glm

The library glm which stands for opengl mathematics is a mathematical library that pairs nicely with opengl. If you are working with glm in your project and also have bullet physics you'll note that that bullet provides us with LinearMath, which has many of the same things that glm provides.

Due to the above, it is useful to have a way to convert these objects back and forth:

glm::vec3 bulletToGlm(const btVector3& v) { return glm::vec3(v.getX(), v.getY(), v.getZ()); }
 
btVector3 glmToBullet(const glm::vec3& v) { return btVector3(v.x, v.y, v.z); }
 
glm::quat bulletToGlm(const btQuaternion& q) { return glm::quat(q.getW(), q.getX(), q.getY(), q.getZ()); }
 
btQuaternion glmToBullet(const glm::quat& q) { return btQuaternion(q.x, q.y, q.z, q.w); }
 
btMatrix3x3 glmToBullet(const glm::mat3& m) { return btMatrix3x3(m[0][0], m[1][0], m[2][0], m[0][1], m[1][1], m[2][1], m[0][2], m[1][2], m[2][2]); }
 
// btTransform does not contain a full 4x4 matrix, so this transform is lossy.
// Affine transformations are OK but perspective transformations are not.
btTransform glmToBullet(const glm::mat4& m)
{
    glm::mat3 m3(m);
    return btTransform(glmToBullet(m3), glmToBullet(glm::vec3(m[3][0], m[3][1], m[3][2])));
}
 
glm::mat4 bulletToGlm(const btTransform& t)
{
    glm::mat4 m(glm::mat4::_null);
    const btMatrix3x3& basis = t.getBasis();
    // rotation
    for (int r = 0; r < 3; r++)
    {
        for (int c = 0; c < 3; c++)
        {
            m[c][r] = basis[r][c];
        }
    }
    // traslation
    btVector3 origin = t.getOrigin();
    m[3][0] = origin.getX();
    m[3][1] = origin.getY();
    m[3][2] = origin.getZ();
    // unit scale
    m[0][3] = 0.0f;
    m[1][3] = 0.0f;
    m[2][3] = 0.0f;
    m[3][3] = 1.0f;
    return m;
}