zAbstract Classes - Complex Plane

classes defining interfaces for PyGeo geometric primitives associated with the geometry of the `complex plane`_

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 _zPoint

definition:

an O dimensional object with a defined postion on the complex plane .

inherits:

class. Element,base.CPosition, base.zdraw.zPoint

site ref:

http://en.wikipedia.org/wiki/Complex_number

attributes:
  • real: the real coordinate
  • imag the imaginary coordinate
keywords:

inherited keywords: from class Element :

class keywords:

Keyword

Definition

Type

Default

pointsize

size of drawn point

numeric

.1

label

label rendered for point

string

None

tracewidth

width of trace curve

numeric

pointsize/2

tracecolor

color of trace curve

list of 3 numbers

color

fontsize

fontsize of label

constant

TINYFONT

fontcolor

color of label font

constant

BLACK

fontXoffset

horizontal offset of label

numeric

pointsize/10.+ 3.0

fontYoffset

vertical offset of label

numeric

pointsize/10.+ 3.0

class _zFreePosition

definition:

an O dimensional object of the complex plane that can picked and moved, either freely on the plnae or constrained to a given geoemtric object of the plane.

inherits:

class _zPoint

site ref:

http://en.wikipedia.org/wiki/Complex_number

attributes:
  • real: the real coordinate
  • imag the imaginary coordinate
keywords:

inherited keywords: from class Element :

inherited keywords: from class _zPoint :

class _zLine

definition:

a straight line of the 'complex plane'_ , representing a 'complex circle'_ of infinite radius

inherits:

class Element , base.zdraw.zLine

site ref:

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

attributes:
  • p1: a complex point on the line
  • p2 a second complex point on the line
  • _hermitian: the hermitian matrix associated with the line
keywords:

inherited keywords from class Element :

class keywords:

Keyword

Definition

Type

Default

linewidth

width of drawn line

numeric

.02

label

label rendered for point

string

None

fontsize

fontsize of label

constant

NORMALFONT

fontcolor

color of label font

constant

BLACK

fontXoffset

horizontal offset of label

numeric

pointsize/10.+ 3.0

fontYoffset

vertical offset of label

numeric

pointsize/10.+ 3.0

label_ratio

relative position of label

numeric

.5 (midpoint)

show_normal

draw line normal?

boolean

False

class _zCircle

definition:

the set of points the complex plane that are equidistant from a given point of the plane

inherits:

class Element , base.zdraw.zCircle

site ref:

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

attributes:
  • _center: the complex point on circle's center
  • _cpoint: a complex point on circle circumference
  • _hermitian: the hermitian matrix associated with the circle
  • _radius: the circle's radius
  • _radiusSquared: the square of the circle's radius
keywords:

inherited keywords from class Element :

class keywords:

Keyword

Definition

Type

Default

style

drawing style

constant

LINES

linewidth

width of drawn lines

numeric

.02

precision

drawing precision

integer

40

show_normal

draw normal

boolean

False

normal_width

width of drawn normal

numeric

.4

fixed

fix to initial radius

boolean

False

class _zPointArray

definition:

an array of class _zPoint s on the complex plane with a defined geometric relationship

inherits:

class Element

site ref:

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

attributes:
  • zpoints: positioned complex points of the array
keywords:

inherited keywords from class Element :

class keywords:

Keyword

Definition

Type

Default

pointsize

size of drawn points

numeric

.4

density

points in the array

integer

50

class _zLineArray

definition:

an array of class _zLine s on the complex plane

inherits:

class Element

site ref:

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

attributes:
  • zlines: positioned lines of the complex plane
keywords:

inherited keywords from class Element :

class keywords:

Keyword

Definition

Type

Default

linewidth

linewidth of drawn circles

numeric

.015

density

lines in the array

integer

50

class _zCirclePencil

definition:

an array of class _zCircle s on the complex plane

inherits:

class Element

site ref:

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

attributes:
  • zcircles: positioned circles of the complex plane
keywords:

inherited keywords from class Element :

class keywords:

Keyword

Definition

Type

Default

style

drawing style for circles

CONSTANT

LINES

linewidth

linewidth of drawn circles

numeric

.015

precision

precision of drawn circles

integer

70

density

lines in the array

integer

30

scale

drawing scale of planes

numeric

1

class _zTransformation

definition:

a Mobius transformation of geometric objects of the complex plane

inherits:

class Element

site ref:

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

attributes:
  • _mobius: the Mobius tranformation matrix defining the transformation
keywords:

inherited keywords from class Element :

class keywords:

Keyword

Definition

Type

Default

normal_form

convert matrix to normal form

boolean

False