Polygon Gradient

Hey all,

for some time i treid to recreate a definition I took from >here<.

The definition was for an older Grasshopper version an did not work with the current release. As it seemed kind of bulky and complcated, I rebuild the logic right from the start and finally got it to work.

Still i got a problem remaining: The internal Grasshopper voronoi component does seeem to produce different results than the sa3-VB script.

While lofts line up with the script voronois. The GH polygons are not all lined up properly.

Anyone here can shed some light on the problem.

Regrads

Hannes

Attachments:

untitled.png, 165 KB
polygon smoothing_1.ghx, 456 KB

Replies to This Discussion

Permalink Reply by Yoann Mescam (Systemiq) on July 11, 2011 at 9:03am

The polylines (polygons) look like they are the same, but their vertices are not in the same order.

This reordering makes sure they do (see attached)

Attachments:

polygonsmoothing_1.ghx, 547 KB

Permalink Reply by Hannes Löschke on July 11, 2011 at 9:50am

Thanks a lot for the reordering.

The actual problem still persists: why is the loft unable to line up the curves? Why do we need the relatively complicated vertex reordering, should the curve alignment of the lofts do this?

... I mean, the smoothed curves are derived from the polygons. There is no obvious reason for any changes in vertex order.

Permalink Reply by Hannes Löschke on July 11, 2011 at 10:28am

Ok, i tried some variations.

To get the alignment working you actually don't need to sort. It helps to extract the Nurbs-CPs and create a polyline from the vertices. No more self interecting loft.

Problem with sorting or without: the polygons are not completely the same and produce different results. Even the sorted version is different from the script output.

In my opinion there should be no difference in outcome for closed curves. I mean, you smooth the rectangular section by increasing the nurbs order of a pipe you want to loft and the results depend on where the first edge is?... Is this a bug or a feature?

Attachments:

polygonsmoothing_2.ghx, 631 KB

Permalink Reply by Yoann Mescam (Systemiq) on July 11, 2011 at 1:17pm

Yeah, grasshopper loft doesnt work perfectly well, and you can not expect the align option to work as well as rhino loft.

If you sort both the script results and GH voronoi results, they should give same polygons, thus same lofts.

Permalink Reply by Hannes Löschke on July 11, 2011 at 3:11pm

Well the smoothed versions are basically the extracted control-points. So I can see no reason why the vertices should be reordered in the process.

Any polygon and its smoothed version should line up to begin with, but it doesn't.

Permalink Reply by Yoann Mescam (Systemiq) on July 11, 2011 at 5:29pm

The way you are smoothing the polygons is perhaps in cause: extracting the corner points then affecting them as control points of a nurbs curve is probably not really smoothing, especially if you set the nurbs order pretty high (like 8 in your example).

What I usually do to smooth curves is using Rebuild with degree 2 or 3 and number of control points for smoothing strength.

I dont master the nurbs at all, so i will just copy/paste wikipedia :

The order of a NURBS curve defines the number of nearby control points that influence any given point on the curve.

.......

The number of control points must be greater than or equal to the order of the curve.

In practice, cubic curves are the ones most commonly used. Fifth- and sixth-order curves are sometimes useful, especially for obtaining continuous higher order derivatives, but curves of higher orders are practically never used because they lead to internal numerical problems and tend to require disproportionately large calculation times.

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