Creating my own Iterators

/EDIT: I see, an own iterator is actually necessary here (I misread the question first). Still, I'm letting the code below stand because it can be useful in similar circumstances.

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Is an own iterator actually necessary here? Perhaps it's sufficient to forward all required definitions to the container holding the actual Points:

// Your class `Piece`
class Piece {
private:
    Shape m_shape;

public:

    typedef std::vector<Point>::iterator iterator;
    typedef std::vector<Point>::const_iterator const_iterator;

    iterator begin() { return m_shape.container.begin(); }

    const_iterator begin() const { return m_shape.container.begin(); }

    iterator end() { return m_shape.container.end(); }

    const_iterator end() const { return m_shape.const_container.end(); }
}

This is assuming you're using a vector internally but the type can easily be adapted.

You should use Boost.Iterators. It contains a number of templates and concepts to implement new iterators and adapters for existing iterators. I have written an article about this very topic; it's in the December 2008 ACCU magazine. It discusses an (IMO) elegant solution for exactly your problem: exposing member collections from an object, using Boost.Iterators.

If you want to use the stl only, the Josuttis book has a chapter on implementing your own STL iterators.