Hi,

Does anyone know the formula to calculate the area of a rectangle on an irregular surface? By irregular I mean a surface that's has curvature with various amounts of deformation.

I found something on the web, but it seemed way overcomplicated (maybe the problem is more involved than I imagine).


–Mark

Probably not what you are looking for - but…

you might be able to get a decent result by using the measure SOP - on a triangulated (divide sop more then likely) version the rectangle.

Summing all the individual “areas” attributes will approximate the total area.

Obviously milage will vary with how precise you wish to get.

Cheers,

G

If you do go down that route it's worth remembering that attribute promote will let you sum up values like this.

Simon
If you do go down that route it's worth remembering that attribute promote will let you sum up values like this.

Hmmm … this spurs some inspiration for another problem …

We (a co-worker and I) found what looks like the right formula, except it's an awfully long algorithm and we couldn't find any supporting documentation … but it appears to work, which I guess is all that matters.


–Mark

Just out of curiousity, is there a chance that you're dealing with a NURBS surface?!

If that's the case, you might want to look at the ratio of the rectangle to the UV domain - scaled by the computed surface area for a clue.

ie: ((s2-s1) * (t2-t1)) [which will always be < 1 on a normalized UV range] * computed surface area.

Or maybe i'm still sleeping… :wink:

Cheers,

G

keyframe
ie: ((s2-s1) * (t2-t1)) [which will always be < 1 on a normalized UV range] * computed surface area.

Well, actually it's for another application (not Houdini) that we use to map data signals of the elements from the gamma ray spectrometer which is orbiting Mars … however, I will need something like this as well but not as accurate as what's needed for this other application. I'm thinking though that the Measure SOP might be exactly what I'll need for when I do similar tasks in Houdini. And yes, the geometry I'd be measuring would be NURBS surfaces.

Thanks for the ideas guys!


–Mark

This is what we're using, as I said, it seems a bit complicated, but I'm not a mathematician …

http://www.lpl.arizona.edu/~umpire/work/spheroid_area.html [lpl.arizona.edu]

Yikes!


–Mark

Ohhhh…you want a *planet*, well why didn't you *say* so? :shock:

Yah, I've heard this simple-sounding math puzzle can actually be quite the challenge depending on how much accuracy you need.

Gack.

J.C.

JColdrick
Ohhhh…you want a *planet*, well why didn't you *say* so? :shock:

ooooppps! :roll: Actually I thought it wouldn't make a difference, but hey, what do I know? I'm still trying get the burned out neurons that used to dream about trigonometry at night (no kidding) to fire again! So many years ago … darn it, where's my Geritol … :-)

Have an excellent weekend John!


–Mark