https://www.eleceng.adelaide.edu.au/personal/dabbott/wiki/index.php?action=history&feed=atom&title=CLUViz_Geometric_Algebra_Animation_SoftwareCLUViz Geometric Algebra Animation Software - Revision history2026-06-25T21:18:50ZRevision history for this page on the wikiMediaWiki 1.43.1https://www.eleceng.adelaide.edu.au/personal/dabbott/wiki/index.php?title=CLUViz_Geometric_Algebra_Animation_Software&diff=12905&oldid=prevA1210435: /* Current Code */2013-11-04T07:17:02Z<p><span class="autocomment">Current Code</span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Current Code==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Current Code==</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The final version of the code is included here: [[Media:3DAnimation.rar|3D Visualisation]] & [[Media:<del style="font-weight: bold; text-decoration: none;">4DAnimation</del>.rar|4D Visualisation]]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The final version of the code is included here: [[Media:3DAnimation.rar|3D Visualisation]] & [[Media:<ins style="font-weight: bold; text-decoration: none;">4DAnimationFinal</ins>.rar|4D Visualisation]]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>After having gotten some background information on 3D & 4D rotations from the reports and/or independent wiki pages, we highly encourage you to follow the link above to download the CLUViz software and our code to have a play around. Naturally, it's recommended that you start with the 3D animation and then move on to the 4D animation if you wish to grasp how 4D rotations could look. All the code if sufficiently commented and it should be relatively easy to navigate throughout the code if you wish to edit elements for whatever reason.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>After having gotten some background information on 3D & 4D rotations from the reports and/or independent wiki pages, we highly encourage you to follow the link above to download the CLUViz software and our code to have a play around. Naturally, it's recommended that you start with the 3D animation and then move on to the 4D animation if you wish to grasp how 4D rotations could look. All the code if sufficiently commented and it should be relatively easy to navigate throughout the code if you wish to edit elements for whatever reason.</div></td></tr>
</table>A1210435https://www.eleceng.adelaide.edu.au/personal/dabbott/wiki/index.php?title=CLUViz_Geometric_Algebra_Animation_Software&diff=12902&oldid=prevA1210435: /* 4D CLUViz Work */2013-11-04T06:58:07Z<p><span class="autocomment">4D CLUViz Work</span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The next step after programming the 3D rotations was to attempt to animate the rotations in 4 dimensions to help give us a better understanding of how they work and hopefully provide us with some conclusive information on whether the rotations could be utilised for secure encryption. In order to represent the 4 dimensional rotations, the previous 3D program was used as the foundation however with several additions.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The next step after programming the 3D rotations was to attempt to animate the rotations in 4 dimensions to help give us a better understanding of how they work and hopefully provide us with some conclusive information on whether the rotations could be utilised for secure encryption. In order to represent the 4 dimensional rotations, the previous 3D program was used as the foundation however with several additions.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>An additional rotation axis was added for each Alice and Bob bringing the total number of rotation axes to four, as two rotation axes were needed to perform each rotation in 4 dimensions<del style="font-weight: bold; text-decoration: none;">. This is due to the rotations actually being 5D rotations embedded into a 4D space as mentioned in the [https://www.eleceng.adelaide.edu.au/personal/dabbott/wiki/index.php/Semester_B_Final_Report_2013_-_Secure_communications_without_key_exchange%3F_2013#4D_Rotations_and_5D_Rotations_in_4D 4D Analytical Section] of the final report</del>. As a result, two support diagrams were added to allow the user to alter the rotation angles of the new rotation axes. Also, as with the 3 dimensional visualisation, we wished to show the vector displacement between each pair of rotation axes during animation to show how it affects the difference in the initial and final message vectors. As a result, five more support diagrams were added to the right.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>An additional rotation axis was added for each Alice and Bob bringing the total number of rotation axes to four, as two rotation axes were needed to perform each rotation in 4 dimensions. As a result, two support diagrams were added to allow the user to alter the rotation angles of the new rotation axes. Also, as with the 3 dimensional visualisation, we wished to show the vector displacement between each pair of rotation axes during animation to show how it affects the difference in the initial and final message vectors. As a result, five more support diagrams were added to the right.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In order to depict the 4th dimension for the initial and final message vectors, two spheres were added as shown in red and magenta. The magnitude of each sphere represented the e4 component of each the initial and final message vectors, with the remaining (e1, e2, e3) elements being represented by the 3D vector as in the previous program. Hence, it was programmed that the initial and final message would only equal when the vectors overlapped and the two corresponding spheres were of equal magnitude. However, as known from our other 4D GA work, the conditions for which the two independent 4D rotations can commute are vastly more complicated than we had originally anticipated and as such we ran into difficulty in making these rotations viable, valid and consistent with the theories behind them. We got to the point with our theoretical work that forced us to start looking into higher dimensions and as a result, the 4D visualisation became obsolete.