"Bald Eagle" <cre### [at] netscapenet> wrote:
> "Kenneth" <kdw### [at] gmailcom> wrote:
>
> > I am looking forward to seeing how you solve your too-smooth problem; I wish
> > that I could offer some suggestions. Some of this triangle stuff is outside my
> > knowledge.  *If* the triangle normals are all unit length, perhaps your summing
> > operation could be made to eliminate some of the identical normals on large flat
> > areas, which might reduce their contribution-- and make the smoothness less
> > smooth. (?)
>
> Triangles typically have a sinlge normal - a vector that is perpendicular to
> it's face (in either direction).
>
> The normal can be of any length.
>
> Typically, for lighting purposes, since the normal vector is used to calculate
> how light interacts with the surface, you want them of unit length.
>
> For smooth, or perturbed-surfaces, you will specify the normals of the vertices,
> and then POV-Ray will interpolate the normals across the surface, (and perhaps
> adding/multiplying by some pattern) to yield a smoothly changing surface.
>
> When dealing with a mesh of triangles that share common vertices and edges, one
> typically averages all of the normals that meet at a common vertex so that
> there's no sudden discontinuity in the way light reflects from the surface,
> appearing as lump, depressions, or creases.
>
> If you have two triangles oriented in different directions, if you multiply the
> length of the normal of one triangle, its contribution to how the triangles
> behave at that vertex will be greater.
>
> I think in order to accomplish what he's looking to do, the way that the
> triangles get interpolated would have to change, other wise I don't see how to
> maintain a common normal direction on one end, and non-linearly change apparent
> curvature at the other.
>
> It's not something I've played with in detail, but it sure seems like something
> that ought to be explored with test renders, diagrams, normal directions and
> lengths explicitly labeled, etc.
>
> Good instructional articles are what draw computer graphics students and
> hobbyists to any given site for the quality content.
>
> We should have that.
> Right on the home page.  Perhaps directing to a specific (new) sub-group titled
> "Articles".

Hi Bill

Here's two relevant articles:

"Weighted Vertex Normals"
http://www.bytehazard.com/articles/vertnorm.html

"On the computation of vertex normals"
http://meshlabstuff.blogspot.com/2009/04/on-computation-of-vertex-normals.html

- And then there's this paper, which delves deep into the topic:

"A comparison of algorithms for vertex normal computation"
Shuangshuang Jin, Robert R. Lewis, David West
The Visual Computer, 2005 - Springer

Vertex normal algorithms investigated in that article:

    Mean edge weighted by cotangents of subtended angles
    Mean weighted by angle
    Mean weighted by areas of adjacent triangles
    Mean weighted equally
    Mean weighted by edge length reciprocals
    Mean weighted by square root of edge length reciprocals
    Mean weighted by sine and edge length reciprocals

From the article's "Conclusions and future work":

Relatively speaking, except for trigonometrically parameterized surfaces,
"Mean weighted by angle" is most frequently a good choice. If speed is a
concern, however, "Mean weighted equally" holds up well in most cases.

--
Tor Olav
http://subcube.com
https://github.com/t-o-k

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