I have no idea how to do this problem Write 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[]. // Represents the polygon with vertices (0, 0), (1, 0), (1, 2), (0, 1). double x[] = { 0, 1, 1, 0 }; double y[] = { 0, 0, 2, 1 }; 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) } Note that the transformation methods scale(), translate() and rotate() mutate the polygons. Here are some example test cases (tests for copy() are not shown): // Scales polygon by the factor 2. StdDraw.setScale(-5.0, +5.0); double[] x = { 0, 1, 1, 0 }; double[] y = { 0, 0, 2, 1 }; double alpha = 2.0; StdDraw.setPenColor(StdDraw.RED); StdDraw.polygon(x, y); scale(x, y, alpha); StdDraw.setPenColor(StdDraw.BLUE); StdDraw.polygon(x, y); // Translates polygon by (2, 1). StdDraw.setScale(-5.0, +5.0); double[] x = { 0, 1, 1, 0 }; double[] y = { 0, 0, 2, 1 }; double dx = 2.0, dy = 1.0; StdDraw.setPenColor(StdDraw.RED); StdDraw.polygon(x, y); translate(x, y, dx, dy); StdDraw.setPenColor(StdDraw.BLUE); StdDraw.polygon(x, y); // Rotates polygon 45 degrees. StdDraw.setScale(-5.0, +5.0); double[] x = { 0, 1, 1, 0 }; double[] y = { 0, 0, 2, 1 }; double theta = 45.0; StdDraw.setPenColor(StdDraw.RED); StdDraw.polygon(x, y); rotate(x, y, theta); StdDraw.setPenColor(StdDraw.BLUE); StdDraw.polygon(x, y);

I have no idea how to do this problem Write 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[]. // Represents the polygon with vertices (0, 0), (1, 0), (1, 2), (0, 1). double x[] = { 0, 1, 1, 0 }; double y[] = { 0, 0, 2, 1 }; 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) } Note that the transformation methods scale(), translate() and rotate() mutate the polygons. Here are some example test cases (tests for copy() are not shown): // Scales polygon by the factor 2. StdDraw.setScale(-5.0, +5.0); double[] x = { 0, 1, 1, 0 }; double[] y = { 0, 0, 2, 1 }; double alpha = 2.0; StdDraw.setPenColor(StdDraw.RED); StdDraw.polygon(x, y); scale(x, y, alpha); StdDraw.setPenColor(StdDraw.BLUE); StdDraw.polygon(x, y); // Translates polygon by (2, 1). StdDraw.setScale(-5.0, +5.0); double[] x = { 0, 1, 1, 0 }; double[] y = { 0, 0, 2, 1 }; double dx = 2.0, dy = 1.0; StdDraw.setPenColor(StdDraw.RED); StdDraw.polygon(x, y); translate(x, y, dx, dy); StdDraw.setPenColor(StdDraw.BLUE); StdDraw.polygon(x, y); // Rotates polygon 45 degrees. StdDraw.setScale(-5.0, +5.0); double[] x = { 0, 1, 1, 0 }; double[] y = { 0, 0, 2, 1 }; double theta = 45.0; StdDraw.setPenColor(StdDraw.RED); StdDraw.polygon(x, y); rotate(x, y, theta); StdDraw.setPenColor(StdDraw.BLUE); StdDraw.polygon(x, y);

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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I have no idea how to do this problem

Write 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[].

// Represents the polygon with vertices (0, 0), (1, 0), (1, 2), (0, 1). double x[] = { 0, 1, 1, 0 }; double y[] = { 0, 0, 2, 1 };

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) }

Note that the transformation methods scale(), translate() and rotate() mutate the polygons. Here are some example test cases (tests for copy() are not shown):

// Scales polygon by the factor 2. StdDraw.setScale(-5.0, +5.0); double[] x = { 0, 1, 1, 0 }; double[] y = { 0, 0, 2, 1 }; double alpha = 2.0; StdDraw.setPenColor(StdDraw.RED); StdDraw.polygon(x, y); scale(x, y, alpha); StdDraw.setPenColor(StdDraw.BLUE); StdDraw.polygon(x, y);

// Translates polygon by (2, 1). StdDraw.setScale(-5.0, +5.0); double[] x = { 0, 1, 1, 0 }; double[] y = { 0, 0, 2, 1 }; double dx = 2.0, dy = 1.0; StdDraw.setPenColor(StdDraw.RED); StdDraw.polygon(x, y); translate(x, y, dx, dy); StdDraw.setPenColor(StdDraw.BLUE); StdDraw.polygon(x, y);

// Rotates polygon 45 degrees. StdDraw.setScale(-5.0, +5.0); double[] x = { 0, 1, 1, 0 }; double[] y = { 0, 0, 2, 1 }; double theta = 45.0; StdDraw.setPenColor(StdDraw.RED); StdDraw.polygon(x, y); rotate(x, y, theta); StdDraw.setPenColor(StdDraw.BLUE); StdDraw.polygon(x, y);

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