rite a library of static methods that performs various geometric transforms on polygons. Mathematically, a polygon is defined by its sequence of vertices (x0, y 0), (x 1, y 1), (x 2, y 2), …. In Java, we will represent a polygon by storing the x– and y-coordinates of the vertices in two parallel arrays x[] and y[]. Three useful geometric transforms are scale, translate and rotate. Scale the coordinates of each vertex (x i, y i) by a factor α. x‘i = α xi y‘i = α yi Translate each vertex (x i, y i) by a given offset (dx, dy). x‘i = xi + dx y‘i = yi + dy Rotate each vertex (x i, y i) by θ degrees counterclockwise, around the origin. x‘i = xi cos θ – yi sin θ y‘i = yi cos θ + xi sin θ 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) }

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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rite a library of static methods that performs various geometric transforms on polygons. Mathematically, a polygon is defined by its sequence of vertices (x₀, y ₀), (x ₁, y ₁), (x ₂, y ₂), …. In Java, we will represent a polygon by storing the x– and y-coordinates of the vertices in two parallel arrays x[] and y[].

Three useful geometric transforms are scale, translate and rotate.

- Scale the coordinates of each vertex (x _i, y _i) by a factor α.
- x^‘_i = α x_i
- y^‘_i = α y_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) by θ degrees counterclockwise, around the origin.
- x^‘_i = x_i cos θ – y_i sin θ
- y^‘_i = y_i cos θ + x_i sin θ

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) }

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