Double dispatch/multimethods in C++

I have a question on C++ double dispatch. In the code below, I want the results from the second set to match the results from the first set.

I don't know the actual type (unless I try dynamic_cast) but I do know that the object inherited from the BaseClass type. What is the most efficient (performance-wise) way to accomplish this?

After googling around for a while I found out about double dispatch and the loki multimethods. The problem I have with the Shape examples is that in my application, Processor and BaseClass are entirely independent and don't have a common method that they can call in each other. Secondly, there is only one Processor (i.e. nothing inherits from it).

Thanks for any help.

#include <iostream>
#include <string>
using namespace std;

class BaseClass{
public:
       BaseClass(){}
       virtual void myFunction(){cout << "base myFunction called" << endl;}
};

class Derived1: public BaseClass{
public:
       Derived1():BaseClass(){}
       void myFunction(){cout << "Derived1 myFunction called" << endl;}
};


class Derived2: public BaseClass{
public:
       Derived2():BaseClass(){}
       void myFunction(){cout << "Derived2 myFunction called" << endl;}
};

class Derived3: public BaseClass{
public:
       Derived3():BaseClass(){}
       void myFunction(){cout << "Derived3 myFunction called" << endl;}

};

class Processor{
public:
       Processor(){}
       virtual void processObj(BaseClass* bc){cout << "got a base object" << endl; bc->myFunction();}
       virtual void processObj(Derived1* d1){cout << "got a derived1 object" << endl; d1->myFunction();}
       virtual void processObj(Derived2* d2){cout << "got a derived2 object" << endl; d2->myFunction(); }
};


int main() {
   BaseClass *bcp=new BaseClass();
   Derived1 *dc1p=new Derived1();   
   Derived2 *dc2p=new Derived2();
   Derived3 *dc3p=new Deri