Topology - Rectangle inside a curve

I was interested in creating a rectangle inside a curve

I found this interesting video which explains the issue

https://www.youtube.com/watch?v=AmgkSdhK4K8

then I tried to use grasshopper to do it, I had to use my permutation algorithm first

but when I needed to go into more precision, I needed to use Ander's Python sample. though, I used only 10 locations per point (4 points)

I still can't go to further precesion, even with Ander's fast tool as it needs about 1.8 Million of permutations

I kept the more precise option below, if someone has better computer, maybe can show me the result

If you have any corrections/recommendations or questions, please let me know

Attachments:

Topology 04 - Python4.gh, 60 KB

Replies to This Discussion

Permalink Reply by Mohamed Naeim on November 18, 2016 at 9:06am

I guess its the right time for a component for this function(mesh-self-intersection)

I tried intersection using contours (not complete yet)

but it's better to use your method

Permalink Reply by Laurent DELRIEU on November 18, 2016 at 3:23pm

I have done some improvement with mesh, as planned mesh/mesh intersection could give intersection on edges, so I have to filter that.

Cross reference (lower strict) to test all faces with all the other faces except itself

Point on curve is used to test if there is in intersection with edges. I exclude intersection on edge.

After that I put a list item to just choose one curve and move the rectangle with slider "point on curve".

The script is not robust because sometimes there are more or less intersection points with the circle, so the polygon is not an approximative rectangle. Here I include something not too bad. It shows that solution is on curves.

Attachments:

Inscribed rectangle proof v3.gh, 30 KB

Permalink Reply by Mohamed Naeim on November 19, 2016 at 3:08am

It's Clear and solved, Thank you

So it's the highest point of mesh intersection's curve that you used to create the centre of the circle, Is it coincidence? because it was the top point on circle case, isn't it?

Permalink Reply by Laurent DELRIEU on November 19, 2016 at 5:19am

All the centers are located on (red) curves after the "join curves" component. So there are an infinity of solutions. So I selected a curve with the slider, then I choose a point on the curve. Point could be high or low depending on the shape of the curve.

Move the sliders to see all the possibilities or supress one slider and change point on curve by range (I think I put thes components) to see all the possibilities.

Permalink Reply by Laurent DELRIEU on November 19, 2016 at 5:35am