Le_Forgeron <lef### [at] freefr> wrote:
> Le 21/12/2010 14:20, Alex a écrit :
> > Hi,
> >
> > The "Mesh2" tool is great, but limited to triangles. If I want the same
> > functionality (e.g., defining the vertex normals, colors, etc. per vertex) for a
> > set of 'non-triangular' polygons (e.g., a mesh made up by rectangles) - which
> > tool can I use then?
>
> Let's just assume you have a polygon with a different colour for each
> vertex.
> If that polygon is a triangle, there is one obvious way to interpolate
> the colour of any point inside that triangle (or even on the border, and
> we could even get outside without problem if negative components are ok).
>
> If that polygon has more than 3 vertexes, there is no such easy
> interpolation.
> Let's take a square has a first polygon. Let's say you have a satisfying
> interpolation for all points inside that square.
> Now, let's add a fifth point to make the square look like a house (the
> fifth point is above the middle of the top segment of the square, making
> a roof).
> Now, should the value of the fifth point change any of the interpolated
> value in the previous square ?
>  - Yes and why ?
>  - No and why ?
> There is no universal solution.
>
> What is true for colour's interpolation is true also for other
> properties like normal and so on.
>
> On the same way, there is no obvious decomposition of polygon into
> triangle. Each way of decomposition would produce its own artefacts.
> (and it will always be the one someone does not want).
>
> Another issue with polygon: they must be planar... which can be a bit
> difficult when the computational limit on numbers comes into play (not
> all numbers can be stored with efficiency within computers, checking for
> planarity is easy, enforcing it is not).
>
> Oh, and there is also the issue of handling self-intersecting "polygon".
>
> So, so much no, and no solutions ?
>
> Well, you might keep using mesh2 and use your own decomposition in
> triangles of your polygons (assuming then YOUR choices and their effects).
> A classical decomposition is the Delaunay's one... but it's one amongst
> many.
>
>
>
> --
> A good Manager will take you
> through the forest, no mater what.
> A Leader will take time to climb on a
> Tree and say 'This is the wrong forest'.

Great - this has clarified a lot - many thanks!
Alexander

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