PHP Exercises: Compute the area of the polygon

Last update on December 20 2024 10:24:16 (UTC/GMT +8 hours)

A convex polygon is a simple polygon in which no line segment between two points on the boundary ever goes outside the polygon. Equivalently, it is a simple polygon whose interior is a convex set. In a convex polygon, all interior angles are less than or equal to 180 degrees, while in a strictly convex polygon all interior angles are strictly less than 180 degrees.
Write a PHP program that compute the area of the polygon . The vertices have the names vertex 1, vertex 2, vertex 3, ... vertex n according to the order of edge connections. However, n is 3 or more and 20 or less. You can also use the following formula to calculate the area S from the lengths a, b, and c of the triangle's three sides.

Input: Multiple character strings are given. One string is given per line

Pictorial Presentation:

Input:
Input is given in the following format.
x1 , y1
x2 , y2
:
xn , yn
xi , yi are real numbers representing the x and y coordinates of vertex i , respectively.

Sample Solution:

PHP Code:

<?php
// Call the calc function to initiate the program
calc();

// Function to calculate the area of a polygon using the Shoelace formula
function calc() {
    // Initialize an array to store Point objects
    $points = array();

    // Read input from standard input (stdin) and create Point objects
    while ($line = trim(fgets(STDIN))) {
        list($x, $y) = explode(',', $line);
        $points[] = new Point($x, $y);
    }

    // Initialize variables for the sum and the origin point
    $sum = 0;
    $o = $points[0];

    // Loop through the points to calculate the area of the polygon
    for ($i = 1; $i < count($points) - 1; $i++) {
        $p1 = $points[$i];
        $p2 = $points[$i+1];

        // Create a Triangle object using the origin and two consecutive points
        $T = new Triangle($o, $p1, $p2);

        // Add the area of the triangle to the total sum
        $sum += $T->getArea();
    }

    // Display the calculated area of the polygon
    echo "Area of the polygon:\n";
    echo $sum . "\n";
}

// Class representing a Triangle with three Point objects
class Triangle {
    public $A, $B, $C;
    public $a, $b, $c;

    // Constructor to initialize the Triangle with three Point objects
    public function __construct(Point $A, Point $B, Point $C) {
        $this->A = $A;
        $this->B = $B;
        $this->C = $C;

        // Calculate the lengths of the sides of the triangle
        $this->a = $B->distanceFrom($C);
        $this->b = $C->distanceFrom($A);
        $this->c = $A->distanceFrom($B);
    }

    // Method to calculate the area of the triangle using Heron's formula
    public function getArea() {
        $z = ($this->a + $this->b + $this->c) / 2;
        return sqrt($z * ($z - $this->a) * ($z - $this->b) * ($z - $this->c));
    }
}

// Class representing a Point with x and y coordinates
class Point {
    public $x, $y;

    // Constructor to initialize the Point with x and y coordinates
    public function __construct($x, $y) {
        $this->x = $x;
        $this->y = $y;
    }

    // Method to calculate the distance between two Point objects
    public function distanceFrom(Point $p) {
        $dx = $this->x - $p->x;
        $dy = $this->y - $p->y;
        return sqrt($dx * $dx + $dy * $dy);
    }
}
?>

Explanation:

Initialize Calculation:

The calc() function is called to start the program.

Define calc() Function:

Creates an empty $points array to store Point objects representing the polygon vertices.
Reads each line from input, splits it into x and y coordinates, and adds a Point object to $points.

Polygon Area Calculation:

Initializes $sum to store the total area of the polygon.
Uses the Shoelace formula by treating the polygon as a series of triangles from a fixed origin ($o = $points[0]).
Loops through pairs of points to form triangles between the origin point ($o) and each pair of consecutive vertices ($p1, $p2).
Creates a Triangle object for each triangle and adds its area (computed with getArea()) to $sum.

Output the Result:

Outputs the calculated area of the polygon.

Triangle Class:

Represents a triangle with points A, B, and C.
Calculates the side lengths ($a, $b, $c) using the distanceFrom method from Point class.
Computes the triangle’s area using Heron’s formula in the getArea() method.

Point Class:

Stores x and y coordinates for a point in the 2D plane.
distanceFrom() method calculates the Euclidean distance between two points.

Sample Input:
1.0, 0.0
0.0, 0.0
1.0, 1.0
2.0, 0.0
-1.0, 1.0

Sample Output:

Area of the polygon:
1.5

Flowchart:

PHP Code Editor:

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