Complex numbers and quaternions
(ns complex-quaternions
(:require [fastmath.complex :as cplx]
[fastmath.quaternion :as quat]
[fastmath.dev.codox :as codox]))Complex numbers
Reference
fastmath.complex
Complex numbers functions.
Complex number is represented as Vec2 type (from clojure2d.math.vector namespace).
To create complex number use complex, vec2 or ->Vec2.
Implementation checks for ##Inf, ##NaN and some of the function distinguish +0.0 and -0.0
-I
I
I-
ONE
TWO
ZERO
abs
(abs z)
Absolute value, magnitude
acos
(acos z)
acos
acosh
(acosh z)
acosh
acot
(acot z)
acot
acoth
(acoth z)
acsc
(acsc z)
acsc
acsch
(acsch z)
add
(add z1 z2)
Sum of two complex numbers
arg
(arg z)
Argument (angle) of the complex number
asec
(asec z)
asec
asech
(asech z)
asin
(asin z)
asin
asinh
(asinh z)
asinh
atan
(atan z)
atan
atanh
(atanh z)
atanh
complex
(complex a b)(complex a)(complex)
Create complex number. Represented as Vec2.
conjugate
(conjugate z)
Complex conjugate. \(\bar{z}\)
cos
(cos z)
cos
cosh
(cosh z)
cosh
cot
(cot z)
csc
coth
(coth z)
coth
csc
(csc z)
csc
csch
(csch z)
csch
csgn
(csgn re im)(csgn z)
Complex sgn.
Returns 0 for 0+0i or calls m/sgn on real part otherwise.
delta-eq
(delta-eq q1 q2)(delta-eq q1 q2 accuracy)
Compare complex numbers with given accuracy (10e-6 by default)
div
(div z1 z2)
Divide two complex numbers.
exp
(exp z)
exp
flip
(flip z)
Exchange imaginary and real parts
im
(im z)
Imaginary part
imaginary?
(imaginary? z)
Is z is a pure imaginary number?
inf?
(inf? z)
Is infinite?
log
(log z)
log, principal value
logb
(logb z b)
log with base b
mult
(mult z1 z2)
Multiply two complex numbers.
mult-I
(mult-I z)
mult-I-
(mult-I- z)
nan?
(nan? z)
Is NaN?
neg
(neg z)
Negate complex number. \(-z\)
norm
(norm z)
Norm (Guass) of the complex number, absolute value squared
pow
(pow z1 z2)
Power. \(z_1^{z_2}\)
re
(re z)
Real part
real?
(real? z)
Is z is a real number?
reciprocal
(reciprocal z)
\(\frac{1}{z}\)
scale
(scale z v)
Multiply by real number
sec
(sec z)
sec
sech
(sech z)
sech
sin
(sin z)
sin
sinh
(sinh z)
sinh
sq
(sq z)
Square complex number. \(z^2\)
sqrt
(sqrt z)
Sqrt of complex number. \(\sqrt{z}\)
sqrt1z
(sqrt1z z)
\(\sqrt{1-z^2}\)
sub
(sub z1 z2)
Difference of two complex numbers
tan
(tan z)
tan
tanh
(tanh z)
tanh
zero?
(zero? z)
Is zero?
Quaternions
Reference
fastmath.quaternion
-I
-J
-K
I
J
K
ONE
ZERO
acos
(acos q)
acosh
(acosh q)
acot
(acot q)
acoth
(acoth q)
acsc
(acsc q)
acsch
(acsch q)
add
(add q1 q2)
Sum of two quaternions
arg
(arg quaternion)
Argument of quaternion, atan2(|vector(q)|, re(q))
asec
(asec q)
asech
(asech q)
asin
(asin q)
asinh
(asinh q)
atan
(atan q)
atanh
(atanh q)
complex->quaternion
(complex->quaternion z)
Create quaternion from complex number
conjugate
(conjugate quaternion)
Returns conjugate of quaternion
cos
(cos q)
cosh
(cosh q)
cot
(cot q)
coth
(coth q)
csc
(csc q)
csch
(csch q)
delta-eq
(delta-eq q1 q2)(delta-eq q1 q2 accuracy)
Compare quaternions with given accuracy (10e-6 by default)
div
(div q1 q2)
Divide two quaternions
exp
(exp q)
from-angles
(from-angles [x y z])(from-angles x y z)
Convert Tait–Bryan angles z-y′-x” to quaternion.
from-euler
(from-euler [roll pitch yaw])(from-euler roll pitch yaw)
Convert Euler ZYX (body 3-2-1) representation to quaternion
Input should be 3d vector contating roll (x), pitch (y) and yaw (z) angles, or individual values.
- roll and yaw should be from
[-pi, pi]range - pitch should be from
[-pi/2, pi/2]range
from-rotation-matrix
(from-rotation-matrix m)
Convert rotation 3x3 matrix to a quaternion
im-i
(im-i quaternion)
Return i imaginary part
im-j
(im-j quaternion)
Return j imaginary part
im-k
(im-k quaternion)
Return k imaginary part
imaginary?
(imaginary? quaternion)
Is q is a pure imaginary number?
inf?
(inf? quaternion)
Is infinitive?
log
(log q)
logb
(logb quaternion b)
log with base b
mult
(mult q1 q2)
Multiply two quaternions.
nan?
(nan? quaternion)
Is NaN?
neg
(neg quaternion)
Negation of quaternion.
norm
(norm quaternion)
Norm of the quaternion, length of the vector
normalize
(normalize quaternion)
Normalize quaternion
pow
(pow q p)
Quaternion power
qsgn
(qsgn re im-i im-j im-k)(qsgn q)
sgn of the quaternion.
Returns 0 for 0+0i+0j+0k or calls m/sgn on real part otherwise.
quaternion
(quaternion a b c d)(quaternion scalar [i j k])(quaternion a)
Create quaternion from individual values or scalar and vector parts, reprezented as Vec4.
re
(re quaternion)
Returns scalar part of quaternion
real?
(real? quaternion)
Is q is a real number?
reciprocal
(reciprocal quaternion)
rotate
(rotate in rotq)(rotate in angle u)
Rotate 3d in vector around axis u, the same as fastmath.vector/axis-rotate.
rotation-quaternion
(rotation-quaternion angle u)
Create rotation quaternion around vector u and angle alpha
scalar
(scalar quaternion)
Returns scalar part of quaternion, double
scale
(scale quaternion scale)
Scale the quaternion
sec
(sec q)
sech
(sech q)
sin
(sin q)
sinh
(sinh q)
slerp
(slerp q1 q2 t)
Interpolate quaternions
sq
(sq quaternion)
Square of quaternion.
sqrt
(sqrt q)
sub
(sub q1 q2)
Difference of two quaternions
tan
(tan q)
tanh
(tanh q)
to-angles
(to-angles q)
Convert quaternion to Tait–Bryan angles, z-y′-x”.
to-euler
(to-euler q)
Convert quaternion to Euler ZYX (body 3-2-1). Quaternion will be normalized before calculations.
Output will contain roll (x), pitch (y) and yaw (z) angles.
to-rotation-matrix
(to-rotation-matrix q)
Convert quaternion to rotation 3x3 matrix
vector
(vector quaternion)
Returns vector part of quaternion, Vec3 type
zero?
(zero? quaternion)
Is zero?
source: clay/complex_quaternions.clj