zHarmonic

the Mobius transformation represented by a given complex 2x2 matrix, assigned to the given point

transform cuurent position as the effect of a rotation of the Riemann sphere around the given point as axis and the given angle

set the position as the projection of a given homogenous complex number to the complex plane

return the vector represnting hte prjojection of the zpoint to the Riemann sphere

set the given point to the projection of the zpoint to the Riemann sphere

set the position on the zplane from the Hermitian matrix representation of the point

set the Hermitian matrix representation of the point

make all objects iterable, returning "self" in the simplest instance

length of the iterable assocaited with the object

method that is called on change events, calling reoutines to find current position based on dependecies, current visibility status, etc.

each object has a 4x4 matrix associated with it, representing the object's axis of rotation and translation from the origin. Needed for the implementation of the Projection class. Set to the identity matrix by default.

test whether any Elements on which there is a dependency have become 'null', i.e. not calculatable - .e.g, imaginary when working within real space

check for change in visibiliy status and toggle visibility as necessary, reset change flag to 0 on effectuating change in visiblity

toggle the 'null' flag, indicating whether the current postion of the object's position is visible - e.g. is real when working in real space

set object and the objects dependant on it to 'null' when its position cannot be made visible- e.g. imaginary when working in real space.

method to be overridden for objects needing an supplementary initiliazation routine after the call to __init___

Routine to return Element to intial position. Default is to run update routine

method to be overridden to erase loci of objects that are traceable

method to be overridden to erase curves traced by point objects

send current position in scene to render object, and render in accordance with style sttribute

If on update, traced point has moved within limits defined by 'mintrace' and 'maxtrace' append its new position to the trace curve

For consistency in iterating Element's rendering objects, all elements rendering information is in a list called self.rend. In the case of Points, it is either a single element list, containing a cvisual sphere object, or a 2 element list with each element an oriented cvisual pyramid object, which together form a diamond shape representing the point

export the scene's points to PovRay SDL