My Blender Journey Part 1: Background Knowledge

1. Cartesian system is right-handed:

Stick out your thumb directly to the right (X). Now aim your pointer finger straight up (Y). Finally, make your middle finger point toward yourself (Z).

Another view of right-handed system

2. Axis of rotation

the right-hand grip rule

Consider a spinning sphere. Every point on it is moving, except the ones along the axis. These form a motionless line around which the rest of the sphere spins. This line is called the axis of rotation.

3. Linear transform

Lines that were straight before the transformation remain straight after linear transform.

Most of the transformations we deal with in 3D modelling have an inverse, but not all.

4. Projection

There are two main ways to perform such projections. One is orthographic projection, where parallel lines are drawn from all points of the three-dimensional object until they intersect a plane representing the display surface:

An orthographic view (or projection) of a 3D scene is a 2D picture of it in which parallel lines appear parallel, and all edges perpendicular to the view direction appear in proportion, at exactly the same scale.

The other way is perspective projection, where the lines drawn are not parallel, but intersect at a point representing the location of the eye of the viewer:

The essence of perspective is to represent parallel edges (in a 3D scene) by edges (in the 2D image) that are not parallel. When done correctly, this produces foreshortening (nearby objects are depicted larger than distant ones) and contributes to the illusion of depth.

5. View coordinates

View coordinates and Projection Plane

View coordinates in viewing direction

6. Normal coordinates

7. UV coordinates

UV coordinates are simply different letters chosen to avoid confusion over “X”, “Y” and “Z”. For example, a raster image is normally laid out on a flat, two-dimensional plane. Each point on the image can be identified by X and Y coordinates. So to avoid confusion, the points on the image are identified using U and V to label their coordinates instead of X and Y. We then refer to “UV mapping” as the process of determining where each (U, V) image point ends up on the (X, Y, Z) object.

Reference

• Blender 3D: Noob to Pro