# Gnomonic projection of a curves with constant latitude

If we consider gnomonic projection, what are projections of curves with constant latitude. For example, we know that great circles are projected to straight lines. So, equator should be projected on a straight line, right? What about curves with constant latitude in general?

Edit: We use North pole as a tangent point.

• If you're assuming that the center of this projection is on the Equator, then you should edit it into your question. Nov 11 '17 at 14:05
• A line of latitude isn't a great circle, but a small circle, so it won't project into a gnomonic projection as a straight line. Nov 11 '17 at 17:27
• Tangent point is North pole.
– Alem
Nov 12 '17 at 14:10
• gis.stackexchange.com might be a better place to ask Nov 12 '17 at 20:56
• @Alem Please edit your question with any further information. If tangent point is a pole, latitude lines are circles while longitude lines are straight lines. Gnomonic displays less than a hemisphere so the equator will not be visible. Nov 13 '17 at 19:40

## Circles!

Well, some of them, anyway.

You can plot any azimuthal projection in polar coordinates, where the radius is a function of the angular distance from the center point.

So where two points' angular distances are the same, their radii are the same, and the projection of any locus of constant angular distance from the center point is a circle, if it appears at all.

Since you said that the tangent point is a pole, that means that parallels (lines of constant latitude) are those lines of constant angular distance. Ergo, Northern Hemisphere parallels appear as circles. (Wikimedia Commons)

Since the Gnomonic projection can show only a single hemisphere, the Equator and parallels in the Southern hemisphere can't appear at all -- they would be an infinite distance from the center point.

The polar orientation of the projection even takes away complications resulting from the earth's not being a perfect sphere -- the radius formula changes a little, but the equal results from the same input remain.