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- is used to place the spheres in this image.
A NURBS surface is a made with a bivariate function.
I.e. the value of the functions varies according
to 2 variables; e.g. u and v
(A curve is a univariate function. It's value
varies along with a single variable; e.g. t)
The value of a trivariate function varies along with
3 variables; e.g. u, v and w or x, y and z
So a trivariate function can be used to build solid
shapes in 3D (that has a volume; like we do with
isosurfaces).
The image enclosed shows a quick try at doing this
with a trivariate NURBS function that controls
the positions of spheres in a 3D grid. (The tone
range in the image is adjusted after rendering.)
But trivariates can also be used to control other
things, like e.g. density, pigments, light,
directions of movement/acceleration, refraction
index, temperature, humidity, vector fields
(gradients) and so on...
Later I'll try to find time to show how trivariate
B-splines can be used to do a kind of 3D morphing
of shapes made from meshes.
I also hope that POV-Ray will render fast enough
to calculate some interesting isosurfaces made
with (simple) trivariate B-splines.
Higher dimensional multivariate B-spline functions
are interesting too, but I fear that the slow
speed of POV's parsing will prevent us from
exploring the possibilities that they provide.
Tor Olav
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Download 'trivariates05_.jpg' (100 KB)
Preview of image 'trivariates05_.jpg'
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