Basic usage

One header covers the library. A translation unit can also include a single module (vecmat/vec.h, vecmat/mat.h, vecmat/quat.h).

#include <vecmat.h>

Values are plain C structs, passed and returned by copy. Components are named fields (.x / .y / .z / .w, or m11, m21, …) and a flat .v[]. Layout is column-major. Angles on unsuffixed APIs are radians; VM_DEG(90) converts a degree literal.

vector3 p = vec3(1.0f, 2.0f, 3.0f);
p.v[1] = 0.0f;          /* same as p.y */

matrix3 mat = mat3_identity();
mat.v[0] = 1.0f;        /* same as mat.m11 */

vector4 and matrix4 are the translation unit's float width. Define VECMAT_USE_F64 before the include to take the 64-bit symbols. Integer vectors (vector2i, vector3i, vector4i) use vm_int_t, chosen when the library is built.

Hot loops use the _ptr form. The by-value helpers call those.

vector3 a = vec3(1.0f, 0.0f, 0.0f);
vector3 b = vec3(0.0f, 1.0f, 0.0f);
vector3 c = vec3_add(a, b);

vector3 out;
vec3_add_ptr(&out, &a, &b);

Putting the pieces together

A renderer, a solver, and a particle step are the same types. The pages below show each layer on its own. This is the usual split:

Frame data stays in vector3 / matrix4 / quaternion. See Vector usage and Matrix usage.
A camera is mat4_look_at_* times mat4_perspective_*. A model matrix is mat4_trs, or a 3×3 packed into a 4×4 with mat4_from_mat3.
A batch of samples is vm_gemm or a heap vm_mat. See Numerics extras.
A particle step is vm_euler_semi or vm_verlet on length-n arrays.

An affine model matrix from a rotation and a translation, without writing the 16 stores by hand:

const quaternion spin = quat_from_axis_angle(vec3(0.0f, 1.0f, 0.0f), VM_DEG(90.0));
const matrix4 model = mat4_trs(vec3(2.0f, 0.0f, 0.0f), spin, vec3_one());
const vector3 world = mat4_mul_vec3(model, vec3(1.0f, 0.0f, 0.0f), 1.0f);

The same packing, if the linear part is already a matrix3:

void affine_matrix(matrix4 *out, const matrix3 *linear, const vector3 *translation)
{
    *out = mat4_from_mat3(*linear);
    out->m14 = translation->x;
    out->m24 = translation->y;
    out->m34 = translation->z;
}