Quaternion

1 Intro

Quaternions are used for rotation of koordinates and vectors.

2 Structures

struct (struct   qvector (x y z)

#:mutable

#:transparent)

x : flonum?

y : flonum?

z : flonum?

struct (struct   quaternion (w v)

#:mutable

#:transparent)

w : flonum?

v : qvector?

3 Basic procedures

procedure (q-add q1 q2) → quaternion?

q1 : (quaternion?)

q2 : (quaternion?)

procedure (q-sub q1 q2) → quaternion?

q1 : (quaternion?)

q2 : (quaternion?)

procedure (q-norm q) → quaternion?

q : (quaternion?)

procedure (q-normalize q) → quaternion?

q : (quaternion?)

procedure (q-multiply-qq q1 q2) → quaternion?

q1 : (quaternion?)

q2 : (quaternion?)

procedure (q-divide-qs q s) → quaternion?

q : (quaternion?)

s : (flonum?)

procedure (q-negate q) → quaternion?

q : (quaternion?)

procedure (q-conjugate q) → quaternion?

q : (quaternion?)

procedure (q-inverse q) → quaternion?

q : (quaternion?)

4 Rotation

5 Examples

; Rotation about one axis:

(let*

([A (q-rotation (fl/ pi 2.0) (qvector 0.0 1.0 0.0))]; Rotation 90degrees about Y-axis.

[B (q-rotate A (quaternion 0.0 (qvector 0.0 0.0 1.0)))]); Apply rotation on quaternion with A.

(begin

(printf "X: ~a\n" (~r(qvector-x (quaternion-v B)))); Print results.

(printf "Y: ~a\n" (~r(qvector-y (quaternion-v B))))

(printf "Z: ~a\n" (~r(qvector-z (quaternion-v B))))))

; Rotation about two axis:

(let*

([A1 (q-rotation (fl/ pi 4.0) (qvector 0.0 1.0 0.0))]; Rotation 90degrees about Y-axis.

[A2 (q-rotation (fl/ pi 4.0) (qvector 1.0 0.0 0.0))]; Rotation 90degrees about X-axis.

[AS (q-multiply-qq A1 A2)]; Combine rotations.

[B (q-rotate AS (quaternion 0.0 (qvector 0.0 0.0 1.0)))]); Apply rotation on quaternion with A.

(begin

(printf "X: ~a\n" (~r(qvector-x (quaternion-v B)))); Print results.

(printf "Y: ~a\n" (~r(qvector-y (quaternion-v B))))

(printf "Z: ~a\n" (~r(qvector-z (quaternion-v B))))))