MOVRAY theory :

Mathematics of Vision Raytracing theory is a pure mathematical theory,based upon an outstanding pioneering work of the author and made for the first time known to the large community of mathematicians,engeneers and scientists after a while of some years work. The theory as its name mentions it is a revolutionary combination of Computer Graphics Programming and Mathematical Analysis. As any new theory in a scientific field,Movray theory or Mathvision Raytracing theory is at its beginning level,which we may call paleontologic era.Therefore needs contribution of Talented people who feel some attraction and interest towards it,to enrich it and produce beautiful results.

What the theory is about :

Movray theory or Mathvision which we may call Mathworld.But “Mathworld the theory” not to be confused with Eric Wiessenstein’s “Mathworld” at Wolfram.Inc which is an encyclopedia of mathematics. It is to produce a computer graphic;in other words a computer image in which all the objects in the picture are pure Mathematical Equations.There is no modeling neither design but only mathematical equations.The objects are 3D Mathematical Surfaces produced with their equations either cartesian,parametric,spherical or cylindrical coordinates.See above the Golden Apple and the Mathematical Apple.These are pure differential geometric Manifolds. Because of its equations based Techniques,no software can do this but only raytracing methods.These latter contain mathematical Functions.Amog these the POVRAY software which I am using becomes therefore a Masterpiece,because of its realism in Raytracing principles and scientific visualisation.

The Principles :

Mathvision Raytracing is to produce a “Mathworld”.A picture,which is a world,composed of objects obtained only through mathematical equations. The object are 2D and 3D Surfaces obtained as mentionned before through,parametric equations,spherical coordinates,cylindrical or fractals. According to our experience of plotting 3D mathematical surfaces,we have three categories of worlds.

(a) AB-world :Abstract world

When you start plotting 3D surfaces,or go into the numerous examples on the internet you notice that the shape or your object has no particular interest but only an abstract surface.In this way any surface belongs to the AB-world even your first plot! However by experience only the best are collected. AB-world should be composed of abstract objects having some interest for the mathematical Community and designers.

(b) VR-world :Virtual Reality world

Virtual world is composed of objects possessing characteritics of virtual reality. between the abstract and the next Real world. The equations behind these objects are usually important for their mathematical research nature,as the Klein bottle and the Mobius strip.Some VR-world objects may become very complex and evoluted,therefore may interest mathematicians,scientists,designers architects,and artists.

(c) AI-world :Artificial intelligency world

The artificial intelligency object is quite a complex shape having the characteristics of a real object existing in Nature! There exists already in the 3D plotting of surfaces some very simple forms as the bottle and the vase,obtained by revolving a curve (Revolution surface). AI-world objects are the most wanted,Their complexity goes sometimes beyond imagination. To produce them needs some real work.As an example,the Golden and Mathematical Apples above are pure AI-world objects. I think that at this stage you already have a good idea about Movray theory.I invite you to go to the Galleries,AI-codes,VR-codes,AB-codes and Mathvision-theorems above to watch some wonderful Movray results.

The Code :

Once you have your Movrayworld or Mathworld, lets say for simplicity one object,the mathematical equations for plotting it are called the Code of the object.After some attempts you classify it as an AI-code,VR-code or AB-code. The AI-codes and VR-codes are the most important according to the difficulty of founding and realising them.This involves real mathematical knowledge of manifolds behaviour and mathematical equations modeling. They have diverses applications in many fields of studies.See the applications of Movray theory below.

The theory :

How mathvision raytracing is a theory? Imagine,you have produced a VR-code or an AI-code,or perhaps something more difficult as a mathworld-code,which is a perfect computer graphic in its beauty,symmetry and complexity composed of combinations of several objects belonging to AI-codes and VR-codes,perhaps only AI-codes (see the gallery Mathvision-theorems at the link above). Once you expose your work,nobody will believe you that it is a Movray realisation,but only A Povray raytracing,or other software modeling graphics.Even if it is professionally well done and classified first in the IRTC competition. To prove mathematically that it is a mathvision or moray graphic,you have two choices:

(1) Either you give the equations or the codes which produce the graphic,in other words you make your codes Public domain or :

(2) Use 3D plotting softwares to plot the objects.These mathematical softwares use only Mathematical equations as;Maple,Mathematica or Matlab.

In this way according to the proofs mentionned in (1) and (2) you may say that you have a Movray theorem or a Mathvision theorem. The most wanted and important objects discovered in Movray theory as mentioned previously (AI-codes and VR-codes) are called Lemmas and Propositions,as in mathematics. It is with these lemmas and propositions that you can build a moray theorem(see Mathvision theorems gallery),which will bear your name.And perhaps obtain a medal or an award through astonishing work in Movray theory and codes search.This is a new era of human thinking and activity combining pure mathematics,computer graphics and codes.To be used in Scientific fields and applications.See uses and applications of Mathvision theory below.

Applications of Mathvision theory :

Mathematics (Analysis,ODE,PDE,Differential Geometry).
Artificial Intelligency,Cybernetics.
Life Sciences,Biology,Genetics.
Architecture ,Design and Arts.

Pioneering work and References :

(1) POVRAY software (Opensource) : Povray.org
(2) F.Loehmuller :for mathematics and Povray.
(3) Mike Williams : for mathematics and Povray,and work on AI-codes for Shells.
(4) Mike Kost : mathematics and Povray Tutorials.
(5) P.Bourke : for wonderful Supershape Formula producing VR-codes and AB-codes.

Bourke.P :
http://local.wasp.uwa.edu.au/~pbourke/
http://local.wasp.uwa.edu.au/~pbourke/rendering/representation/
http://local.wasp.uwa.edu.au/~pbourke/surfaces/supershape3d/
Coffman.A :
www.ipfw.edu/math/Coffman/steinersurface.html
Kost.M :
http://povray.tashcorp.net/tutorials/
http://povray.tashcorp.net/tutorials/dd_parametric_objects/
Isosurface Manual :
http://users.skynet.be/smellenbergh/iso_ind.html
Lohmueller.F :
www.f-lohmueller.de/index.htm
www.f-lohmueller.de/pov_tut/pov__eng.htm
www.f-lohmueller.de/homepage.htm
PovRay :
www.povray.org
Williams.M :
www.econym.demon.co.uk/isotut/index.htm
www.econym.demon.co.uk/isotut/shells.htm
www.econym.demon.co.uk/