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In order to depict the 4th dimension for the initial and final message vectors, two spheres were added as shown in red and magenta. The magnitude of each sphere represented the e4 component of each the initial and final message vectors, with the remaining (e1, e2, e3) elements being represented by the 3D vector as in the previous program. Hence, it was programmed that the initial and final message would only equal when the vectors overlapped and the two corresponding spheres were of equal magnitude. However, as known from our other 4D GA work, the conditions for which the two independent 4D rotations can commute are vastly more complicated than we had originally anticipated and as such we ran into difficulty in making these rotations viable, valid and consistent with the theories behind them. We got to the point with our theoretical work that forced us to start looking into higher dimensions and as a result, the 4D visualisation became obsolete.</div></td></tr>
</table>A1210435https://www.eleceng.adelaide.edu.au/personal/dabbott/wiki/index.php?title=CLUViz_Geometric_Algebra_Animation_Software&diff=12889&oldid=prevA1210435: /* Difficulties & Possible Extensions */2013-11-04T05:50:47Z<p><span class="autocomment">Difficulties & Possible Extensions</span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>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.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>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.</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Hypercube===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Hypercube===</div></td></tr>
</table>A1210435https://www.eleceng.adelaide.edu.au/personal/dabbott/wiki/index.php?title=CLUViz_Geometric_Algebra_Animation_Software&diff=12888&oldid=prevA1210435: /* Difficulties & Possible Extensions */2013-11-04T05:50:31Z<p><span class="autocomment">Difficulties & Possible Extensions</span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Image:hypercube.gif|thumb|3350px|left|Projection of a rotating tesseract.]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Image:hypercube.gif|thumb|3350px|left|Projection of a rotating tesseract.]]</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>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.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>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.</div></td></tr>
</table>A1210435https://www.eleceng.adelaide.edu.au/personal/dabbott/wiki/index.php?title=CLUViz_Geometric_Algebra_Animation_Software&diff=12887&oldid=prevA1210435: /* Difficulties & Possible Extensions */2013-11-04T05:50:23Z<p><span class="autocomment">Difficulties & Possible Extensions</span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Difficulties & Possible Extensions==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Difficulties & Possible Extensions==</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>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'. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>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'. </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Image:hypercube.gif|thumb|3350px|left|Projection of a rotating tesseract.]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Image:hypercube.gif|thumb|3350px|left|Projection of a rotating tesseract.]]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
</table>A1210435https://www.eleceng.adelaide.edu.au/personal/dabbott/wiki/index.php?title=CLUViz_Geometric_Algebra_Animation_Software&diff=12886&oldid=prevA1210435: /* Difficulties & Possible Extensions */2013-11-04T05:50:13Z<p><span class="autocomment">Difficulties & Possible Extensions</span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:20, 4 November 2013</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l43">Line 43:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Difficulties & Possible Extensions==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Difficulties & Possible Extensions==</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>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'. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>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'. </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Image:hypercube.gif|thumb|3350px|left|Projection of a rotating tesseract.]]</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>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.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>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.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">[[Image:hypercube.gif|thumb|3350px|left|Projection of a rotating tesseract.]]</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Hypercube===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Hypercube===</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>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''</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>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''</div></td></tr>
