SmirkingMan
Aug21-08, 04:55 PM
I would like to make visualisations of calabi-yau manifolds, like this http://en.wikipedia.org/wiki/Calabi-Yau_manifold (the image on the right).
It would appear that POVRay (http://www.povray.org/) is the appropriate tool (I suspect, after much Googling, that the image was created with POVRay), but it can only handle 3 dimensions: here is the answer that a kind POVRay wizard gave me:
POVRay doesn't solve 6-dimensional polynomials of complex variables, so
you'll need to find a way to express a 3-dimensional cross section of
the manifold using only expressions that are available in POVRay.
If you end up with something that can be expressed as a polynomial of x,
y and z, then you can use the poly object.
If you end up with something that can be expressed as
F(x,y,z) = 0
where F is a function that uses only trig functions, hyperbolic trig
functions, logs, powers and simple arithmetic on real variables, then
you can use an isosurface.
If you end up with something that can be expressed as
x = Fx(u,v)
y = Fy(u,v)
z = Fy(u,v)
Then you can use a parametric object. Parametric objects can be
extremely slow, but you can use Ingo Janssen's Param.inc to approximate
them with smooth meshes.
Is there a way to express CY projections like this with a 3-dimensional formula?
My apologies if this question provokes only mirth because it's so stupid - my education stopped at a manifold being a part of an internal combustion engine :redface:.
Thanks in advance
Maurice
It would appear that POVRay (http://www.povray.org/) is the appropriate tool (I suspect, after much Googling, that the image was created with POVRay), but it can only handle 3 dimensions: here is the answer that a kind POVRay wizard gave me:
POVRay doesn't solve 6-dimensional polynomials of complex variables, so
you'll need to find a way to express a 3-dimensional cross section of
the manifold using only expressions that are available in POVRay.
If you end up with something that can be expressed as a polynomial of x,
y and z, then you can use the poly object.
If you end up with something that can be expressed as
F(x,y,z) = 0
where F is a function that uses only trig functions, hyperbolic trig
functions, logs, powers and simple arithmetic on real variables, then
you can use an isosurface.
If you end up with something that can be expressed as
x = Fx(u,v)
y = Fy(u,v)
z = Fy(u,v)
Then you can use a parametric object. Parametric objects can be
extremely slow, but you can use Ingo Janssen's Param.inc to approximate
them with smooth meshes.
Is there a way to express CY projections like this with a 3-dimensional formula?
My apologies if this question provokes only mirth because it's so stupid - my education stopped at a manifold being a part of an internal combustion engine :redface:.
Thanks in advance
Maurice