Interpolating a vector

[Olumide]

Hello -

I've got a triangle whose vertices possess a special metric/vector T
i.e. the vertexes V1, V2, and V3 of the triangle possess the metric/
vectors: T1, T2 and T3 respectively. I would like to interpolate the
value of this metric at any point on the surface of this triangle. The
approach I'm currently investigating interpolates each component of
each T[i] using barycentric coordinates using formulate derived here:
http://www.blackpawn.com/texts/pointinpoly/default.html
(If it matters, the metric in question is the principal tangent/
direction computed by the following function/library http://tinyurl.com/5hwayn
)

Is this the recommended approach to solving the problem? I know
barycentric coordinates can be used to interpolate scalars but can
they be used to interpolate vectors?

Thanks,

- Olumide

[jindra]

On May 21, 4:21 am, Olumide <50...@web.de> wrote:
> Hello -
>
> I've got a triangle whose vertices possess a special metric/vector T
> i.e. the vertexes V1, V2, and V3 of the triangle possess the metric/
> vectors: T1, T2 and T3 respectively. I would like to interpolate the
> value of this metric at any point on the surface of this triangle. The
> approach I'm currently investigating interpolates each component of
> each T[i] using barycentric coordinates using formulate derived here:http://www.blackpawn.com/texts/pointinpoly/default.html
> (If it matters, the metric in question is the principal tangent/

> direction computed by the following function/libraryhttp://tinyurl.com/5hwayn

> )
>
> Is this the recommended approach to solving the problem? I know
> barycentric coordinates can be used to interpolate scalars but can
> they be used to interpolate vectors?
>
> Thanks,
>
> - Olumide

Hi, barycentric coordinates works fine for scalar values. It may work
for vector quantities as well but it strongly depends what kind of
special metric/tensor are you interpolating. Those principal
directions, they are perpendicular to one another, aren't they? If so,
then I'm afraid that the "per component interpolation" would destroy
the orthogonality of interpolated directions.
Perhaps, the paper http://herakles.zcu.cz/publications/view.php?ID=137
might help you. It deals with a temporal interpolation of normal
vectors but some ideas can be used for spatial interpolation as well.

jindra