Geometric Transformations for Computer Graphics

Three lab exercises for the Geometric Transformations for Computer Graphics course (MIRI, UPC), each a self-contained SageMath notebook.

Lab 1 — Affine transformations

First contact with affine transformations and matrix multiplication: rotating, scaling and translating objects in 3D by composing transformation matrices. The final exercise consists of building cubes and positioning them at specific coordinates purely through matrix math.

Qualification: 9.00/10.00 — feedback: some dot products (angles) in the last exercise were not really needed.

Lab 2 — Parametric surfaces

Introduction to defining and drawing objects using parametric surfaces. The final exercise is a toothpaste tube, modeled and rendered entirely from parametric equations.

Qualification: 10.00/10.00

Lab 3 — Quaternions and rotations

Using quaternions and Rodrigues’ rotation formula to model rigid-body rotations. The final exercise renders two champagne glasses at the exact moment of a toast, touching at a single point, with their orientation computed via Rodrigues’ formula.

Qualification: 10.00/10.00

Exercise presentation

Qualification: 2.00/2.00