Quaternion🔗 i

1Intro🔗 i

Quaternions are used for rotation of koordinates and vectors.

2Structures🔗 i

struct

(struct qvector(xyz)

#:mutable

#:transparent)

x:flonum?

y:flonum?

z:flonum?

struct

(struct quaternion(wv)

#:mutable

#:transparent)

w:flonum?

v:qvector?

3Basic procedures🔗 i

procedure

( q-addq1q2)→quaternion?

q1:(quaternion?)

q2:(quaternion?)

procedure

( q-subq1q2)→quaternion?

q1:(quaternion?)

q2:(quaternion?)

procedure

( q-normq)→quaternion?

q:(quaternion?)

procedure

( q-normalizeq)→quaternion?

q:(quaternion?)

procedure

( q-multiply-qqq1q2)→quaternion?

q1:(quaternion?)

q2:(quaternion?)

procedure

( q-divide-qsqs)→quaternion?

q:(quaternion?)

s:(flonum? )

procedure

( q-negateq)→quaternion?

q:(quaternion?)

procedure

( q-conjugateq)→quaternion?

q:(quaternion?)

procedure

( q-inverseq)→quaternion?

q:(quaternion?)

4Rotation🔗 i

5Examples🔗 i

;Rotation about one axis:

(let*

([A(q-rotation(fl/ pi 2.0)(qvector0.01.00.0))];Rotation 90degrees about Y-axis.

[B(q-rotateA(quaternion0.0(qvector0.00.01.0)))]);Apply rotation on quaternion with A.

(begin

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

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

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

;Rotation about two axis:

(let*

([A1(q-rotation(fl/ pi 4.0)(qvector0.01.00.0))];Rotation 90degrees about Y-axis.

[A2(q-rotation(fl/ pi 4.0)(qvector1.00.00.0))];Rotation 90degrees about X-axis.

[AS(q-multiply-qqA1A2)];Combine rotations.

[B(q-rotateAS(quaternion0.0(qvector0.00.01.0)))]);Apply rotation on quaternion with A.

(begin

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

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

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