Le 01/08/2016 à 12:19, clipka a écrit :
> Am 01.08.2016 um 01:51 schrieb Christian Froeschlin:
>> On 24.07.2016 4:13, clipka wrote:
>>
>>> What's been bothering me about POV-Ray's Bezier patches is that we don't
>>> have some kind of bezier mesh to support non-union CSG. Do you think you
>>> can throw together a nurbs mesh primitive?
>>
>> From what I remember of B-splines I think a B-spline patch
>> of degree d is essentially the same thing as a mesh of bezier
>> patches of degree d (with the smoothest possible transition
>> where the bezier control blocks are joined).
>>
>> So I'm not sure an extra mesh object is needed since you can simply
>> increase the number of control points. Or maybe I misunderstood?
> 
> You misunderstood indeed. While B-splines and Bezier splines are indeed
> equivalent (in the sense that whatever you can model with one you can
> also model with the other), this is not true for NURBS (non-uniform
> rational B-splines), as they are a more general superset of B-splines.
> As such they obviously need more parameters than plain vanilla B-splines
> or Bezier splines, and are also more difficult to compute.
> 
> It is therefore reasonable to presume that a dedicated Bezier patch mesh
> would be more performant than a NURBS patch mesh.
> 

for the time being, what I called "nurbs" object is actually a
non-uniform-rational-bezier :
* the order of the rational B-spline is the number of control point (it's an implict
value), so actually that a ration Bezier.

It is non-uniform before the also implicit (hard-coded) knot vectors are not uniform
(because bezier are clamped: passing through the first and last control point)
(knot vector would be something along 0{order), 1/n, 2/n, ..., n-1/n, 1{order} , not
something uniform as 0, 1, 2, ... m-1, m )
It is rational because there is a weight on control points.

Sorry for the false joy, maybe I should rename it to "nurbz" (Non Uniform Rational
BeZier) and try to provide a real nurbs.
But for the time being, all I could provide easily for nurbs would be a function to
compute the vertex for any u,v value. Even that would apply to only the clamped on
each side of nurbs. (and "easily" is not really the right term)
(nurbs can be clamped, opened or closed; and while "closed" on a direction apply to
both ends, the alternative clamped or opened could be different for each extremity (or
they can be the same).
I cannot so far even compute the normal at a u,v value for a nurbs.
And having a solver for ray intersection seems even more difficult.

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