TAPESTRY: The Art of Representation and Abstraction

# The Camera Lens: Projection

### What's this about?

*Projection* is the formal name for the process of "squashing" an N-dimensional space into an (N-1)-dimensional space. In the case of 3D applications, this is the process of converting your 3D *DATA* coordinates into 2D *IMAGE* coordinates. There are actually quite a number of ways to do this. The common ones are known by names like *perspective*, *axonometric*, *isometric*, *parallel*, and *elevation*.

The most fundamental distinction is that between *parallel* projections, a term which describes plans, elevations, isometric and axonometric drawings, and *perspective* projections, which covers traditional 1-point, 2-point, and 3-point perspectives (with or without "perspective correction").

### Normal ≈ Perspective Projection

In the Renaissance artists "discovered" the principles of perspective drawing, wherein objects close to us are drawn larger than the same object at a greater distance. This observed similarity between "objective perception" and the drawing is quite strong, underlying trompoli of the Renaissance and the VR of today.

### Telephoto ≈ Parallel Projection

Photographers talk about telephoto lenses "flattening" the scene. What's flatter than an elevation or plan drawing? Imagine standing infinitely far away (or above) the building, with an infinitely-long telephoto lens. The resulting image would be a parallel projection, in which all the light traveled along parallel paths.

Note that the *common* parallel projections include plans, elevations, sections, in which the view-vector is perpendicular to major planes of the building. However, there is nothing in the drawing process itself that requires this condition, which is why we also classify various types of isometrics and axonometric drawings as parallel projections.

### Other: Fish-Eye lens ≈ Ellipsoidal Projection

There are actually many other (admittedly obscure) projections, but the ellipsoidal (a special case of which is spherical) projection is possibly the best example of a "different" way to do these things.

Ellipsoidal projections present the entire forward hemisphere within a circular frame, where the radial distance from the center of the frame is proportional to the angular distance from the view vector. They appear quite like fish-eye photographs, and unlike the above projections, do not assume that straight lines remain straight lines in the image (for pretty obvious reasons).

*Last updated: April, 2014*