Quaternions

The functions provided by this module add support for quaternions. The algorithms take care to avoid unnecessary intermediate underflows and overflows, allowing the functions to be evaluated over as much of the quaternion plane as possible.

Features

• Quaternion arithmetic: Addition, subtraction, multiplication, division
• Rotations: Create rotations from axis-angle, Euler angles, spherical coordinates
• Interpolation: SLERP, NLERP, LERP for smooth rotation animations
• Mathematical operations: Conjugate, inverse, normalization, exponentiation
• Distance metrics: Measure distances between rotations

Quick Start

import vsl.quaternion
import math

// Create rotation: 90 degrees around x-axis
q := quaternion.from_axis_anglef3(math.pi / 2.0, 1.0, 0.0, 0.0)

// Rotate a point
p := quaternion.quaternion(0.0, 1.0, 0.0, 0.0) // Point (1, 0, 0)
q_conj := q.conjugate()
rotated := q.multiply(p).multiply(q_conj)
println('Rotated: (${rotated.x}, ${rotated.y}, ${rotated.z})')

Visualization Examples

Check out these examples that combine quaternions with plotting:

• quaternion_rotation_3d - Visualize 3D rotations
• quaternion_interpolation_animation - Animated interpolation
• quaternion_julia_fractal - Quaternion Julia sets
• quaternion_orientation_tracking - Track orientations over time
• quaternion_rotation_composition - Compose multiple rotations

Tutorials

Comprehensive tutorials are available in the docs directory:

• Introduction - Quaternion basics
• Rotations - Rotating 3D points
• Interpolation - Smooth rotation animations
• Visualization - Visualizing quaternions

Integration Examples

Examples combining quaternions with other VSL modules:

• ml_quaternion_features - Quaternions as ML features
• fft_quaternion_signal - Quaternion signal processing
• noise_quaternion_fractal - Fractals with noise

API Reference

See the VSL API Documentation for complete API reference.

fn from_axis_anglef3(angle f64, x f64, y f64, z f64) Quaternion

fn from_euler_angles(alpha f64, beta f64, gamma f64) Quaternion

fn from_spherical_coords(theta f64, phi f64) Quaternion

fn id() Quaternion

fn quaternion(w f64, x f64, y f64, z f64) Quaternion

struct Quaternion {
pub:
	w f64
	x f64
	y f64
	z f64
}

fn (q1 Quaternion) * (q2 Quaternion) Quaternion

fn (q1 Quaternion) + (q2 Quaternion) Quaternion

fn (q1 Quaternion) - (q2 Quaternion) Quaternion

fn (q1 Quaternion) / (q2 Quaternion) Quaternion

fn (q Quaternion) abs() f64

fn (q1 Quaternion) add(q2 Quaternion) Quaternion

fn (q Quaternion) angle() f64

fn (q Quaternion) conjugate() Quaternion

fn (q Quaternion) copy() Quaternion

fn (q1 Quaternion) divide(q2 Quaternion) Quaternion

fn (q1 Quaternion) equal(q2 Quaternion) bool

fn (q Quaternion) exp() Quaternion

fn (q Quaternion) inverse() Quaternion

fn (q Quaternion) is_finite() bool

fn (q1 Quaternion) is_greater(q2 Quaternion) bool

fn (q1 Quaternion) is_greaterequal(q2 Quaternion) bool

fn (q Quaternion) is_inf() bool

fn (q1 Quaternion) is_less(q2 Quaternion) bool

fn (q1 Quaternion) is_lessequal(q2 Quaternion) bool

fn (q Quaternion) is_nan() bool

fn (q Quaternion) is_zero() bool

fn (start Quaternion) lerp(end Quaternion, tau f64) Quaternion

fn (q Quaternion) log() Quaternion

fn (q1 Quaternion) multiply(q2 Quaternion) Quaternion

fn (start Quaternion) nlerp(end Quaternion, tau f64) Quaternion

fn (q Quaternion) norm() f64

fn (q Quaternion) normalized() Quaternion

fn (q Quaternion) opposite() Quaternion

fn (q Quaternion) parity_antisymmetric_part() Quaternion

fn (q Quaternion) parity_conjugate() Quaternion

fn (q Quaternion) parity_symmetric_part() Quaternion

fn (q Quaternion) pow(p Quaternion) Quaternion

fn (q1 Quaternion) rotation_chordal_distance(q2 Quaternion) f64

fn (q1 Quaternion) rotation_intrinsic_distance(q2 Quaternion) f64

fn (q1 Quaternion) rotor_chordal_distance(q2 Quaternion) f64

fn (q1 Quaternion) rotor_intrinsic_distance(q2 Quaternion) f64

fn (q Quaternion) scalar_add(s f64) Quaternion

fn (q Quaternion) scalar_divide(s f64) Quaternion

fn (q Quaternion) scalar_multiply(s f64) Quaternion

fn (q Quaternion) scalar_pow(s f64) Quaternion

fn (q Quaternion) scalar_subtract(s f64) Quaternion

fn (start Quaternion) slerp(end Quaternion, tau f64) Quaternion

fn (q Quaternion) sqrt() Quaternion

fn (qi Quaternion) squad(taui f64, ai Quaternion, bip1 Quaternion, qip1 Quaternion) Quaternion

fn (q Quaternion) str() string

To String method w + xi + yj + zk

fn (q1 Quaternion) subtract(q2 Quaternion) Quaternion

fn (q Quaternion) x_parity_antisymmetric_part() Quaternion

fn (q Quaternion) x_parity_conjugate() Quaternion

fn (q Quaternion) x_parity_symmetric_part() Quaternion

fn (q Quaternion) y_parity_antisymmetric_part() Quaternion

fn (q Quaternion) y_parity_conjugate() Quaternion

fn (q Quaternion) y_parity_symmetric_part() Quaternion

fn (q Quaternion) z_parity_antisymmetric_part() Quaternion

fn (q Quaternion) z_parity_conjugate() Quaternion

fn (q Quaternion) z_parity_symmetric_part() Quaternion