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Maths - How diagrams were generated

These graphs were drawn by an open source 3D program called Blender, the meshes were generated by a Blender python script as described on this page. The scripting mechanism for blender is described here.

euclidean metric

<BAG version="0.0.1">
<Reference>Cartesian</Reference>
<Coords min="-5.0" max="5.0" zero="-5.0" line="0.00999999977648" />
<CamPos x="10.0" y="3.0" z="3.0" />
<CamDir x="-2.0" y="3.0" z="-1.29999995232" />
<Label>
multiply
</Label>
<ParU Min="-2.0" Max="2.0">
16
</ParU>
<ParV Min="-2.0" Max="2.0">
24
</ParV>
<Curve>
0
</Curve>
<Surface Wireframe="1" Smooth="0" alpha="0.9" emit="0.2" glow="0.2">
<matCol r="0.5" g="0.5" b="0.5" />
<fn1>
u
</fn1>
<fn2>
v
</fn2>
<fn3>
sqrt(u*u+v*v)-5
</fn3>
</Surface>
<Surface Wireframe="0" Smooth="0" alpha="0.9" emit="0.2" glow="0.2">
<matCol r="0.40000000596" g="0.40000000596" b="0.40000000596" />
<fn1>
u
</fn1>
<fn2>
v
</fn2>
<fn3>
sqrt(u*u+v*v)-5
</fn3>
</Surface>
</BAG>

minkowski metric

<BAG version="0.0.1">
<Reference>Cartesian</Reference>
<Coords min="-5.0" max="5.0" zero="-5.0" line="0.00999999977648" />
<Offset x="0.0" y="0.0" z="-5.0" />
<CamPos x="10.0" y="3.0" z="3.0" />
<CamDir x="-2.0" y="3.0" z="-1.29999995232" />
<Label>
multiply
</Label>
<complex in="0" out="1" />
<ParU Min="-2.0" Max="2.0">
16
</ParU>
<ParV Min="-2.0" Max="2.0">
24
</ParV>
<Surface m1="4" m2="5" m3="6" m4="7">
<fn1>
u
</fn1>
<fn2>
v
</fn2>
<fn3>
sqrt(u*u-v*v)
</fn3>
</Surface>
<Material Wireframe="0" Smooth="1" alpha="0.8" emit="0.2" glow="0.2">
<matCol r="0.5" g="0.0" b="0.0" />
</Material>
<Material Wireframe="1" Smooth="0" alpha="0.9" emit="0.2" glow="0.2">
<matCol r="0.0" g="0.0" b="0.0" />
</Material>
<Material Wireframe="0" Smooth="1" alpha="0.8" emit="0.0" glow="0.0">
<matCol r="0.0" g="0.5" b="0.0" />
</Material>
<Material Wireframe="1" Smooth="0" alpha="0.9" emit="0.4" glow="0.3">
<matCol r="0.0" g="0.0" b="0.0" />
</Material>
</BAG>

null vectors

<BAG version="0.0.1">
<Reference>Cartesian</Reference>
<Coords min="-5.0" max="5.0" zero="-5.0" line="0.00999999977648" />
<Offset x="0.0" y="0.0" z="-5.0" />
<CamPos x="5.0" y="5.0" z="3.0" />
<CamDir x="-2.3900001049" y="2.96000003815" z="-1.11000001431" />
<Label>
multiply
</Label>
<complex in="0" out="1" />
<ParU Min="-2.0" Max="2.0">
16
</ParU>
<ParV Min="-2.0" Max="2.0">
24
</ParV>
<Surface m1="4" m2="5" m3="6" m4="7">
<fn1>
(u+v)/2
</fn1>
<fn2>
(u-v)/2
</fn2>
<fn3>
sqrt(u*u-v*v)
</fn3>
</Surface>
<Material Wireframe="0" Smooth="1" alpha="0.899999976158" emit="0.20000000298" glow="0.0">
<matCol r="0.5" g="0.0" b="0.0" />
</Material>
<Material Wireframe="1" Smooth="0" alpha="0.9" emit="0.2" glow="0.2">
<matCol r="0.0" g="0.0" b="0.0" />
</Material>
<Material Wireframe="0" Smooth="1" alpha="0.899999976158" emit="0.20000000298" glow="0.0">
<matCol r="0.0" g="0.5" b="0.0" />
</Material>
<Material Wireframe="1" Smooth="0" alpha="0.9" emit="0.4" glow="0.3">
<matCol r="0.0" g="0.0" b="0.0" />
</Material>
</BAG>


metadata block
see also:
Correspondence about this page

Book Shop - Further reading.

Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.

cover Roger Penrose - The Road to Reality: Partly a 'popular science' book as it tries to minimise the number of equations but it still has lots of interesting results that its difficult to find elsewhere.

Commercial Software Shop

Where I can, I have put links to Amazon for commercial software, not directly related to the software project, but related to the subject being discussed, click on the appropriate country flag to get more details of the software or to buy it from them.

 

Can you help?

Please send me any improvements to here. I would appreciate ideas to make the pages more useful including error correction, ideas for new pages, improvements to wording. It helps if you quote the full URL of the page.

 

progam

I am working on a project which uses these principles, if you would like to help me with this you are welcome to join in, here:

http://sourceforge.net/projects/mjbworld/

This site may have errors. Don't use for critical systems.

Copyright (c) 1998-2008 Martin John Baker - All rights reserved - privacy policy.