Quaternions

Overview

Quaternion types for representing 3D rotations efficiently, with SLERP/NLERP interpolation, Euler angle and axis-angle conversions, and vector rotation.

Why Use This?

Quaternions avoid gimbal lock, interpolate smoothly, concatenate efficiently, and are more compact than rotation matrices (4 values vs 9).

Types

Type	Scalar	Description
`lm2_quat_f64`	`double`	64-bit quaternion
`lm2_quat_f32`	`float`	32-bit quaternion

Format: [x, y, z, w] where w is the scalar part and (x, y, z) is the vector part.

Functions

Construction

Function	Description
`lm2_quat_identity_f32()`	Identity quaternion (no rotation)
`lm2_quat_zero_f32()`	Zero quaternion
`lm2_quat_make_f32(x, y, z, w)`	From components

Conversions

Function	Description
`lm2_quat_from_axis_angle_f32(axis, angle)`	From axis and angle (radians)
`lm2_quat_from_euler_f32(pitch, yaw, roll)`	From Euler angles
`lm2_quat_from_euler_vec_f32(euler)`	From Euler angles as v3
`lm2_quat_to_axis_angle_f32(q, &axis, &angle)`	Extract axis and angle
`lm2_quat_to_euler_f32(q)`	Convert to Euler angles (v3)

Operations

Function	Description
`lm2_quat_conjugate_f32(q)`	Conjugate (negate vector part)
`lm2_quat_inverse_f32(q)`	Inverse rotation
`lm2_quat_norm_f32(q)`	Normalize to unit quaternion
`lm2_quat_multiply_f32(a, b)`	Combine rotations
`lm2_quat_add_f32(a, b)`	Component-wise addition
`lm2_quat_sub_f32(a, b)`	Component-wise subtraction
`lm2_quat_scale_f32(q, s)`	Scale by scalar

Analysis

Function	Description
`lm2_quat_dot_f32(a, b)`	Dot product
`lm2_quat_length_f32(q)`	Length (magnitude)
`lm2_quat_length_squared_f32(q)`	Squared length
`lm2_quat_equals_f32(a, b, epsilon)`	Approximate equality (returns `bool`)

Rotation

`lm2_quat_rotate_vector_f32`

Rotate a 3D vector by the quaternion.

Signature: lm2_v3_f32 lm2_quat_rotate_vector_f32(lm2_quat_f32 q, lm2_v3_f32 v)

Interpolation

`lm2_quat_slerp_f32`

Spherical linear interpolation. Gives constant angular velocity.

Signature: lm2_quat_f32 lm2_quat_slerp_f32(lm2_quat_f32 a, lm2_quat_f32 b, float t)

Parameters:

a — Start rotation
b — End rotation
t — Interpolation factor [0, 1]

`lm2_quat_nlerp_f32`

Normalized linear interpolation. Faster than SLERP but non-constant velocity.

Signature: lm2_quat_f32 lm2_quat_nlerp_f32(lm2_quat_f32 a, lm2_quat_f32 b, float t)

Example

// Create rotation: 90 degrees around Y axis
lm2_quat_f32 q = lm2_quat_from_axis_angle_f32(
    lm2_v3_make_f32(0, 1, 0),
    LM2_HPI_F32
);

// Rotate a point
lm2_v3_f32 point = lm2_v3_make_f32(1, 0, 0);
lm2_v3_f32 rotated = lm2_quat_rotate_vector_f32(q, point);
// rotated ~ {0, 0, -1}

// Interpolate between two rotations
lm2_quat_f32 q2 = lm2_quat_from_euler_f32(0, LM2_PI_F32, 0);
lm2_quat_f32 halfway = lm2_quat_slerp_f32(q, q2, 0.5f);

// Convert to matrix for rendering
lm2_m4x4_f32 mat = lm2_m4x4_from_quat_f32(q);