Yeah, Tony, I agree with you completely, and I think it's a great
direction for DX & IHV's (that is, adding features that improve
the gfx without any real work from developers).
As for G1 vs. C1, G1 means that the tangents of the two connecting
patches are identical. C1 means that the parametric velocities of
the two connecting patches are identical. eg. if you had a particle
flying along a bezier curve at a constant speed in parametric
coordinates, then it would keep going the same direction at a G1
joint, but it would suddenly change speed (which it wouldn't do with
C1). G1 or G2 is really what we care about for graphics, C1 and C2
are unecessarily strong constraints.
At 12:15 PM 7/26/2000 -0700, you wrote:
>Refresh my memory, what's the difference between G1 and C1 continuity?
>
>Anyway, no matter. The key points about this technique are:
>
>1: It works with a lot of existing content, and gives surprisingly good
>results in many cases. Argue about the theoreticals all you like, but it
>*looks* pretty good.
>
>2: Since it's completely per-triangle, it's very friendly for hardware
>acceleration, which is why we're actually seeing hardware that does it.
>
>Sure, the more advanced subdivision surface techniques are the way to go in
>the long term, but as games developers pragmatism has a certain merit. If
>you can bolt this technique on late in the day to give your some of your
>existing artwork a better look on systems with appropriate hardware (or fast
>CPUs) with very little effort, then why not?
>
>Tony Cox - DirectX Luminary
>Windows Gaming Developer Relations Group
>http://msdn.microsoft.com/directx
>
>-----Original Message-----
>From: Charles Bloom [mailto:cb...@cb...]
>Sent: 26 July 2000 19:51
>To: gda...@li...
>Cc: cb...@su...
>Subject: [Algorithms] "N-Patches" (ATI/DX8 triangle bezier heuristic)
>
>
>
>Well, ATI's posted this on their website, so I guess we
>can talk about it freely now.
>
>http://www.ati.com/na/pages/resource_centre/dev_rel/devrel.html
>
>I don't give a hoot about the DX8 implementation of this, I
>want to talk about the algorithm of making a curved triangle
>only using its vertices and normals. I worked on this for
>a while, and decided it wasn't such a hot thing to do, because
>you can't even guarantee G1 continuity, so I abandonded
>it and moved on to butterfly subdivision, where continuity
>can be gauranteed.
>
>So, first of all, I remember hearing that this heuristic was
>invented by the wise Charles Loop. Is that correct? Are there
>any papers on this? I imagine there aren't, because it's a
>little trick that's not exactly up to Pixar quality standards.
>
>BTW you can see easily the problems with this scheme. Each
>triangle is made into a cubic Bezier Triangle. There are two
>new control points associated with each original vertex, and
>one in the middle. The two control points at each vertex
>are made to lie on the plane defined by the vertex and its
>normal. This gaurantees that the final Bezier surface is
>tangent to that same plane at that vertex, thereby giving
>you G1 (but actually not C1, if you want to be nit-picky)
>at that vertex. However, at every other point on the triangle,
>G1 is in trouble. Let me try to draw a little picture :
>
> a
> /|\
> / | \
> / | \
>b---c---d
>
>So we have two neighboring triangles, abc and acd.
>At the points a and c, they smoothly meet after Bezier
>tesselation. However, everywhere else along the edge ac
>they are not G1 in general, because the slope coming
>into the edge ac from triangle acd depends on the point
>d, and the slope coming in from triangle abc depends on
>the point b, so that you can't have G1 unless b and d
>are related in some very restrictive way.
>
>To get G1, you need to go to Quartic Bezier Triangles,
>and you need to find the control points of each triangle
>by looking at its neighbors. See, for example, Charles
>Loop's papers on finding the Quartic Bezier Triangles
>that are equivalent to Catmull-Clark subdivision (in
>Siggraph).
>
>I can see why hardware manufacturers like this scheme,
>because it is totally per-triangle (eg. you don't need
>any connectivity information). However, we are much
>smarter, and we know how are triangles are connected,
>so we can use the fast subdivision tesselation scheme
>of Kari Pulli (for example), or we can use Tom's
>subdivision + displacement + VIPM technique. (I'm
>imagining for the moment that I don't have a GPU that
>can do these Patches in hardware, so I would have to
>implement them in software, obviously they are cool/free
>when the hardware does them for you).
>
>--------------------------------------
>Charles Bloom www.cbloom.com
>
>_______________________________________________
>GDAlgorithms-list mailing list
>GDA...@li...
>http://lists.sourceforge.net/mailman/listinfo/gdalgorithms-list
>
>
--------------------------------------
Charles Bloom www.cbloom.com
|
