chickadee » quaternions

Quaternions

Quaternions are an extension to the number system: real numbers may be thought of as points on a line, complex numbers as points in a plane, and quaternion numbers as points in four-dimensional space.

Apart from mathematical curiosity, quaternions are useful for specifying rotations in three dimensional space (e.g. in this game), and also for image analysis.

An introduction to quaternions and this scheme library is available here.

Exported Procedures

(make-rectangular w [x [y z]]) procedure

Constructs a number, complex number, or quaternion number depending on if given 1, 2 or 4 arguments.

> (make-rectangular 1)
1
> (make-rectangular 1 2)
1+2i
> (make-rectangular 1 2 3 4)
1+2i+3j+4k
(make-polar mu theta [phi psi]) procedure

An alternative way of defining a quaternion, through the magnitude mu, the angle theta, the colatitude phi and longitude psi.

(real-part n) procedure

Returns the real part of a number.

> (real-part (make-rectangular 1 2 3 4))
1
(imag-part n) procedure

Returns the imaginary part (the i) of a complex or quaternion number.

> (imag-part (make-rectangular 1 2 3 4))
2
(jmag-part n) procedure

Returns the j part of a quaternion number.

> (jmag-part (make-rectangular 1 2 3 4))
3
(kmag-part n) procedure

Returns the k part of a quaternion number.

> (kmag-part (make-rectangular 1 2 3 4))
4
(magnitude n) procedure

The length of n treated as a vector.

(angle n) procedure

See make-polar.

(number? n) procedure

Checks if given argument is any kind of number.

> (number? 3)
#t
> (number? 1+2i)
#t
> (number? (make-rectangular 1 2 3 4))
#t
(quaternion? n) procedure

The same as number?.

(= q1 ...) procedure

Tests for equality of given numbers.

(+ q1 ...) procedure

Returns the sum of given numbers.

> (+ 3 2+3i (make-rectangular 1 2 3 4))
6+5i+3j+4k
(- q1 ...) procedure

Returns the difference of given numbers, associating to left.

(* q1 ...) procedure

Returns the product of given numbers.

> (* 2 (make-rectangular 1 2 3 4))
2+4i+6j+8k
(/ q1 ...) procedure

Returns quotient of given numbers, associating to left.

(exp n) procedure

Usual exp function extended to quaternions.

(log n) procedure

Usual log function extended to quaternions.

(expt m n) procedure

Usual expt function extended to quaternions.

(sqrt n) procedure

Usual sqrt function extended to quaternions.

(sin n) procedure

Usual sin function extended to quaternions.

(cos n) procedure

Usual cos function extended to quaternions.

(tan n) procedure

Usual tan function extended to quaternions.

(asin n) procedure

Usual asin function extended to quaternions.

(acos n) procedure

Usual acos function extended to quaternions.

(atan n) procedure

Usual atan function extended to quaternions.

(atan y x) procedure

Usual atan function extended to quaternions.

(vector-part q) procedure

Returns the quaternion with its real part set to 0.

(colatitude q) procedure

See make-polar.

(longitude q) procedure

See make-polar.

(conjugate q) procedure

Returns quaternion with same real part and sign of i j and k part of q reversed.

> (conjugate (make-rectangular 1 2 3 4))
1-2i-3j-4k
(unit-vector q) procedure

Returns a quaternion in same direction as q but of unit length; the real part of q is set to 0.

(dot-product q1 q2) procedure

Real parts of q1 and q2 must be 0. The dot product is the negative of the real part of q1 x q2.

(cross-product q1 q2) procedure

Real parts of q1 and q2 must be 0. The cross product is the vector part of q1 x q2.

Author

The original version of this library was created by Dorai Sitaram.

This port to chicken scheme is by Peter Lane.

License

GPL version 3.0.

Version History

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