代做data、代写Java语言、program代写、Java程序设计调试

日期：2020-07-11 11:16

Functions and Recursion – 55 course points

This assignment consists of two parts. First, write a library of static methods that

performs geometric transforms on polygons. Next, write a program that plots

a Sierpinski triangle.

Programming

Write 2 programs and submit on Sakai.

We provide a zip containing PolygonTransform.java, and Sierpinski.java. For each

problem update and submit the corresponding file.

DO NOT use System.exit()

DO NOT add any import statements

DO NOT add the project or package statements

DO NOT change the class name

DO NOT change the headers of ANY of the given methods

DO NOT add any new class fields

ONLY print the result as specified by the example for each problem.

DO NOT print other messages, follow the examples for each problem.

USE StdIn, StdOut, and StdDraw libraries.

1. Polygon transform (25 points). 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[].

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:

3. Sierpinski (30 points). The Sierpinski triangle is an example of a fractal pattern

like the H-tree pattern from Section 2.3 of the textbook.

The Polish mathematician Wac?aw Sierpiński described the pattern in 1915, but it

has appeared in Italian art since the 13th century. Though the Sierpinski triangle

looks complex, it can be generated with a short recursive function. Your main

task is to write a recursive function sierpinski() that plots a Sierpinski triangle of

order n to standard drawing. Think recursively: sierpinski() should draw one filled

equilateral triangle (pointed downwards) and then call itself recursively three

times (with an appropriate stopping condition). It should draw 1 filled triangle for n

= 1; 4 filled triangles for n = 2; and 13 filled triangles for n = 3; and so forth.

API specification. When writing your program, exercise modular design by organizing it

into four functions, as specified in the following API:

Restrictions: You may not change either the scale or size of the drawing window.

Before submission

1. Collaboration policy. Read our collaboration policy here.

2. Update @author. Update the @author tag of the files with your name, email and

netid.

3. Submitting the assignment. Submit PolygonTransform.java, and Sierpinski.java

separately on Sakai.