# Creating ellipse around line in 3D space using PostGIS

In Postgis 2.1.1, I have a line in 3 dimensional space connecting two antenna points on the earth's surface.

Is it possible to create an ellipse around that line?

I have a formula to compute the radius of the ellipse at any given point along the bisecting line.

The ellipse is described as the Fresnel zone in this article: http://en.wikipedia.org/wiki/Fresnel_zone

I feel like I need some kind of 3D version of ST_PROJECT. ST_PROJECT allows me to plot an approximation of this ellipse on its side, but I need the ellipse to be oriented such that the bottom half lies between the bisecting line and the earth, below it.

It would be simple if I could form the bottom of the ellipse by modifying just the Z coordinate of points running along the bisecting line, but this isn't quite correct because one antenna is taller than the other, causing the line to slope.

• Yeah, it's possible. Do you want it perpendicular to the ground or the line? A drawing would be nice. Commented Sep 20, 2014 at 16:16
• @JakubKania I tried linking to the .svg image in Wikipedia, but it wouldn't display for some reason. Just open up that link, and that first cross-section picture is what I'm going for if I were to look at this from the side. From above, the ellipse would be hidden by the straight direct line, and from the side it would show a parabola above and below the straight direct line. Bonus points if you can figure out how to make a 3D ellipsoid out of it, but that's not necessary =) Commented Sep 22, 2014 at 12:19