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
- version 1.0: released.