Control Distribution of Points within Boundary

I'm looking for a way to create an uneven distribution of points within a boundary. In this case the boundary is a triangle. I want more points toward the corners of the triangle and fewer points toward the center.

Even though the density of the points will vary throughout the area within the triangle, I'm looking for a nice and even transition between the dense corner areas and the sparse central area.

I have made several unsuccessful attempts at this, where the logic involves offsetting the points of a uniform grid using an attractor point. However, one of the problems with that approach, is that the points towards the edges get pushed beyond the boundary. I need the points to stay within the boundary at all times.

Thanks everybody

Replies to This Discussion

Permalink Reply by Hannes Löschke on January 14, 2014 at 1:54am

Do you want it to be a regular or irregular distribution?

For irregular put some points inside the triangle with pop3d. Then use the corners as attractor points to displace the points towards the closest corner.

Permalink Reply by Bret Vanderhyden on January 21, 2014 at 5:51pm

Hi Hannes -- your method works well, thanks for the tip.

-Bret

Permalink Reply by Nik Willmore on June 8, 2014 at 3:40pm

Regular seems to be the hard part. How to do it regular then, like this?

Permalink Reply by Bret Vanderhyden on June 9, 2014 at 6:53am

yes, that is awesome.

Permalink Reply by David Rutten on June 9, 2014 at 11:52am

I'm sure Daniel (I think Daniel Piker made that original image) did something incredibly clever to get that result. Here's a way to kinda sorta get the same result:

David Rutten

david@mcneel.com

Attachments:

regularmesh.gh, 15 KB

Permalink Reply by Nik Willmore on June 12, 2014 at 9:15am

Thanks. That's kind of eccentric. Let's see...it relies on mesh relaxation and its ability to skip naked vertices, meaning the outside ones. It starts by dividing a border curve into points, also fills the interior with points, and then...uh...I'll study it further later. It's not as regular (nearly equilateral) as I imagine is possible, perhaps using physical forces so the points repel each other with there force being determined by distance from the boundary.

What I'm also interested in eventually is that this could be converted into a relief that amounts to the sort of puffing that Delcam Artcam or RhinoEmboss does so well, by adding Z value heights to each point according to the area of of mesh faces around each point or the length of lines around them.

Permalink Reply by Daniel Piker on June 12, 2014 at 9:17am

Hi Nik - did you see this update?

http://www.grasshopper3d.com/profiles/blogs/meshmachine-update

Permalink Reply by Bret Vanderhyden on June 12, 2014 at 9:19am

Very cool. Thanks for sharing Daniel. Can't wait to try it out.

Permalink Reply by Nik Willmore on June 12, 2014 at 9:28am

YOU DID IT!!! This is perfect. Just perfect. My bit of nagging paid off. Big time. With this I can really start playing with meshes that aren't so damn ugly or overly uniform, both artistically and mathematically. Though I don't here have the option of setting a specific fall off curve of size versus distance, I can do that with height values myself, based on inputting the circle or face area and rescaling unevenly as I desire.

Permalink Reply by Sergio Roa on May 17, 2016 at 9:17pm