Question

In other words, given a base class shape and a derived class rectangle:

class shape
{
public:
  enum shapeType {LINE, RECTANGLE};
  shape(shapeType type);
  shape(const shape &shp);
}

class rectangle : public shape
{
public:
  rectangle();
  rectangle(const rectangle &rec);
}

I’d like to know if I could create an instance of rectangle by calling:

shape *pRectangle = new shape(RECTANGLE);

and how could I implement the copy constructor, in order to get a new rectangle by calling:

shape *pNewRectangle = new shape(pRectangle);

Answer 1

Short Answer: No

Long Answer:

You need a factory object/method.
You can add a static factory method to the base class the creates the appropriate object type.

class Shape
{
    static Shape* createShape(shapeType type)
    {
        switch (type)
        {
             case RECTANGLE:return new rectangle();
           ...
        }
    }
 }; 

Personal preference:

I would go with a completely different class to be the factory rather than using a static method on the base class. The reason for this is that every time you create a new Shape class the above style forces you to re-build the Shape class each time.

So I would separator out the factory into a ShapeFactory class.