Quaternion
1 Intro
2 Structures
qvector
quaternion
3 Basic procedures
q-add
q-sub
q-norm
q-normalize
q-multiply-qq
q-divide-qs
q-negate
q-conjugate
q-inverse
4 Rotation
q-rotation
q-rotate
5 Examples
7.0

Quaternion

APOS80

 (require quaternion) package: 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

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

; 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))))))