<h2>Circles!</h2>

<p>Well, some of them, anyway.</p>

<p>You can plot any <a href="http://www.progonos.com/furuti/MapProj/Normal/ProjAz/projAz.html" rel="nofollow noreferrer">azimuthal projection</a> in polar coordinates, where the radius is a function of the angular distance from the center point.</p>

<p>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.  </p>

<p>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. </p>

<p><img src="https://upload.wikimedia.org/wikipedia/commons/8/81/Usgs_map_gnomic.PNG" alt="Different graticules for various centerings of the Gnomonic projection">
(Wikimedia Commons)</p>

<p>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.</p>

<p>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.</p>

CC BY-SA 3.0
2017-11-15T01:03:04.820Z
2017-11-15T11:07:17.850Z
2017-11-15T11:07:17.850Z
Spencer
<p>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?</p>

<p>Edit: We use North pole as a tangent point.</p>

CC BY-SA 3.0
2017-11-11T14:05:21.980Z
If you're assuming that the center of this projection is on the Equator, then you should edit it into your question.
Spencer
CC BY-SA 3.0
2017-11-11T17:27:46.657Z
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.
mkennedy
CC BY-SA 3.0
2017-11-12T14:10:39.877Z
Tangent point is North pole.
Alem
CC BY-SA 3.0
2017-11-12T20:56:57.230Z
gis.stackexchange.com might be a better place to ask
haresfur
CC BY-SA 3.0
2017-11-13T19:40:24.030Z
@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](https://en.wikipedia.org/wiki/Gnomonic_projection) displays less than a hemisphere so the equator will not be visible.
mkennedy
<geography><mapping>
Gnomonic projection of a curves with constant latitude
Alem
# Gnomonic projection of a curves with constant latitude

(Asked by: username_0 on 2017-11-11)

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.

**Tags:** geography, mapping

> **Comments:**
> **username_1**: If you're assuming that the center of this projection is on the Equator, then you should edit it into your question.  
> **username_2**: 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.  
> **username_0**: Tangent point is North pole.  
> **username_3**: gis.stackexchange.com might be a better place to ask  
> **username_2**: @username_0 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](https://en.wikipedia.org/wiki/Gnomonic_projection) displays less than a hemisphere so the equator will not be visible.  

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## 1 answers

### Answer by username_1 on 2017-11-15. Score: 3 | Accepted answer

## Circles!

Well, some of them, anyway.

You can plot any [azimuthal projection](http://www.progonos.com/furuti/MapProj/Normal/ProjAz/projAz.html) 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.

![Different graticules for various centerings of the Gnomonic projection](https://upload.wikimedia.org/wikipedia/commons/8/81/Usgs_map_gnomic.PNG)
(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.


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