> (beginning of original message)

> Subject: Re: Using surface normals with on a triangulated surface

> Date: 1999/10/03

> Newsgroups: comp.graphics.algorithms

> > > This thread appears regularly--computing vertex normals for

> > > a triangle mesh. My proposal is not to average even with

> > > weights. Instead use the axis of the minimal cone containing

> > > the normals of the triangles sharing the vertex.

> > I said in one of the threads that angles at a vertex

> > is a good idea.

> I never said it was a bad idea :)

Thanks. (:

Quote:> > But I dont have any inkling of such a proof for Dave's proposal.

> > Can someone give me an insight of why this should be better than

> > angles...

> I also never "proved" anything, just stated my preference for

> constructing a normal. The minimal cone construction

> is a geometric construction on the sphere and, in a sense,

> computes a "median" of vectors. In that sense I view

> it as a natural algorithm to use and find it relatively easy

> to understand how the final vector relates to the original

> input. My objection to averaging normals, then unitizing, is

> that I find a linear combination of normals not intuitive in

> a geometric sense. Weighting by some quantity such

> as triangle area always seemed ad hoc.

Yes, Area seems to be adhoc. But Angles should be ok, IFF the

surface is well approximated by the triangles and the surface

is itself Smooth. Anyway in that case I think most heuristics

that we can think of will work.

Quote:> Also, I indicated that the minimal cone algorithm has

> problems when the cone angle is larger than pi radians.

I think that's a real bad case U are talking about. And

anything will have problems there.

Quote:> I can picture the ruffled surface when this happens.

> It is not clear to me what the averaging method tells me

> about the surface at the ruffled point.

Nothing can provably work out in this case I suppose.

Heuristics may work well in one case and fail in another.

Quote:> > And above all, Does anyone have a backing of an implementation to

> > what we are talking about, I mean has anyone seen how the results

> > are when one uses the angle and cone proposals..., and which one

> > is better when the surface is good, I mean say the cones Dave

> > is talking about are small.(Say pi/4 or pi/6) at every vertex,

> > And I apply both the proposals,

> > Which one gives me better results...

> Like any algorithms you want to compare, someone is going

> to have to quantify what "better" means. I am also not sure

> how to define what a "good surface" is.

This is a good question. What is better. I think I meant this

by its quantification: I take a surface, Densely approximate it

with a mesh.[Assume the surface is real good, I mean homeomorphic

to a ball + smooth, to begin with] And then I calculate the normals

at the sampled vertices using the ways we talked about. Which one

provably comes closest to the actual normal(2 the initial surface)

at the vertices.

Thanks and Best Regards,

--Piyush

--

Piyush Kumar

--

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