Projective Space Example

The example on this page attempts to show, not just how to create an image in FriCAS but also how to use it with other programs.

 I wanted to make the image on the right to illustrate the topology of projective space discussed on this page. We can use FriCAS to generate a parametric surface. In this case, for all x,y then z=x*y We can do this by using the following SPAD code:
 This code generates the 3D surface and also a 2D grid which we can use to texture the surface. ```)expose SCartesian )expose SArgand )expose SConformal )expose SceneIFS )expose SceneNamedPoints )expose STransform )expose SBoundary )expose ExportXml DF ==> DoubleFloat PT ==> SCartesian(3) xyfn(x:DF,y:DF):DF == x*y view := boxBoundary(sipnt(0,-500)\$PT,sipnt(1200,500)\$PT) sc := createSceneRoot(view)\$Scene(PT) tr2 := addSceneTransform(sc,identity()\$STransform(PT))\$Scene(PT) gd := addPlot2Din3D(tr2,xyfn,-1..1,-1..1,49)\$Scene(PT) writeX3d(sc,"projectiveSpace.x3d") PT ==> SArgand view2 := boxBoundary(sipnt(0,-500)\$PT,sipnt(1200,500)\$PT) sc := createSceneRoot(view2)\$Scene(PT) gd := addSceneGrid(sc,view2)\$Scene(PT) writeSvg(sc,"grid.svg")```

First we use a program called Inkscape to convert the grid from a SVG file to a PNG file. (that is convert from a vector format to a raster format)

In Inkscape

Start Inkscape

open grid.svg

export it as grid.png

We now import this into Blender and do the following:

In Blender

 Start blender and remove default cube select camera view import projectiveSpace.x3d file rotate shape so we can see the corners starting to move together. Now select the object and add material to it remove spectial effects select material and add texture create new image and animation open (not new) file: grid.png in Render tab Set alpha channel Render

Further Information

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.

 Axiom Volume 1: Tutorial. Documentation is freely availible from: http://www.axiom-developer.org/axiom-website/documentation.html

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

Copyright (c) 1998-2018 Martin John Baker - All rights reserved - privacy policy.