Quaternion

8.12

Quaternion🔗ℹ

APOS80

(require quaternion)

package: Quaternion

1 Intro🔗ℹ

Quaternions are used for rotation of koordinates and vectors.

2 Structures🔗ℹ

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🔗ℹ

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🔗ℹ

procedure
(q-rotation angl qv) → quaternion?
angl : (flonum?)
qv : (qvector?)

Rotation in radians about an arbitrary axis. Positive rotation is anticlockwise!

procedure
(q-rotate rotation object) → quaternion?
rotation : (quaternion?)
object : (quaternion?)

Applyes the rotation on an object. Object quaternion’s w has to be 0!

5 Examples🔗ℹ

; 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))))))