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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.
- (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 nprocedure
Returns the real part of a number.
> (real-part (make-rectangular 1 2 3 4)) 1
- imag-part nprocedure
Returns the imaginary part (the i) of a complex or quaternion number.
> (imag-part (make-rectangular 1 2 3 4)) 2
- jmag-part nprocedure
Returns the j part of a quaternion number.
> (jmag-part (make-rectangular 1 2 3 4)) 3
- kmag-part nprocedure
Returns the k part of a quaternion number.
> (kmag-part (make-rectangular 1 2 3 4)) 4
- magnitude nprocedure
The length of n treated as a vector.
- number? nprocedure
Checks if given argument is any kind of number.
> (number? 3) #t > (number? 1+2i) #t > (number? (make-rectangular 1 2 3 4)) #t
- = 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.
- vector-part qprocedure
Returns the quaternion with its real part set to 0.
- conjugate qprocedure
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 qprocedure
Returns a quaternion in same direction as q but of unit length; the real part of q is set to 0.
- dot-product q1 q2procedure
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 q2procedure
Real parts of q1 and q2 must be 0. The cross product is the vector part of q1 x q2.
The original version of this library was created by Dorai Sitaram.
This port to chicken scheme is by Peter Lane.
GPL version 3.0.
- version 1.0: released.