uAbstract Classes - Riemann Sphere

classes defining interfaces for PyGeo geometric primitives associated with the unit (Riemann) origin centered sphere representing the extended complex plane

Contents

class Element

definition:

the abstract class from which all PyGeo geometric objects derive
keywords:

Keyword

Definition

Type

Default

color

drawn color of object

list of 3 numbers

[0,0,0] (BLACK)

level

visibility "level" - see GUI

integer

1

trace

toggle for tracing function

boolean

False

texture

texture for Povray output

string

None

class _rPoint

definition:

an O dimensional object with a defined position in space.
inherits:

class Real._Point
site ref:

http://mathworld.wolfram.com/Point.html
attributes:
  • x: x coord
  • y: y coord
  • z: z coord
keywords:

inherited keywords from class Element :

inherited keywords: from class Real._Point :

class _uPoint

definition:

an O dimensional object on the unit sphere.
inherits:

class Real._Point
site ref:

http://mathworld.wolfram.com/Point.html
attributes:
  • x: x coord
  • y: y coord
  • z: z coord
keywords:

inherited keywords: from class Element :

inherited keywords: from class Real._Point :

class _uFreePosition

definition:

an O dimensional object that can be picked and moved either freely on the unit sphere or on an object of the unit sphere
inherits:

class _uPoint
site ref:

http://mathworld.wolfram.com/Point.html
attributes:
  • x: x coord
  • y: y coord
  • z: z coord
keywords:

inherited keywords: from class Element :

inherited keywords: from class Real._Point :

class _uCircle

definition:

a spheric section of the unit sphere
inherits:

class Real._Circle
site ref:

http://mathworld.wolfram.com/SphericSection.html
attributes:
  • _u : the unit normal of the circle's plane
  • _d : the distance from origin of the circle's plane
  • _s : unit vector perp to normal of the circle's plane
  • _center: the circle's center point
  • _cpoint: a point of the circle's circumference
  • _radius: the circle's radius
  • _radiusSquared: the square of circle's radius
keywords:

inherited keywords from class Element :

inherited keywords from class Real._Circle :

class _uSphere

definition:

the orign centered Riemann (unit) sphere representing the extended complex plane
inherits:

class Real._Sphere
site ref:

http://mathworld.wolfram.com/UnitSphere.html
attributes:
  • _center the sphere's center point
  • _cpoint a point on the sphere's circumference
  • _radius: the sphere's radius
  • _radiusSquared: the square of the sphere's radius
keywords:

inherited keywords from class Element :

inherited keywords from class Real._Sphere :

class _uCirclePencil

definition:

an array of circle s on the Riemann sphere
inherits:

class Real._CirclePencil
site ref:

http://mathworld.wolfram.com/SphericSection.html
attributes:
  • circles: the positioned circles of the array
keywords:

inherited keywords from class Element :

inherited keywords from class Real._CirclePencil :

class _uTransformation

definition:

a stereographic mapping of geometric objects of the complex plane to the unit sphere
inherits:

class Element
site ref:

http://mathworld.wolfram.com/StereographicProjection.html
attributes:
  • transforms: the transformed positions of the given objects
keywords:

inherited keywords from class Element :

class _rLine

definition:

an 1 dimensional object representing "breathless length"
inherits:

class Real._Line
site ref:

http://mathworld.wolfram.com/Line.html
attributes:
  • p1: point on line
  • p2: point on line
keywords:

inherited keywords from class Element :

inherited keywords from class Real._Line :