</table>A1210435https://www.eleceng.adelaide.edu.au/personal/dabbott/wiki/index.php?title=CLUViz_Geometric_Algebra_Animation_Software&diff=12885&oldid=prevA1210435: /* Difficulties & Possible Extensions */2013-11-04T05:49:57Z<p><span class="autocomment">Difficulties & Possible Extensions</span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:19, 4 November 2013</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Difficulties & Possible Extensions==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Difficulties & Possible Extensions==</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>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'. 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.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>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'. </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>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.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Image:hypercube.gif|thumb|3350px|left|Projection of a rotating tesseract.]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Image:hypercube.gif|thumb|3350px|left|Projection of a rotating tesseract.]]</div></td></tr>
</table>A1210435https://www.eleceng.adelaide.edu.au/personal/dabbott/wiki/index.php?title=CLUViz_Geometric_Algebra_Animation_Software&diff=12874&oldid=prevA1210435: /* See also */2013-11-04T05:00:55Z<p><span class="autocomment">See also</span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 14:30, 4 November 2013</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l65">Line 65:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [[Geometric_algebra|Geometric Algebra]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [[Geometric_algebra|Geometric Algebra]]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [[CLUViz Geometric Algebra Animation Software]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [[CLUViz Geometric Algebra Animation Software]]</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [[Secure communications without key exchange]] (main page)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [[Secure communications without key exchange]] (main page)</div></td></tr>
</table>A1210435https://www.eleceng.adelaide.edu.au/personal/dabbott/wiki/index.php?title=CLUViz_Geometric_Algebra_Animation_Software&diff=12801&oldid=prevA1210435: /* Current Code */2013-10-29T07:19:28Z<p><span class="autocomment">Current Code</span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 16:49, 29 October 2013</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l54">Line 54:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The final version of the code is included here: [[Media:3DAnimation.rar|3D Visualisation]] & [[Media:4DAnimation.rar|4D Visualisation]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The final version of the code is included here: [[Media:3DAnimation.rar|3D Visualisation]] & [[Media:4DAnimation.rar|4D Visualisation]]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>After having gotten some background information on 3D & 4D rotations from the reports and/or independent wiki pages, we highly encourage you to follow the link above to download the CLUViz software and our code to have a play around. Naturally, it's recommended that you start with the 3D animation and then move on to the 4D animation if you wish to grasp how 4D rotations could look. All the code if sufficiently commented and it should be relatively easy to navigate throughout the code if you wish to edit elements for whatever reason. </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>After having gotten some background information on 3D & 4D rotations from the reports and/or independent wiki pages, we highly encourage you to follow the link above to download the CLUViz software and our code to have a play around. Naturally, it's recommended that you start with the 3D animation and then move on to the 4D animation if you wish to grasp how 4D rotations could look. All the code if sufficiently commented and it should be relatively easy to navigate throughout the code if you wish to edit elements for whatever reason.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==See also==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==See also==</div></td></tr>
</table>A1210435https://www.eleceng.adelaide.edu.au/personal/dabbott/wiki/index.php?title=CLUViz_Geometric_Algebra_Animation_Software&diff=12800&oldid=prevA1210435 at 07:19, 29 October 20132013-10-29T07:19:12Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 16:49, 29 October 2013</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>As a part of our project, we've developed a series of images and animations using CLUViz to visually demonstrate how an encryption system based on rotations in 3-dimensions works in accordance with the Double-Padlock Protocol. CLUViz is a freely available software tool for 3D visualizations and scientific calculations that was conceived and written by Dr. Christian Perwass. CLUCalc interprets a script language called ‘CLUScript’, which has been designed to make mathematical calculations and visualisations very intuitive.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>As a part of our project, we've developed a series of images and animations using CLUViz to visually demonstrate how an encryption system based on rotations in 3-dimensions works in accordance with the Double-Padlock Protocol. CLUViz is a freely available software tool for 3D visualizations and scientific calculations that was conceived and written by Dr. Christian Perwass. CLUCalc interprets a script language called ‘CLUScript’, which has been designed to make mathematical calculations and visualisations very intuitive.</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Follow the link http://www.clucalc.info/ for more information regarding CLUCalc and http://www.raytrix.de/tl_files/downloads/CLUVizSetup.exe to download the software.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Follow the link http://www.clucalc.info/ for more information regarding CLUCalc and http://www.raytrix.de/tl_files/downloads/CLUVizSetup.exe to download the software.</div></td></tr>
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