Doug Kerr
Well-known member
Most modern panoramic image assembly programs offer us a number of "projections" under which the final image can be prepared. There is a lot of confusion afoot in this area.
Much of the difficulty comes from the fact that the topic of projections inhabits two worlds - the context of cartography (the making of maps representing things on the surface of the Earth) and the context of photography.
Notions that come from cartography are often transported mindlessly into the realm of photography, with baffling result.
For example, we are often shown a number of tidy graphics that show us how a particular hypothetical "test scene" would be rendered into an image under each of several projections. The problem is that the test scene is a hollow sphere with parallels of latitude and meridians of longitude "painted" inside it, photographed from its center.
How does this help us grasp the effect of choosing one projection or another on, for example, photography of a really wide building facade, with a lot of little windows, or an entire sector of a city, with a grid of streets and lots of buildings? Not at all.
Then we hear statements like this, describing the unique features of various projections:
• "Under the equirectangular projection, the vertical scale is constant regardless of elevation", and
• "Under the Mercator projection, for any elevation, the vertical scale is equal to the horizontal scale"
When we look at actual images prepared under these projections, we don't seem to see that at all. In fact, it looks as if the cylindrical projection, not the equirectangular, has unchanging vertical scale. And we don't see any evidence at all of horizontal scale ever changing with altitude, so just what is it that the Mercator projection does?
The fact is that here, the definitions of "scale" that are involved make sense in a certain cartographic context, but do not relate to any common photographic context. They imply things that are just not so in our context.
In an effect to lead us out of this morass, I have just completed a new tutorial article, "Projections in Photography". It explains the concepts of projection, and how the topic has moved from the world of cartography to that of photography. I then use a basic geometric model, involving a pinhole camera, no less, to demonstrate the definition of two important projections (the other two I will discuss can't be explained by any such geometric model).
Then I use charts that show how an understandable "test object" - a building facade with a uniform grid of decorative lines, vertical and horizontal - will be rendered into an image under four different projections.
Two appendixes give technical details related to the topic (including a discussion about the different meanings of "scale" in the two contexts, one of the troublesome points).
The article is extensively illustrated with drawings and charts.
The article is available here:
http://doug.kerr.home.att.net/pumpkin/index.htm#Projections
Much of the difficulty comes from the fact that the topic of projections inhabits two worlds - the context of cartography (the making of maps representing things on the surface of the Earth) and the context of photography.
Notions that come from cartography are often transported mindlessly into the realm of photography, with baffling result.
For example, we are often shown a number of tidy graphics that show us how a particular hypothetical "test scene" would be rendered into an image under each of several projections. The problem is that the test scene is a hollow sphere with parallels of latitude and meridians of longitude "painted" inside it, photographed from its center.
How does this help us grasp the effect of choosing one projection or another on, for example, photography of a really wide building facade, with a lot of little windows, or an entire sector of a city, with a grid of streets and lots of buildings? Not at all.
Then we hear statements like this, describing the unique features of various projections:
• "Under the equirectangular projection, the vertical scale is constant regardless of elevation", and
• "Under the Mercator projection, for any elevation, the vertical scale is equal to the horizontal scale"
When we look at actual images prepared under these projections, we don't seem to see that at all. In fact, it looks as if the cylindrical projection, not the equirectangular, has unchanging vertical scale. And we don't see any evidence at all of horizontal scale ever changing with altitude, so just what is it that the Mercator projection does?
The fact is that here, the definitions of "scale" that are involved make sense in a certain cartographic context, but do not relate to any common photographic context. They imply things that are just not so in our context.
In an effect to lead us out of this morass, I have just completed a new tutorial article, "Projections in Photography". It explains the concepts of projection, and how the topic has moved from the world of cartography to that of photography. I then use a basic geometric model, involving a pinhole camera, no less, to demonstrate the definition of two important projections (the other two I will discuss can't be explained by any such geometric model).
Then I use charts that show how an understandable "test object" - a building facade with a uniform grid of decorative lines, vertical and horizontal - will be rendered into an image under four different projections.
Two appendixes give technical details related to the topic (including a discussion about the different meanings of "scale" in the two contexts, one of the troublesome points).
The article is extensively illustrated with drawings and charts.
The article is available here:
http://doug.kerr.home.att.net/pumpkin/index.htm#Projections
