You will write a library of static methods that performs various geometric transforms on polygons. Mathematically, a polygon is defined by its sequence of vertices (x0, y0), (x1, y1), (x2, y2), …. In Java, we will represent a polygon by storing the x- and y-coordinates of the vertices in two parallel arrays x[] and y[]. For example: // a polygon with these four vertices: // (0, 0), (1, 0), (1, 2), (0, 1) double x[] = { 0, 1, 1, 0 }; double y[] = { 0, 0, 2, 1 }; // Draw the polygon StdDraw.polygon(x, y); Transform2D.java Write a two-dimensional transformation library Transform2D.java by implementing the following API: public class Transform2D { // 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) } Requirements The API expects the angles to be in degrees, but Java's trigonometric functions take the arguments in radians. Use Math.toRadians() to convert from degrees to radians. The transformation methods scale(), translate(), and rotate() mutate the arrays, while copy() returns a new array. The main method must test each method of the Transform2D library. In other words, you must call each Transform2D method from main. You should experiment with various data so you are confident that your methods are implemented correctly. You can assume the following about the inputs: the arrays passed to scale(), translate(), and rotate() are not null, are the same length, and do not contain the values NaN, Double.POSITIVE_INFINITY, or Double.NEGATIVE_INFINITY. The array passed to copy() is not null. The values for the parameters alpha, theta, dx, and dy are not NaN, Double.POSITIVE_INFINITY, or Double.NEGATIVE_INFINITY.

Question

You will write a library of static methods that performs various geometric transforms on polygons. Mathematically, a polygon is defined by its sequence of vertices (x0, y0), (x1, y1), (x2, y2), …. In Java, we will represent a polygon by storing the x- and y-coordinates of the vertices in two parallel arrays x[] and y[]. For example:

// a polygon with these four vertices:

// (0, 0), (1, 0), (1, 2), (0, 1)

double x[] = { 0, 1, 1, 0 };

double y[] = { 0, 0, 2, 1 };

// Draw the polygon

StdDraw.polygon(x, y);

Transform2D.java

Write a two-dimensional transformation library Transform2D.java by implementing the following API:

public class Transform2D {

// 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)

}

Requirements

The API expects the angles to be in degrees, but Java's trigonometric functions take the arguments in radians. Use Math.toRadians() to convert from degrees to radians.
The transformation methods scale(), translate(), and rotate() mutate the arrays, while copy() returns a new array.
The main method must test each method of the Transform2D library. In other words, you must call each Transform2D method from main. You should experiment with various data so you are confident that your methods are implemented correctly.
You can assume the following about the inputs: the arrays passed to scale(), translate(), and rotate() are not null, are the same length, and do not contain the values NaN, Double.POSITIVE_INFINITY, or Double.NEGATIVE_INFINITY.
The array passed to copy() is not null.
The values for the parameters alpha, theta, dx, and dy are not NaN, Double.POSITIVE_INFINITY, or Double.NEGATIVE_INFINITY.