CSE5280 3D Transformations

Like 2D transformations, 3D transformations can be represented using homogeneous coordinates by 4 × 4
matrices, providing we represent our points using homogeneous coordinates.

P = *(x,y,z)* ----> P´ = *(x,y,z,W)
*The corresponding point in 3D is P =

- The
*W*coordinate of a homogeneous point is typically 1 - Decreasing
*W*makes the point "bigger" meaning further from the origin - Homogeneous points with
*W = 0*are points at infinity*,*infinitely far away in a particular direction

Note: All transformations below apply to a right-handed coordinate system

Scaling changes the dimension of an object. The scale factor* S *determines whether the scaling is magnification,
*S *> 1, or a reduction, *S* < 1. Scaling with respect to the origin, where the origin remains
fixed is represented by the scale matrix below.

Translate

Rotate about X-Axis

Rotate about Y-Axis

Rotate about Z-Axis

Example(s)

- Rotating Cube Applet ---> Here. Complete source available ----> Here.
- Transforming your virtual world