Final Exam 2-2: Compute Object Area (15%)

• Inputs: The gemoetry object.
  1. The first line of the input contains the type of the object and the number of points.
     1. The type of the object is one of the following:
        1. point: a point.
        2. circle: a circle, which is defined by two points, center of the circle and a point on the circle.
        3. triangle: a triangle, which is defined by three points.
        4. rectangle: a rectangle, which is defined by two points.
     2. The number of points is an int between (1) and (100).
  2. The remaining lines of the input contain the coordinates of the points.
     1. The coordinates of the points are double between (-100) and (100).
     2. The order of the points is always counter-clockwise or down to up.
• Outputs:
  1. The type of the object, the number of points, the coordinates of the points, and the area of the object.
     1. The format is shown below.
     2. The coordinates of the points are in defualt double format in std::cout.
     3. The area of the object is in double format in std::cout.
  2. If the object is invalid, the output is Invalid Object and exit.
     1. If the coordinates of the points are out of the range.
     2. If the number of points is not equal to the defined number.
     3. If the type of the object is not one of the defined types.
     4. If the coordinates of the points are not in the order of counter-clockwise.
• File name: final2_2_<student_id>.cpp (e.g. final2_2_106062802.cpp)

Notice：

• The program will not print any user prompts.
• The program should use functions to process the input and output.
• The program should define structures to store the data of the objects.
• The program should be finished within 30 seconds. Any test cases will garuntee the program is finished within 30 second

Format

<type> <number_of_points>⏎
<x_1> <y_1>⏎
...
<x_n> <y_n>⏎
Object Type: <type>
Number of Points: <number_of_points>
Points: (<x_1>, <y_1>), ..., (<x_n>, <y_n>)
Area: <area>

Example

$ ./a.out⏎
point 1⏎
0.0 0.0⏎
Object Type: point
Number of Points: 1
Point: (0, 0)
Area: 0
$ ./a.out⏎
circle 2⏎
0.0 0.0⏎
1.0 1.0⏎
Object Type: circle
Number of Points: 2
Point: (0, 0), (1, 1)
Area: 6.28319
$ ./a.out⏎
triangle 3⏎
0.0 0.0⏎
2.0 0.0⏎
1.0 1.0⏎
Object Type: triangle
Number of Points: 3
Point: (0, 0), (2, 0), (1, 1)
Area: 1
$ ./a.out⏎
rectangle 2⏎
0.0 0.0⏎
1.0 2.0⏎
Object Type: rectangle
Number of Points: 2
Point: (0, 0), (1, 2)
Area: 2
$ ./a.out⏎
rectangle 3⏎
Invalid Object
$ ./a.out⏎
circle -1⏎
Invalid Object
$ ./a.out⏎
circle 2⏎
-100.1 -100.1⏎
1.0 1.0⏎
Invalid Object
$ ./a.out⏎
point 101⏎
Invalid Object
$ ./a.out⏎
square 2⏎
Invalid Object
$ ./a.out⏎
circle 2⏎
1.0 1.0⏎
-100.0 -100.0⏎
Invalid Object
$ ./a.out⏎
triangle 3⏎
0.0 0.0⏎
1.0 1.0⏎
2.0 0.0⏎
Invalid Object

Pseudo code

#include <iostream>
#include <vector>
#include <string>
#include <cmath>

using namespace std;

typedef struct Point_t
{
    double x;
    double y;
} Point;

typedef struct Triangle_t
{
    Point p[3];
} Triangle;

typedef struct Circle_t
{
    Point p[2];
} Circle;

typedef struct Rectangle_t
{
    Point p[2];
} Rectangle;

const double PI = 3.14159265358979323846;

// parse_header
// Parses the first line of the input.
void parse_header(string &type, int &number_of_points);
// parse_geometry
// Parses the list of points based on the type of geometry.
// Hint: check the number of points and the coordinates.
void parse_geometry(Point &p, const int &number_of_points);
void parse_geometry(Triangle &t, const int &number_of_points);
void parse_geometry(Circle &c, const int &number_of_points);
void parse_geometry(Rectangle &r, const int &number_of_points);
// check_geometry
// Checks if the geometry is valid.
bool check_geometry(const Point &p);
bool check_geometry(const Triangle &t);
bool check_geometry(const Circle &c);
bool check_geometry(const Rectangle &r);
// print_geometry
// Prints the geometry.
void print_geometry(const Point &p);
void print_geometry(const Triangle &t);
void print_geometry(const Circle &c);
void print_geometry(const Rectangle &r);
// print_point
// Prints the coordinates of a point.
void print_point(const Point &p);
// area_geometry
// Calculates the area of the geometry.
double area_geometry(const Point &p);
double area_geometry(const Triangle &t);
double area_geometry(const Circle &c);
double area_geometry(const Rectangle &r);

