getPixel Function Runtime - Quadtree Data Structure (C++)

Question

so for a class I am supposed to create a function that gets a pixel given an x and y value from a node in my Quadtree, and in this case it represents and PNG image. This function needs to be O(logn). I am just looking for suggestions on how I could possibly improve my run time. Thank you!

RGBAPixel Quadtree::getPixel(int x, int y) const{
   if(root != NULL && x <= root->resolution && y <= root->resolution){
    return getPixel(x, y, root);
    }

    return RGBAPixel();
}

//getPixel helper function
RGBAPixel Quadtree::getPixel(int x, int y, QuadtreeNode * root) const{
    //base case, resolution reaches 1 it returns element
    if((root->x == x && root->y == y && root->resolution ==1) || root->nwChild == NULL){
    return root->element;
    }

    //if statements to see if x and y are within a specific child
    if(range(x, y, root->nwChild)){
        return getPixel(x, y, root->nwChild);
    }
    else if(range(x, y, root->neChild)){
        return getPixel(x, y, root->neChild);
    }
    else if(range(x, y, root->swChild)){
        return getPixel(x, y, root->swChild);
    }
    else{
        return getPixel(x , y, root->seChild);
    }

}

//getPixel helper function (returns weather or not x and y lies within a specific child passed by previous helper fucntion
bool Quadtree::range(int x, int y, QuadtreeNode * root) const{
    int xr = root->x + root->resolution;
    int yr = root->y + root->resolution;

    return ((x >= root->x && x < xr) && (y >= root->y && y < yr));
}