Correctly implementing inheritance

Question

Given following classes:

class Geometry {
  public:
    double distanceBetweenGeometries(const Geometry& g);
  private:        
    Shape myShape;
};

class Shape {
  public:
    double distance(const Shape& s1, const Shape& s2);
};

class Rectangle : public Shape {
  private:
    double i,j,length,width;
};

class Circle : public Shape {
  private:
    double i,j,radius;
};

So each geometry got a shape of type Rectangle or Circle. In my program I need to calculate the (Euclidean) distance between two geometries. Thus, given two geometries g1 and g2 I call

g1.distanceBetweenGeometries(g2);

and I want to return the distance between g1.myShape and g2.myShape.

I already know how to calculate the distance between two rectangles, two circles or between a rectangle and a circle. Somehow, I did not achieve an object-orientated solution for implementing the distance-function.

My idea is: Call the distance-function from a given geometry. This distance function calls the distance-function of a shape. In Shape::distance(..) I somehow need to differentiate of which type s1 and s2 are. Afterwards, I have to choose the correct mathematical formula to compute the distance between them. Can you tell me if my inheritance-idea is adequate here and how to implement the Shape::distance(..) function so that it can automatically determine which formula is requested for distance-computation?

Answer 1

You may do something like:

class Circle;
class Rectangle;

// Your existing methods to do the real computation:
double distanceRC(const Rectangle&, const Circle&);
double distanceRR(const Rectangle&, const Rectangle&);
double distanceCC(const Circle&, const Circle&);

class Shape {
public:
    virtual ~Shape() = default;
    virtual double distanceWith(const Shape&) const = 0;
    virtual double distanceWith(const Rectangle&) const = 0;
    virtual double distanceWith(const Circle&) const = 0;
};

class Rectangle : public Shape {
public:
    double distanceWith(const Shape& s) const override { return s.distanceWith(*this); }
    double distanceWith(const Rectangle& r) const override { return distanceRR(*this, r);}
    double distanceWith(const Circle& c) const override { return distanceRC(*this, c); }
private:
    double i,j,length,width;
};

class Circle : public Shape {
public:
    double distanceWith(const Shape& s) const override { return s.distanceWith(*this); }
    double distanceWith(const Rectangle& r) const override { return distanceRC(r, *this);}
    double distanceWith(const Circle& c) const override { return distanceCC(*this, c); }
private:
    double i,j,radius;
};