method to get orthonormal basis without normalization by Jeppe Revall Frisvad (jrf@imm.dtu.dk)

fast_orho_basis.c

void getBasis(const vec3 &n, vec3 &t, vec3 &b) {
    if (n.z < -0.9999999f) {
        t = vec3( 0.0f, -1.0f, 0.0f);
        b = vec3(-1.0f,  0.0f, 0.0f);
        return;
    }
    const float x = 1.0f / (1.0f + n.z);
    const float y = -n.x*n.y*x;
    t = vec3(1.0f - n.x*n.x*x, y, -n.x);
    b = vec3(b, 1.0f - n.y*n.y*x, -n.y);
}