first zcircle argument is tranformed to second zcircle argument by inversion . required 'alt=FUNDAMENTAL' keyword when initializing with zCircle facotry function to disambiguate the argument signature from class zInverseCircle

site ref:

http://whistleralley.com/inversion/inversion.htm