Vector Specifics

Overview

Higher-level vector operations including dot product, cross product, length, distance, normalization, angle computation, rotation, reflection, and projection. These operate on floating-point vector types.

Why Use This?

These are the essential geometric operations needed for lighting calculations, physics, camera systems, collision detection, and spatial queries.

Functions

Dot Product

Returns the scalar dot product of two vectors.

Function	Description
`lm2_v2_dot_f32(a, b)`	2D dot product (float)
`lm2_v3_dot_f32(a, b)`	3D dot product (float)
`lm2_v4_dot_f32(a, b)`	4D dot product (float)

Also available for _f64 and integer types (_i64, _i32, _i16, _i8).

Cross Product

3D Cross Product

Returns the cross product vector, perpendicular to both inputs.

Signature: lm2_v3_f32 lm2_v3_cross_f32(lm2_v3_f32 a, lm2_v3_f32 b)

Also available for _f64 and integer types (_i64, _i32, _i16, _i8).

2D Cross Product

Returns the scalar z-component of the cross product (a.x * b.y - a.y * b.x).

Signature: float lm2_v2_cross_f32(lm2_v2_f32 a, lm2_v2_f32 b)

Also available for _f64 and integer types (_i64, _i32, _i16, _i8).

2D Cross Product (3-point)

Returns the cross product of vectors (b-a) and (c-a). Useful for turn detection:

> 0: Left turn (counterclockwise)
< 0: Right turn (clockwise)
= 0: Collinear

Signature: float lm2_v2_cross3_f32(lm2_v2_f32 a, lm2_v2_f32 b, lm2_v2_f32 c)

Also available for _f64 and integer types (_i64, _i32, _i16, _i8).

Length / Magnitude

Function	Description
`lm2_v2_length_f32(v)`	2D vector length
`lm2_v3_length_f32(v)`	3D vector length
`lm2_v4_length_f32(v)`	4D vector length
`lm2_v2_length_sq_f32(v)`	2D squared length (no sqrt, faster)
`lm2_v3_length_sq_f32(v)`	3D squared length
`lm2_v4_length_sq_f32(v)`	4D squared length

Distance

Function	Description
`lm2_v2_distance_f32(a, b)`	2D distance between points
`lm2_v3_distance_f32(a, b)`	3D distance between points
`lm2_v4_distance_f32(a, b)`	4D distance between points
`lm2_v2_distance_sq_f32(a, b)`	2D squared distance (no sqrt, faster)
`lm2_v3_distance_sq_f32(a, b)`	3D squared distance
`lm2_v4_distance_sq_f32(a, b)`	4D squared distance

Normalize

Returns a unit vector in the same direction.

Function	Description
`lm2_v2_norm_f32(v)`	Normalize 2D vector
`lm2_v3_norm_f32(v)`	Normalize 3D vector
`lm2_v4_norm_f32(v)`	Normalize 4D vector

Angle

Returns the angle between two vectors in radians.

Function	Description
`lm2_v2_angle_f32(a, b)`	Angle between 2D vectors
`lm2_v3_angle_f32(a, b)`	Angle between 3D vectors

2D Rotation

`lm2_v2_rotate_f32`

Rotate a 2D vector by an angle (radians).

Signature: lm2_v2_f32 lm2_v2_rotate_f32(lm2_v2_f32 v, float angle)

`lm2_v2_rotate_around_f32`

Rotate a 2D vector around a pivot point by an angle (radians).

Signature: lm2_v2_f32 lm2_v2_rotate_around_f32(lm2_v2_f32 v, lm2_v2_f32 point, float angle)

Perpendicular Vectors (2D)

Function	Description
`lm2_v2_perp_ccw_f32(v)`	90-degree counter-clockwise rotation
`lm2_v2_perp_cw_f32(v)`	90-degree clockwise rotation

Available for all signed types.

Reflection

Reflect a vector across a normal.

Function	Description
`lm2_v2_reflect_f32(v, normal)`	2D reflection
`lm2_v3_reflect_f32(v, normal)`	3D reflection

Projection

Project vector a onto vector b.

Function	Description
`lm2_v2_project_f32(a, b)`	2D projection
`lm2_v3_project_f32(a, b)`	3D projection

Conversions

See also the vector conversion functions in lm2_vector_conversions.h:

Type conversions: lm2_v2_f32_to_i32(v), lm2_v3_f64_to_f32(v), etc.
Upcast: lm2_v2_upcast_f32(v, z) — v2 to v3 by adding z component
Downcast: lm2_v3_downcast_f32(v) — v3 to v2 by dropping z component

Example

lm2_v3_f32 forward = lm2_v3_make_f32(0, 0, -1);
lm2_v3_f32 normal  = lm2_v3_make_f32(0, 1, 0);

// Reflect off a surface
lm2_v3_f32 bounce = lm2_v3_reflect_f32(forward, normal);

// Project onto a plane normal
lm2_v3_f32 projected = lm2_v3_project_f32(forward, normal);

// Angle between vectors
float angle = lm2_v3_angle_f32(forward, normal); // ~1.5708 (PI/2)