DSBA Introduction to Programming // Workshops 15+

Spring semester 2022/23

Useful resource about operators: https://en.cppreference.com/w/cpp/language/expressions

Exercise 1. Building the class Vector3D

Create a class Vector3D that represents a three-dimensional point (x,y,z) in the Cartesian space, and complete the class methods, as well as operator overloads, as indicated in each of the tasks below.

class Vector3D
{
public:
    /* class methods */
private:
    /* attributes */
    double _x;
    double _y;
    double _z;
};

Task 1 – Empty Constructor

Create the empty constructor Vector3D() where every attribute is set to 0.0. (_x = 0.0, _y = 0.0 and _z = 0.0).

Task 2 – Constructor with Arguments

Create the constructor Vector3D(double x, double y, double z) that sets every attribute of the vector according to the arguments (_x = x, _y = y, _z = z).

Task 3 – Copy Constructor

Create the constructor Vector3D(const Vector3D& v2) that sets every attribute of the vector according to the attributes of an input vector v2 (for example, _x = v2._x )

Task 4 – getters/setters

For every attribute of the vector, write a method that returns the attribute (a getter) and a method that sets the value of the attribute according to a given argument (a setter).
For example, for attribute _x you should do:

// getter
double getX() const
{
    return x;
}

// setter
void setX(double x)
{
    _x = x;
}

Then, you should write a similar getter and a similar setter for attributes _y and _z.

Task 5 – Overload the + operator

Create the overload of the operator + as follows: Vector3D operator+ (const Vector3D& v1, Vector3D& v2),
where you should return a new vector v3 whose attributes will be the sum of v1 and v2’s attributes.

For example for v3._x, you can implement it as: v3.setX( v1.getX() + v2.getX() ); or v3.x = v1.x + v2.x;.

Task 6 – Overload the * operator

Create the overload of the operator * as follows: double operator* (const Vector3D& v1, Vector3D& v2) where you should return the dot product between vectors v1 and v2.

Task 7 – Overload the * operator (another version!)

Create the overload of the operator * as follows: Vector3D operator* (const Vector3D& v1, double d) where you should return a new vector v2 whose attributes will be multiplication of every attribute of v2 by d For example, for v2._x you can implement it as:
v2.setX( v1.getX() * d );

Task 8 – Vector magnitude

Create a member function double magnitude() to get the magnitude of the Vector3D defined as:

$$ \sqrt{x^2 + y^2 + z^2} $$

Task 9 – Overload the < operator

Overload the operator < as follows: bool operator<(const Vector3D& v1, const Vector3D& v2), where:
vector v1 < vector v2 if and only if v1.magnitude() < v2.magnitude().

Task 10 – Overload the << operator

Overload the print operation << for a Vector3D to print a vector in the terminal in format (x, y, z)
For example, if we have a vector with attributes _x = 3.4, _y = 1.0, _z = -1.4, then you print in the terminal

(3.4, 1.0, -1.4)

Task 11 – Overload the >> operator

Overload the read operation >> for a Vector3D to read a vector from the terminal.
For example, if the user puts in the terminal 3.4 1.0 -1.4, then you create an object Vector3D with attributes _x = 3.4, _y = 1.0, _z = -1.4.

Exercise 2. Using the class Vector3D

Part 1

Create a container std::multiset<Vector3D> s and add 100 Vector3D objects to this container. The attributes _x, _y and _z should be random numbers generated in the interval [-1.0, 1.0].

For generating random real numbers you may use the class std::uniform_real_distribution - https://www.cplusplus.com/reference/random/uniform_real_distribution/

Part 2

Print all elements stored in the container s using the overloaded operator.

Part 3

Calculate and print the average magnitude of all vectors contained in s.