Fixed area polygon

Replies to This Discussion

Permalink Reply by djordje on January 31, 2013 at 3:38pm

Hi Jon,

Are sides of your pentagon suppose to be equal or not?

Permalink Reply by jon kontuly on January 31, 2013 at 3:40pm

Nope, it does not have to be a regular polygon ie a pentagon.

Permalink Reply by djordje on January 31, 2013 at 5:22pm

This looks like an ideal job for Galapagos. Or even Octopus. The second one would probably give you a couple of different choices, but I do not own a Rhino 5 so can not test it (Octopus currently works on Rhino 5 only).

Here is the Galapagos result:

To start the calculation process, open the attached pentagon.gh file, and double click on pink component Galapagos (far right). In "Solvers" tab, choose "Start Solver", and wait a couple of minutes/seconds. When it stops, click on "Ok" in the lower right corner.

Attachments:

• pentagon.gh, 11 KB

Permalink Reply by jon kontuly on February 1, 2013 at 7:40am

Thanks djordje. I am still trying to understand how the grasshopper setup works. I noticed that no matter how I change the sliders the solver always seems to find almost the same shape. I guess that's because there is one optimal solution? Ideally I would like to find a bunch of polygons that come close to these requirements. I will try stopping the solver earlier to see if I get something that satisfies the requirements but may not be the optimal solution. If you get a chance I would love an explanation as to how this works. Until then I will try and reverse engineer it myself. Thanks again.

Permalink Reply by jon kontuly on February 1, 2013 at 8:31am

djordje, I believe I now understand how you set this up and I have to say it is genius. Thanks. I thought that Galapagos might be the way to go for this problem but I could not figure out how to deal with more than one requirement. The way that you set this up has already allowed me to add more requirements.

The only question I have is why the radius slider goes between 0 and 120 and not 0 and 60?

Permalink Reply by djordje on February 1, 2013 at 9:06am

Thank you for the kinds words Jon.
Thank David Rutten, he created Grasshopper and Galapagos.

Getting diverse combinations of your shape could probably be achieved using Octopus. instead of Galapagos:
Try the same definition with Octopus solver instead of Galapagos.
You will need Rhino 5 instead of Rhino 4.

Again, double click on the pink (far right) Octopus solver component, and in the far upper corner choose "Start". When the calculation process ends, you will see some black "balls". Each of them represents a solution. Each generation has a few (or none) number of solutions. You can change the generation by using the slider at the bottom left corner. What you need to do is to left-click on a "ball" which is as closer as possible to the coordinate beginning, and choose "Reinstate solution". Slide through the number of generations and search for the another appropriate solution (ball). Bear in mind that the fact that the solution is very close to the coordinate beginning does not mean it is closer to 0,0 point. This depends on the red value written on each of two axis.


And yes, you are right - I made a mistake - it should be 60, instead of 120, as circle inputs the radius value, not diameter.

Attachments:

• pentagon2.gh, 12 KB

Permalink Reply by jon kontuly on February 1, 2013 at 9:42am

I will definitely give Octopus a try. I am also going to try and see if I can get rid of the implicit requirement that all of the vertices of the polygon lie on a circle.

Permalink Reply by jon kontuly on February 5, 2013 at 11:05am

Djordje, I manage to get rid of the requirement that all of the vertices lie on a circle. Given 5 points the first part of the definition creates a non self-intersecting polygon.

thought I would share in case you were interested. thanks again.

Attachments:

• create non intersecting polygon with constraints.gh, 18 KB