int main()
{
    string type;
    int number_of_points;

    parse_header(type, number_of_points);

    if (type == "point")
    {
        Point p;
        parse_geometry(p, number_of_points);
        print_geometry(p);
    }
    else if (type == "triangle")
    {
        Triangle t;
        parse_geometry(t, number_of_points);
        print_geometry(t);
    }
    else if (type == "circle")
    {
        Circle c;
        parse_geometry(c, number_of_points);
        print_geometry(c);
    }
    else if (type == "rectangle")
    {
        Rectangle r;
        parse_geometry(r, number_of_points);
        print_geometry(r);
    }
    else
    {
        cout << "Invalid Object" << endl;
        return EXIT_FAILURE;
    }
    return EXIT_SUCCESS;
}

Reference Code:

#include <iostream>
#include <vector>
#include <string>
#include <cmath>

using namespace std;

typedef struct Point_t
{
    double x;
    double y;
} Point;

typedef struct Triangle_t
{
    Point p[3];
} Triangle;

typedef struct Circle_t
{
    Point p[2];
} Circle;

typedef struct Rectangle_t
{
    Point p[2];
} Rectangle;

const double PI = 3.14159265358979323846;

// parse_header
// Parses the first line of the input.
void parse_header(string &type, int &number_of_points);
// parse_geometry
// Parses the list of points based on the type of geometry.
// Hint: check the number of points and the coordinates.
void parse_geometry(Point &p, const int &number_of_points);
void parse_geometry(Triangle &t, const int &number_of_points);
void parse_geometry(Circle &c, const int &number_of_points);
void parse_geometry(Rectangle &r, const int &number_of_points);
// check_geometry
// Checks if the geometry is valid.
bool check_geometry(const Point &p);
bool check_geometry(const Triangle &t);
bool check_geometry(const Circle &c);
bool check_geometry(const Rectangle &r);
// print_geometry
// Prints the geometry.
void print_geometry(const Point &p);
void print_geometry(const Triangle &t);
void print_geometry(const Circle &c);
void print_geometry(const Rectangle &r);
// print_point
// Prints the coordinates of a point.
void print_point(const Point &p);
// area_geometry
// Calculates the area of the geometry.
double area_geometry(const Point &p);
double area_geometry(const Triangle &t);
double area_geometry(const Circle &c);
double area_geometry(const Rectangle &r);

int main()
{
    string type;
    int number_of_points;

    parse_header(type, number_of_points);

    if (type == "point")
    {
        Point p;
        parse_geometry(p, number_of_points);
        print_geometry(p);
    }
    else if (type == "triangle")
    {
        Triangle t;
        parse_geometry(t, number_of_points);
        print_geometry(t);
    }
    else if (type == "circle")
    {
        Circle c;
        parse_geometry(c, number_of_points);
        print_geometry(c);
    }
    else if (type == "rectangle")
    {
        Rectangle r;
        parse_geometry(r, number_of_points);
        print_geometry(r);
    }
    else
    {
        cout << "Invalid Object" << endl;
        return EXIT_FAILURE;
    }
    return EXIT_SUCCESS;
}

