Projection methods



This is the first method for displaying 3D objects in 2D (display plane). As it can be seen in the figure below, the method maps (P) point to (P') on the display plane. (P') is the orthogonal projection of (P). Lines remain lines and parallel lines remain parallel. This property makes it useful for engineer applications (CAD, technical drawing), because from the drawing distances can be measured.


Perspective projection is a cenered projection. We need a point (S), the center or the eye. With this, (P') is constructed that is the intersection of the plane and the (SP) line. This method produces further objects smaller. Some refer this as one-, two- or three point perspective, but the projection model is the same for those, it only depends of the place and orientation of the scene and the eye.

Six point perspective

Gif: Circle Gif: Fullerene

In six point perspective, parallel lines converge in both direction. Thus, lines no longer remain lines. It is basically a 360° fish eye lens.

This method requires the eye (S), a sphere (g) with center (S), and which touches the plane in (T). First, we map point (P) to the surface of the sphere -> (P'), then "peel" the sphere to the plane. We got (P''), in a way that S, T, P' and P'' are on the same plane, and distance of line TP'' equals TP' arc length.

So we get the image of the sourrinding space in a circle. And for example, the image in the concentric circle with half the radius is what is in front of us. (180° fish eye lens) What is outside this half, is behind us.



This method is unique in a way that a point maps to a circle, not an other point. (P) point -> (P') circle. The center of (P') is the orthogonal projection of (P), and its radius is the distance of (P) and the plane.

Java program to download

Enter - base state
x,y - only rotate around selected axis

Running on more processor cores can cause trouble.
(Windows: Task Manager - Applications - right click on Abrazolo - Go to Process - right click - Set Affinity)

Last modification: 2012 feb 15