מבוא למדעי המחשב עבודה # 3

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1 מבוא למדעי המחשב עבודה # 3 תרגיל זה עוסק ברקורסיות ובתכנות מונחה עצמים. הוראות כלליות לעבודה: ניתן ומומלץ להגיש את העבודה בזוגות. כל איחור בהגשת התרגיל יגרום להורדת ציון, כפי שהוגדר בנהלים שבאתר הקורס..1.2 תרגיל אותו לא ניתן להדר )לקמפל( או להריץ, יקבל ציון נכשל..3 העבודה תבדק באופן אוטומטי לפי הפלט אשר התוכניות שלכם ידפיסו למסך. לכן יש להקפיד על ההוראות ולבצע אותן במדויק.כל הדפסה אשר אינה עונה באופן מדויק לדרישות המופיעות בעבודה עלולה לגרום לתוכנית הבדיקה האוטומטית להיכשל. סגנון כתיבת הקוד יבדק באופן ידני. יש להקפיד על כתיבת קוד ברור, מתן שמות משמעותיים למשתנים, הזחות והוספת הערות בקוד המסבירות את תפקידם של מקטעי קוד שונים..4.5 כתיבת קוד אשר אינו עומד בסטנדרטים אלו תגרור הפחתה בציון העבודה. במידה ואינכם בטוחים מהו הפרוש המדויק להוראה מסוימת, או בכל שאלה אחרת הקשורה בתוכן העבודה, אנא העזרו בפורום. בכל בעיה אישית הקשורה לעבודה )מילואים, אישפוז וכו'(, אנא צרו את הפניה המתאימה ב- System Submission כפי שמוסבר בסילבוס שבאתר הקורס. לעבודה מצורפים שלושה קבצים example.java,painter.java ו-.Main.java הקובץ Painter.java מספק לכם ממשק גרפי שיעזור לכם לבדוק את הקוד שתכתבו על ידי יצירת התמונה. בקובץ example.java תמצאו דוגמא לשימוש בממשק הגרפי Painter ובקובץ main.java תמצאו בדיקות לכל המחלקות היוצרות את התמונות כפי שהם מופיעות בעבודה. הגשת העבודה תתבצע אך ורק ב- System.Submission הקבצים להגשה הם:,Snowflake.java,BasicStar.java,Pixel.java,Painter.java.KochSnowflake.java,KochCurve.java,SuperSnowflake.java יש להגיש את הקבצים האלו בלבד )ללא קבצי ה class וכו(. כדי להגיש יש לכווץ אותם לקובץ zip בשם.Ass3.zip שאלות הקשורות לתרגיל יש לשאול אך ורק בפורום.הצוות יענה לשאלות נבחרות בFAQ. הימנעו מהעתקות! ההגשה היא בזוגות. ניתן להגיש גם בקבוצות של 3 או 4 סטודנטים, אך נקודות יופחתו בהתאם! במידה ומוגשות עבודות בנפרד עם קוד זהה או אפילו דומה- זוהי העתקה אשר תדווח לועדת משמעת לאלתר. 1

2 Assignment Description: In this assignment you will create graphic images by using recursive Java methods. Graphic Images Graphic images are drawn in a rectangle. The dimensions of the rectangular are measured in pixels. The rectangular may be width pixels across and height pixels in height. A location in the rectangle is given as a point (X,Y) where both fields are integers. The(0,0) location is at the top-left. Think of graphic images representation as rectangle where each small square is a pixel. The columns of pixels are numbered 0 to width-1 starting at the left. The rows of pixels are numbered 0 to height-1 starting at the top. The Painter Use the provided Painter class (i.e., Painter.java) to open a window frame and draw images. In main.java you will find an example for using the Painter class. The Painter has the following useful methods: void draw(string shape) Creates a frame and displays the shape name. int getframewidth() Returns the width of the frame(integer). int getframeheight() Returns the height of the frame(integer). void setcolor(string c)- Sets the pencil color to c (e.g., red, blue ). void drawline(int x1,int y1,int x2,int y2)- Draws a straight line from point(x1,y1) to point(x2,y2). 2

3 Part I Starry Night (70 Points) In this part you will write recursive methods for drawing stars and snowflakes. 1. Pixel (10 Points) Create the Pixel Class. Create a new class called Pixel.java. The Pixel class should have two fields (i.e., x and y), two constructors and two getter methods. Please see below the structure for this class. public class Pixel{ private int x; private int y; public Pixel(){ x=0; y=0; public Pixel(int x, int y){ // Your code here public int getx(){ // Your code here public int gety(){ // Your code here 3

4 The Fields The field x describes the x-coordinate of the pixel. The field y describes the y-coordinate of the pixel. The Constructor The empty constructor initializes the fields to the pixel (0,0). The second constructor that receives two parameters initializes the class fields from the given arguments. The Getters The two getter methods will help you access the fields of the Pixel class (see example in the main function). 2. BasicStar(20 Points) This program creates the Basic Star. It draws a 6-pointed star. Think of this figure as six lines that originate from a center point. public class BasicStar { public BasicStar(){ public void draw(){ int height = Painter.getFrameHeight()/2; int width = Painter.getFrameWidth()/2; int maxradius = Math.min(height, width)/2; int radius = maxradius/4; Pixel p = new Pixel(height, width); Painter.setColor("blue"); draw(p, radius); public void draw(pixel p, int radius) { // Your code here 4

