Vector Algebra

Dot Products

Matrix Products

(Euclidean) Geometric Concepts Through Matrix-Vector Algebra

Points and Lines in Euclidean 2D

Points and Planes in Euclidean 3D (shortcut ℝ3)

Transformations

• Shift (Translation)
• Rotation
• Reflection

Hierarchy of Transformations

Point at infinity / “ideal” points

Cross Ratios

Cross Ratios of Collinear Points

Cross ratios for metrology

In the real 3-D world, you can compare one object with known length to another to “transfer” its length. This is what you do with a ruler, for example.

Pose From Homography

Pose from Point Correspondences,

the Perspective N Point Problem (PnP)

Calibrating Camera Under More General Intrinsics