Put a "discrete" in front of that, and you're on to something.

*Put a "discrete" in front of that, and you're on to something.

LOL!  BTW Should we share the short cut with Replicand or let him work through this figure first?

I wasn't actually joking about the "discrete" part, although it makes for a nice pun (I think the word you were thinking of is spelled "discreet", though). Discrete differential geometry is a fairly new discipline which analyzes the properties of meshes and such not as approximations of continuous entities like classical differential geometry would, but as objects of their own. Google it and you will see.

There's been a bit of activity since I last looked. I'll go through these when I get home (boss is reading over the shoulder)

*Discrete differential geometry is a fairly new discipline which analyzes the properties of meshes and such not as approximations of continuous entities like classical differential geometry would, but as objects of their own. Google it and you will see.

Most excellent!  Thanks!

Replicand,  here's a short cut.  http://www.renderosity.com/mod/rrfilelock/download.php?fileid=37821&key=7229

 You guys suck! My calculus class doesn't start until the fall so I can't currently appreciate what you've presented here. I hate being "out-nerded".

The Gauss-Bonnet article briefly touches on manifolds and reminded me about the other manifold - as in non-manifold geometry - which the Maya manual says is bad for subdivision surfaces. (rolls eye) Jeez Rep, you can be so one track-minded sometimes. And how exactly can you use manifolds to aid in deformations?

The tensor article did nothing for me which means that it probably contains information leading to my next revolutionary breakthrough.

I can only visualize differential geometry one of two ways - either as discreet points on a NURBS surface or as dpdu / dpdv functions used to anti-alias shaders in a Renderman-compliant shader builder.

While the possibility that a solid theoretical understand will create optimized meshes, I can't yet see the connection between the two. Once I can, well, the universe will be in serious trouble (again).

replicand: In my experience, there's only so much information you can pick up and internalize at any given time. Also, theoretical knowledge is all fine, but one often needs a certain level of experience before being able to apply that knowledge in practice. So don't worry if we've been talking over your head a little bit.

I actually have a Ph.D. in Mathematics (I hate to brag ... wait, who am I kidding, I love to brag), but I tend to think about mesh geometry and topology in rather intuitive terms. It's nice to have all that background and to know that if I really needed to catch up on all the underlying nitty-gritty, I could. But in day-to-day modeling, I hardly ever think about things in terms of tangent plane or curvature tensors and such. :lol:

 My tone was supposed to rude but friendly, so forgive me if I've offended. The conversation - while enlightening - warped my brain a little, which is a good thing. PhD in math - I'm a little out of my league but flattered to have your expertise.

I'm in a bit of a funk right now, the mesh being part of the reason. I'm upset that it's not deforming the way that it should and after perusing subdivsionmodelling.com, I think I might start over again.

Argh! i feel like I'm running around in circles.

Quote -  My tone was supposed to rude but friendly, so forgive me if I've offended.

Rude but friendly is what I took it for. No offense taken.

*You guys suck! My calculus class doesn't start until the fall so I can't currently appreciate what you've presented here. I hate being "out-nerded".

Do you play Dungeons and Dragons?

No need to wait 'til fall.  http://www.math.cornell.edu/~hatcher/ 

*While the possibility that a solid theoretical understand will create optimized meshes, I can't yet see the connection between the two. Once I can, well, the universe will be in serious trouble (again).

What ever you do... do not... repeat do not... violate any of the theorems as this might lead to a rift in the space time continuum,  then we would all have to reset our clocks.

*I'm in a bit of a funk right now, the mesh being part of the reason. I'm upset that it's not deforming the way that it should and after perusing subdivsionmodelling.com, I think I might start over again.

Let's see what you have so far.

 I have nothing. I threw it away last night and decided to speed model one of my guitars. Maybe I'll try again later.

*I have nothing. I threw it away last night and decided to speed model one of my guitars. Maybe I'll try again later.

Don't give up.  You've got the talent and genius to see this through.

The head was all jacked up so I had to rebuild it. I shaped the torso a bit. I applied the most minimal controls possible to test deformations. Quickly rigged and spent about an hour painting weights (the advantage of <= 30k poly mesh, though it will not stand up to extreme poses at the moment).

It's crude yeah but I finally feel like I have a nearly production-ready mesh, with an eye towards major topological changes later.  

Lookin good!

2 for 1.  Good move.  Have you started your thin and heavy morphs?  Also,  have you uv mapped it?

BTW sims2 figures 4k,  next gen game figures 10k-20k,  poser figures 20k+

 This mesh is the basis from which other characters will be sculpted. For my pilot project I have already five of the six required characters.  The only real morphs will be facial expressions and pose space deformers. In contrast to the DAZ meshes, this one is meant to be specific on a per-character basis.

The original design goal (thread entitled: My First Humanoid) was to have a reasonably photo-realistic character which is light on system resources. So minimum morphs and light poly weight were key design elements.

Light poly weight has three advantages in my workflow: rendertime subdivision smoothing,  relatively fast rigging and fast SSS.  Rendertime subdivision smoothing doesn't require your base mesh to be heavy but it renders as smooth as a "real" subdivided mesh. Low number of polys also speeds (weight mapped based) rigging. Finally, Renderman calculates SSS by creating a 3d texture map derived from the mesh for radiance; using such a map on Vicky 3 required five hours per frame which I feel is unacceptable compared to the one minute is currently takes. So yes, most times low polys are undesirable but not always.

It was never my intention to distribute it. I would consider it if there was any interest. The male would need a different face though because I would not force the public to use mine :)

Oh yeah, I haven't UV mapped it yet but I have considerable practice. Also textures will be "air-brushed" rather than photographed. While I collect my last few pennies for Mudbox (which is far more intuitive than ZBrush and has features I'll never use) I will do hair and cloth tests.

Incase you're wondering,  mouth open/closed,  mouth smile/frown are the base facial expressions and phonemes for which the others are based off of.  Get a mirror,  too.

 There's an AWESOME rigging book from CGtoolkit.com. FACial rigging approach is a hybrid of joints and morphs. I can't wait to begin.

 We're probably not allowed to plug products but 3D Human Modeling and Animation by Peter Ratner (3rd edition) is my new favorite tome. More to follow....

*We're probably not allowed to plug products but 3D Human Modeling and Animation by Peter Ratner (3rd edition) is my new favorite tome. More to follow....

Got it sittin' on my desk.

When I used to run the shop here, I had no problem with folks posting about good experiences using educational material.  I don't think that's changed even though I'm not the mod anymore.