void parse_header(string &type, int &number_of_points)
{
    cin >> type >> number_of_points;
}
void parse_geometry(Point &p, const int &number_of_points)
{
    if (number_of_points != 1)
    {
        cout << "Invalid Object" << endl;
        exit(EXIT_FAILURE);
    }
    for (int i = 0; i < number_of_points; i++)
    {
        cin >> p.x >> p.y;
    }
    if (!check_geometry(p))
    {
        cout << "Invalid Object" << endl;
        exit(EXIT_FAILURE);
    }
}
void parse_geometry(Triangle &t, const int &number_of_points)
{
    if (number_of_points != 3)
    {
        cout << "Invalid Object" << endl;
        exit(EXIT_FAILURE);
    }
    for (int i = 0; i < number_of_points; i++)
    {
        cin >> t.p[i].x >> t.p[i].y;
    }
    if (!check_geometry(t))
    {
        cout << "Invalid Object" << endl;
        exit(EXIT_FAILURE);
    }
}
void parse_geometry(Circle &c, const int &number_of_points)
{
    if (number_of_points != 2)
    {
        cout << "Invalid Object" << endl;
        exit(EXIT_FAILURE);
    }
    for (int i = 0; i < number_of_points; i++)
    {
        cin >> c.p[i].x >> c.p[i].y;
    }
    if (!check_geometry(c))
    {
        cout << "Invalid Object" << endl;
        exit(EXIT_FAILURE);
    }
}
void parse_geometry(Rectangle &r, const int &number_of_points)
{
    if (number_of_points != 2)
    {
        cout << "Invalid Object" << endl;
        exit(EXIT_FAILURE);
    }
    for (int i = 0; i < number_of_points; i++)
    {
        cin >> r.p[i].x >> r.p[i].y;
    }
    if (!check_geometry(r))
    {
        cout << "Invalid Object" << endl;
        exit(EXIT_FAILURE);
    }
}
bool check_geometry(const Point &p)
{
    if (p.x < -100.0 || p.y < -100.0 || p.x > 100.0 || p.y > 100.0)
    {
        return false;
    }
    return true;
}
bool check_geometry(const Triangle &t)
{
    for (int i = 0; i < 3; i++)
    {
        if (!check_geometry(t.p[i]))
        {
            return false;
        }
    }
    double ccw = (t.p[1].x - t.p[0].x) * (t.p[2].y - t.p[0].y) 
                - (t.p[2].x - t.p[0].x) * (t.p[1].y - t.p[0].y);
    return (ccw > 0);
}
bool check_geometry(const Circle &c)
{
    if (!check_geometry(c.p[0]) || !check_geometry(c.p[1]))
    {
        return false;
    };
    return (c.p[1].y > c.p[0].y);
}
bool check_geometry(const Rectangle &r)
{
    if (!check_geometry(r.p[0]) || !check_geometry(r.p[1]))
    {
        return false;
    }
    return (r.p[1].y > r.p[0].y);
}
void print_geometry(const Point &p)
{
    cout << "Object Type: point" << endl;
    cout << "Number of Points: 1" << endl;
    cout << "Point: ";
    print_point(p);
    cout << endl;
    cout << "Area: " << area_geometry(p) << endl;
}
void print_geometry(const Triangle &t)
{
    cout << "Object Type: triangle" << endl;
    cout << "Number of Points: 3" << endl;
    cout << "Point: ";
    for (int i = 0; i < 3; i++)
    {
        if (i != 0)
        {
            cout << ", ";
        }
        print_point(t.p[i]);
    }
    cout << endl;
    cout << "Area: " << area_geometry(t) << endl;
}
void print_geometry(const Circle &c)
{
    cout << "Object Type: circle" << endl;
    cout << "Number of Points: 2" << endl;
    cout << "Point: ";
    for (int i = 0; i < 2; i++)
    {
        if (i != 0)
        {
            cout << ", ";
        }
        print_point(c.p[i]);
    }
    cout << endl;
    cout << "Area: " << area_geometry(c) << endl;
}
void print_geometry(const Rectangle &r)
{
    cout << "Object Type: rectangle" << endl;
    cout << "Number of Points: 2" << endl;
    cout << "Point: ";
    for (int i = 0; i < 2; i++)
    {
        if (i != 0)
        {
            cout << ", ";
        }
        print_point(r.p[i]);
    }
    cout << endl;
    cout << "Area: " << area_geometry(r) << endl;
}
void print_point(const Point &p)
{
    cout << "(" << p.x << ", " << p.y << ")";
}
double area_geometry(const Point &p)
{
    return 0.0;
}
double area_geometry(const Triangle &t)
{
    double area = 0.0;
    for (int i = 0; i < 3; i++)
    {
        area += t.p[i].x * t.p[(i + 1) % 3].y - t.p[i].y * t.p[(i + 1) % 3].x;
    }
    return abs(area / 2.0);
}
double area_geometry(const Circle &c)
{
    double x_diff = c.p[1].x - c.p[0].x;
    double y_diff = c.p[1].y - c.p[0].y;
    double radius = sqrt(x_diff * x_diff + y_diff * y_diff);
    return PI * radius * radius;
}
double area_geometry(const Rectangle &r)
{
    return abs(r.p[0].x - r.p[1].x) * abs(r.p[0].y - r.p[1].y);
}

C++ References

1. unzip html-book-20201016.zip.
2. open html-book-20201016/reference/en/index.html.
3. Find what you want.