Editing CLUViz Geometric Algebra Animation Software (section)

==Difficulties & Possible Extensions==
Over the course of the development of both the 3D and 4D CLUViz animations a bunch of possible extensions were identifed. Most of which were features that we attempted to implement and had no luck with as a result of the difficulties faced or the suspected time demands. The main of which, was ''Mouse Control'', where we ideally would've loved to have it so that the user/viewer could interactively control each of the rotation axes and attempt to line them up with one another (more so for 3D) in order to show commuting operators. This was initially suggested by James, as he loved the prospect of the visualisation being like a 'game'. 

[[Image:hypercube.gif|thumb|3350px|left|Projection of a rotating tesseract.]]


This became difficult however, as the mouse control was very hard to control and it's implemented in such a way so that by moving the mouse around the length of the vector itself is altered as well as the direction (which caused a unit vector of length 1 to rapidly grow to 100x larger). In an attempt to rectify this problem, instead of displaying the actual rotation axis a unit vector in the direction of each rotation axis was shown, hence giving the impression that you're simply moving the axis around. This was a simple fix, as the length of the rotation axis makes absolutely no difference to it's functionality.

===Hypercube===
In accordance with the original project description, it was suggested that we attempt to program an animated hypercube (also known as a tesseract). This would have helped viewers fundamentally visualise 4-dimensions rather than rotations in 4-dimensions as shown by the other 4D CLUViz work, however due to the difficulty of programming such a visualisation for what we percieved to be of little value to the project we decided not to program it- however it's noteworthy that efforts were made with CLUViz and with more time it would've been completed. For more on 4D projections, please follow the link - ''http://eusebeia.dyndns.org/4d/vis/10-rot-1''


''{{nowrap|“}}In geometry, a '''hypercube''' is an n-dimensional analogue of a Square (n = 2) and a cube (n = 3). It is a closed, compact, convex figure whose 1-skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length.{{nowrap|”}}'' ''http://en.wikipedia.org/wiki/Hypercube''