5 draw() method The width and height are needed to determine the radius of the star that fits in the frame. To draw a symmetrical star, it finds its radius, which is the minimum of the frame s width and height, divided by 2. Let us make the size/4 so that there is room for the rest of the snowflake. The star is drawn in the center of the rectangle. draw(pixel p, int radius) method You will have to implement this method. 1. Each line (of the six) starts at the center, (x, y), and ends at a point on the circle of radius size. The X distance from the center of a point on a circle is radius*cos(θ). The Y distance from the center of a point on a circle is radius *sin(θ) 2. The method finds the six values for theta to find the six endpoints of the lines. The Java trigonometric functions are static methods of the Math. 3. The circle is divided into six pieces. There are two pi radians per Math.Pi circle. One sixth of a circle is The "-" sign is used for endy because y increases in value going down. 3. Snowflake- Recursive star (20 Points) Create a Snowflake class, similar to BasicStar, that draws a snowflake. A snowflake will be drawn by adding another star centered at the tip of each of the six lines, and continuing the recursive process to create a snowflake image. The Fields The Snowflake class has a single field, a BasicStar Object. The Constructor The Snowflake class has an empty constructor that initializes a new BasicStar object. 5

6 draw() method The draw() method in the Snowflake is similar to the draw() method in BasicStar with one exemption, the call in the last line to draw(p, radius) should be replaced by draw(pixel p, int radius, int depth), with depth=4. draw(pixel p, int radius, int depth) method Create a method draw(pixel p, int radius, int depth), and call it from the draw() method. Draw each small star by adding a recursive call to the draw(pixel p, int radius, int depth) method with different parameter values. The new stars need to be smaller than the central star. Thus, the radius of the new stars should be radius/3. The integer depth will represent the number of times left to recursively call the method draw( Pixel p, int radius, int depth ). Add a check in draw( Pixel p, int radius, int depth ) to check if depth is 0. If so, the work is done. As long as depth is greater that 0, the process continues. Decrease depth by 1 with each recursive call. Change the first call to draw( Pixel p, int radius, int depth ) in draw() to have depth=4. 4. Super Snowflake (20 Points) Create a SuperSnowflake class, that draws a super snowflake. The super snowflake image contains the original snowflake and additional circles of snowflakes. There is a central snowflake and around it there are 3 circles, each with 6 snowflakes. Each circle has 6 snowflakes which are 2 times smaller in radius than the previous snowflake's radius (see example below). Each circle has a circleradius which is larger than the previous circleradius by 3*radius (radius is the radius of the snowflake in the previous circle) 6

7 radius circleradius radius radius The Fields The SuperSnowflake class has a single field, a Snowflake Object. The Constructor The SuperSnowflake class has an empty constructor that initializes a new Snowflake object. The draw() method The draw() method in the Snowflake is similar to the draw() method in BasicStar with two exemptions: a. The draw() method should draw the central snowflake. b. The call in the last line to the draw method should be replaced by draw(pixel p, int radius, int depth, int circleradius), with circleradius = 3*radius. The draw(pixel p, int radius, int depth, int circleradius) method This draw method should draw the three circles of snowflakes. Each time this draw method is recursively called another circle of snowflakes is added around the center. 7

8 Part II The Von Koch Curve- Recursion in Fractal Geometry (30 Points) In this part you will write recursive methods for drawing Koch Snowflake. Swedish mathematician Helge von Koch introduced the "Koch curve" in Starting with a line segment, recursively replace the line segment as shown below: 0 1 The single line segment in Step 0, is broken into four equal-length segments in Step 1. This same "rule" is applied an infinite number of times resulting in a figure with an infinite perimeter. Here are the next few steps: For more information and further reading, 8

9 5. The Von KochCurve (15 Points) Create a KochCurve class, which draws the curve shown below. The Fields The KochCurve class has no fields. The Constructor The KochCurve class contains an empty constructor. draw() method Use the following draw() method: public void draw() { int height = Painter.getFrameHeight()/2; int width = Painter.getFrameWidth()/2; Painter.setColor("blue"); Pixel p1 = new Pixel(height/2, width/2); Pixel p2 = new Pixel(height, width); draw(p1,p2, 4); draw(pixel p1, Pixel p2,int depth) method Write a recursive method draw(pixel p1, Pixel p2, int depth) and call it from draw() method. This method accepts the 2 end points of the line, and an integer depth, which is the depth of the recursion. In draw(pixel p1, Pixel p2, int depth ): Find 2 new pixels p 3=(x3,y3) and p4=(x4,y4) which equally divide the segment p1p2 into 3 identical segments. Find a pixel p5=(x5, y5) that creates the equilateral triangle with p3 and p4. Add a recursive call for each of the 4 segments. 9

10 6. The Von Koch Snowflake (15 Points) Create a KochSnowflake class, which draws the KochSnowflake shown in the image below. The Fields The KochSnowflake class contains a single field, a KochCurve object. The Constructor The KochSnowflake class has an empty constructor that initializes a new KochCurve object. draw() method In the draw() method you should first decide on the coordinates of an equilateral triangle. Then, you should call the draw(pixel p1, Pixel p2, int depth) method of KochCurve 3 times, once for each of the triangles sides. public void draw() { int height = Painter.getFrameHeight(); int width = Painter.getFrameWidth(); int side = (int)((height*2/3)/math.cos(math.pi/6)); int x1 = width/2; int y1 = 40; int x2 = 300+side/2; int y2 = 440; int x3 = 300-side/2; int y3 = 440; // Your code here.good Luck!!! 10