rite a library of static methods that performs various geometric transforms on polygons . Mathematically, a polygon is defined by its sequence of vertices ( x 0 , y 0 ), ( x 1 , y 1 ), ( x 2 , y 2 ),...

rite a library of static methods that performs variousgeometric transforms onpolygons. Mathematically, a polygon is defined by its sequence of vertices (x
₀,y₀), (x₁,y₁), (x₂,y₂), …. In Java, we will represent a polygon by storing thex– andy-coordinates of the vertices in two parallel arrays x[] and y[].

Three useful geometric transforms arescale,translate androtate.

• 
  
  
  
  • 
    Scale the coordinates of each vertex (x
    _i
    ,y
    _i
    ) by a factor α.
  
  
  • 
    x
    ^‘
    _i = αx
    _i
    
  
  
  • 
    y
    ^‘
    _i = αy
    _i
    
  
  
  • 
    Translate each vertex (x
    _i
    ,y
    _i
    ) by a given offset (dx,dy).
  
  
  • 
    x
    ^‘
    _i =x
    _i +dx
    
  
  
  • 
    y
    ^‘
    _i =y
    _i +dy
    
  
  
  • 
    Rotate each vertex (x
    _i
    ,y
    _i
    ) byθ degrees counterclockwise, around the origin.
  
  
  • 
    x
    ^‘
    _i =x
    _i cosθ –y
    _i sinθ
    
  
  
  • 
    y
    ^‘
    _i =y
    _i cosθ +x
    _i sinθ
    
  
  
  
  

Write a two-dimensional transformation library by implementing the following API:

public class PolygonTransform {

// Returns a new array object that is an exact copy of the given array. // The given array is not mutated.

public static double[] copy(double[] array)

// Scales the polygon by the factor alpha.

public static void scale(double[] x, double[] y, double alpha)

// Translates the polygon by (dx, dy).

public static void translate(double[] x, double[] y, double dx, double dy)

// Rotates the polygon theta degrees counterclockwise, about the origin.public static void rotate(double[] x, double[] y, double theta)

// Tests each of the API methods by directly calling them.

public static void main(String[] args)}