Hi guys!

So I have a 3D vector representing the direction a object is facing in my game engine, I calculate this direction by multiplying the objects rotation (which is a quaternion) by a vector which represents forwards (in my case: (0, 0, -1)). However the way I have modelled all the objects in my game engine is via a scene graph where each object can have a parent object. Each object has a local transformation which is relative to its parents transformation.

Each frame I recursively go though each object in the scene graph and calculate the transform matrix (posMatrix * rotMatrix * scaleMatrix) and save this for each object. In the case that the object is a child of another objects then i also multiply the transform matrix by the parents transform matrix, and I am able to get the correct hierarchy transformation in world space coordinates.

However I am having issues with calculating the direction a object is facing while maintaining the hierarchy. I found one solution which works but it is not very efficient, this was:

glm::quat Entity::getRotation(void)
{
  if (parentEntity == NULL) {
    return transform.getRotation();
  } else {
    return parentEntity->getRotation() * transform.getRotation();
  }
}

glm::vec3 Entity::getDirection(void)
{
  if (parentEntity == NULL) {
    return transform.getDirection();
  } else {
    return getRotation() * glm::vec3(0, 0, -1);
  }
}
 

I dont like this solution as I feel there must be a more efficient way to just reuse the parents world transformation matrix that I already calculate to transform this direction vector for me.

I have tried something like this, but it doesn't seem to work correctly:

glm::vec3 Transform::getDirection(void)
{
  return getRotation() * glm::vec3(0, 0, -1);
}

glm::vec3 Entity::getDirection(void)
{
  if (parentEntity == NULL) {
    return transform.getDirection();
  } else {
    return glm::quat_cast(parentEntity->worldMatrix) * transform.getDirection();
  }
}

... there must be a more efficient way to just reuse the parents world transformation matrix ...

If W_n is the world matrix of the model from which the viewing vector is of interest, so that

W_n := M₀ * M₁ * ... * M_n

and transform the model local viewing vector with it to yield in its world space equivalent

v_n' := W_n * v_n w/ v_n := (0 0 -1)^t

then you effectively have picked the 3rd column of W_n and negated it (see that any influence of the 1st and 2nd columns is avoided due to the both zeros in the vector, that the 3rd element in the vector has the absolute value of 1 so does not scale the result).

Thanks got it!

I ended up doing this for anyone interested:

glm::vec3 Entity::getDirection(void)
{
  if (parentEntity == NULL) {
    return transform.getDirection();
  } else {
    return glm::normalize(glm::vec3(parentEntity->worldMatrix * glm::vec4(transform.getDirection(), 0)));
  }
}

I think I made the mistake where my vectors representing directions did not have a 4th component of 0 and were being translated. Also I needed to normalise the vector as scaling was affecting the magnitude.