Cone brep with peak at origin and base at polar angle

I want to create a Grasshopper solution to making multiple (parametrically configured) annotated projected solid angle / steridian diagrams for research papers and books on radiometry related topics. You can just search Google Images for “projected solid angle” to see various examples. Here is one by Pat Hanrahan, which he said he did in Illustrator.

I first started with the cone primitive, and attempted to transform it into position and then rotate, but with the rotate point being at the base of the cone, I got confused and also wonder if that’s the best starting point. So then I set about creating a cone from a circle, line, and points, and have the cone exactly where I want it… but I’m so horrible at Grasshopper, I can’t figure out how to wrap that stuff into a surface.

Because I’m a Rhino/Grasshopper n00b, I always make things more complicated than they should be. I’ve spent half a day on this already, and I’m sure you awesome people on these forums can do what I’m trying to accomplish in 5 minutes or less :confused: Here is my Grasshopper attempt. It has a hemisphere and solid angle cone stubbed out and programmable, but the cone is incomplete.

.gh file
.3dm file

Can someone help me complete the cone surface in this setup?
And/or suggest/present a better solution to doing this?

Got the actual projection working… just need help turning these curves into breps now.

Hi Jdelrocco,
Attached is one way to do it.
psa (12.3 KB) (11.7 KB)

Below, showing only the hole left in the sphere with the cone removed: (15.5 KB) (17.0 KB)

…and with the vertical part.

psa (13.2 KB)

Ug, of course…

Thanks so much. Those are both better versions of my attempts, @Joseph_Oster @Drew. I’m going to use yours as a start @Drew, instead of my mess, and add various annotations to it.

Thank you again, guys!

@Joseph_Oster, your solution actually answers the post title correctly. I guess my intentions and post title were not aligned :confused: Sorry about that.

This another solution (10.9 KB)


Nice! I dig the use of the MD slider! Didn’t even think of that. Thank you.

Really appreciate the help. Already have some nice images to use…



I forgot to mention that I started a repository for such radiometry diagrams, if anyone is interested in contributing to it. I’ve already used some in research papers.