Algebra and abstract structures · Maths EE idea · Ambitious

Rotating in 3D with quaternions

A research question to start from

How do unit quaternions represent rotations in three dimensions, and what advantages do they have over rotation matrices?

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Why it works as a maths EE

Non-commutative algebra with a geometric payoff, and a natural comparison for the evaluation.

Mathematics you would need

Quaternion algebra
Rotation matrices
Vectors and cross products
Composition of rotations

Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.

One possible line of attack

Define quaternions and prove key algebraic properties.
Show that q v q⁻¹ rotates a vector and find the angle and axis.
Compare composition and interpolation with matrices.
Evaluate accuracy and efficiency claims carefully.

Scope and difficulty

Ambitious. Ambitious; the proof of the rotation formula is the heart of it.

Pitfalls

Computer graphics essay without proofs.
Stating advantages without checking them.

Where to start reading

Search a library catalogue or a university's open lecture notes for: quaternion rotation proof q v q inverse; unit quaternions. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).

Make it your EE

Plan this EEOpens the free EE planner with this question as a starting point. Sharpen the questionSix quick checks for a focused research question. Self-check a draftCheck a section against each criterion, free.