Computer Graphics
CSE5280 3D Transformations

References

• On-line introduction to 3D Transformations

3D Base 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 = (x/W, y/W, z/W)

• 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

Scale Transformation

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