zAbstract Classes - Complex Plane

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

class Element
class _zPoint
class _zFreePosition
class _zLine
class _zCircle
class _zPointArray
class _zLineArray
class _zCirclePencil
class _zTransformation

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

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