const Vec3 forward = normalized(target - eye);

const Vec3 right = normalized(cross(forward, up));

const Vec3 vertical = cross(right, forward);

if (!finite(eye) || !finite(target) || !finite(up) || length(right) < 0.5f)

throw std::invalid_argument("camera eye/target/up do not define a view");

Mat4 m = Mat4::identity();

m.m[0][0] = right.x;

m.m[0][1] = right.y;

m.m[0][2] = right.z;

m.m[0][3] = -dot(right, eye);

m.m[1][0] = vertical.x;

m.m[1][1] = vertical.y;

m.m[1][2] = vertical.z;

m.m[1][3] = -dot(vertical, eye);

m.m[2][0] = -forward.x;

m.m[2][1] = -forward.y;

m.m[2][2] = -forward.z;

m.m[2][3] = dot(forward, eye);

return m;

if (!(fov > 0 && fov < 3.14159f && aspect > 0 && near_plane > 0 && far_plane > near_plane) ||

!std::isfinite(aspect) || !std::isfinite(far_plane))

throw std::invalid_argument("invalid perspective parameters");

const float f = 1 / std::tan(fov / 2);

Mat4 m;

m.m[0][0] = f / aspect;

m.m[1][1] = f;

m.m[2][2] = -(far_plane + near_plane) / (far_plane - near_plane);

m.m[2][3] = -2 * far_plane * near_plane / (far_plane - near_plane);

m.m[3][2] = -1;

return m;

if (!(clip.w > 0))

throw std::invalid_argument("perspective divide requires positive w");

return {(clip.x / clip.w + 1) * static_cast<float>(width) / 2,

(clip.y / clip.w + 1) * static_cast<float>(height) / 2, (clip.z / clip.w + 1) / 2};