3.8-04 Homogeneous coordinates in 3D

Homogeneous coordinates in 3D — linear algebra practice

Read four-by-four affine transforms through their linear block, translation column and final row. Distinguish point and direction inputs, compute both types of output and analyze composition and inversion. A nonstandard last-row example marks the boundary between ordinary affine encoding and projective normalization.

What you will practise

• Interpret four-by-four affine blocks
• Transform points and directions correctly
• Compose, invert and recognize non-affine last-row behavior

This microlearning belongs to Module 3 of the Complete Linear Algebra Course. Single-select and multiselect questions progress from interpretation to calculation, application and error diagnosis. Each problem is self-contained, and the explanations show how to justify a result rather than only identify a choice. In multiselect tasks, assess each statement separately; the number of correct choices varies.

Before starting, review three-dimensional vectors and homogeneous 2D coordinates. Work through the reasoning on paper, compare your method with the explanation and revisit the assumptions behind any missed item. These skills prepare you to apply matrix methods to spatial graphics.