Objective

Write a java program about the topic Scalar multiplication of a point in object-oriented program.

The Theory 

Scalar multiplication of a point is a mathematical operation performed on a point in object-oriented programming, specifically in the context of geometric objects or vector spaces. It involves multiplying the coordinates of a point by a scalar value, resulting in a new point with modified coordinates. 

Sample examples are given below. 

1. public class Point{ 
2.  private int x; 
3.  private int y; 
4.  Point() { 
5.   this.x = 0; 
6.   this.y = 0; 
7.  } 
8.  Point(int xInit, int yInit) { 
9.   this.x = xInit; 
10.   this.y = yInit; 
11.  } 
12.  private void setX(int xCoord) { 
13.   this.x = xCoord; 
14.  } 
15.  private void setY(int yCoord) { 
16.   this.y = yCoord; 
17.  } 
18.  private int getX() { 
19.   return this.x; 
20.  } 
21.  private int getY() { 
22.   return this.y; 
23.  } 
24.  private void print() { 
25.   System.out.println("(" + this.x + "," + this.y+ ")"); 
26.  } 
27.  private boolean isOrigin() { 
28.   if((this.x==0)&&(this.y==0)) 
29.    return true; 
30.   else 
31.    return false; 
32.  } 
33.  public int whichQuadrant() { 
34.   if(isOrigin()) 
35.    return "origin"; 
36.   else if((this.x < 0)&&(this.y < 0)) 
37.    return "quadrant 3"; 
38.   else if((this.x < 0)&&(this.y == 0)) 
39.    return "-ve X-Axis"; 
40.   else if((this.x == 0)&&(this.y < 0)) 
41.    return "-ve Y-Axis"; 
42.   else if((this.x > 0)&&(this.y > 0)) 
43.    return "quadrant 1"; 
44.   else if((this.x > 0)&&(this.y < 0)) 
45.    return "quadrant 4"; 
46.   else if((this.x < 0)&&(this.y > 0)) 
47.    return "quadrant 2"; 
48.   else if((this.x > 0)&&(this.y == 0)) 
49.    return "+ve X-Axis"; 
50.   else if((this.x == 0)&&(this.y > 0)) 
51.    return "+ve Y-Axis"; 
52.  } 
53.  public void scalarMultiply(int c) { 
54.   x = c * x; 
55.   y = c * y; 
56.  } 
57.  public void scalarMultiplyNonMutable(int c) { 
58.   Point s = new Point(c*x,c*y); 
59.   return s; 
60.  } 
61. } 
62. public class Driver { 
63.  public static void main(String[]){ 
64.   Point p0 = new Point(3,8); 
65.   p0.scalarMultiply(5); 
66.   p0.print(); 
67.   Point p1 = new Point(4,5); 
68.   Point q = p1.scalarMultiplyNonMutable(6); 
69.   q.print(); 
70.  } 
71. } 

The above code is written in Java and consists of two classes: Point and Driver. Let's break down the code step by step: 

Point class: 

• The Point class represents a point in a two-dimensional coordinate system. 
• It has two private instance variables, x and y, which store the coordinates of the point. 
• The class provides two constructors: a default constructor (Point()) that initializes the point at the origin (0, 0), and a parameterized constructor (Point(int xInit, int yInit)) that allows you to initialize the point with specific coordinates. 
• Private methods like setX(), setY(), getX(), and getY() are provided to manipulate and retrieve the x and y values. 
• The print() method is used to display the coordinates of the point in the format (x, y). 
• The isOrigin() method checks if the point is located at the origin (0, 0) and returns a boolean value. 
• The whichQuadrant() method determines in which quadrant the point is located or if it lies on the axes, and returns a string representing the quadrant or axis. 
• The scalarMultiply() method takes an integer c as a parameter and multiplies the x and y coordinates of the point by c, effectively scaling the point. 
• The scalarMultiplyNonMutable() method is similar to scalarMultiply(), but instead of modifying the coordinates of the existing point, it creates a new Point object s with the scaled coordinates and returns it. 

Driver class: 

• The Driver class contains the main() method, which serves as the entry point of the program. 
• Inside the main() method: 
• An instance of the Point class, p0, is created with initial coordinates (3, 8). 
• The scalarMultiply() method is called on p0, multiplying its coordinates by 5 and updating the values. 
• The print() method is called on p0 to display the updated coordinates. 
• Another instance of the Point class, p1, is created with initial coordinates (4, 5). 
• The scalarMultiplyNonMutable() method is called on p1, multiplying its coordinates by 6 and creating a new Point object, q, with the scaled coordinates. 
• The print() method is called on q to display its coordinates. 
• The execution starts from the main() method in the Driver class, and the program creates points, performs operations on them, and prints the result.

Learning Outcomes 

• By implementing the scalar multiplication of a point in an object-oriented manner, the code becomes more structured, maintainable, and extensible. It allows for the creation of Point objects, encapsulates their data and behavior, and provides well-defined interfaces to manipulate and analyze the points, including scalar multiplication. 
• Problem-solving skills: Scalar multiplication of a point is often a key component in solving various computational problems, such as transforming shapes or implementing algorithms. By mastering this concept, you develop problem-solving skills that can be applied to a wide range of programming tasks.