GraohicsGraohics

CSC 171 FALL 2001

LECTURE 16

History: COBOLHistory: COBOL 1960 - Conference on Data

System Languages (CODASYL) - led by Joe Wegstein of NBS developed the first standardized business computer programming language, COBOL (Common Business Oriented Language).

For the next 20 years there were more programs written in COBOL than any other single language.

That same year the second of the mathematical languages, ALGOL 60 was developed, not widely implemented ALGOL became the conceptual basis of many programming languages.

Coordinate SystemCoordinate System Origin in upper left X increases to right Y increases down

(0,0) Increasing x

Increasing y

Coordinate SystemCoordinate System So:

g.drawLine(30,40,50,70);

(0,0) Increasing x

Increasing y

(30,40)

(50,70)

Basic Graphics OperationsBasic Graphics Operations

Translation– Change the position

Scale– Change the size

Rotation– Change the angle

TranslationTranslation/*Moving an object is addition */

int x1,y1,x2,y2;

x1=30; y1=40; x2=60; y2=80;

g.drawLine(x1,y1,x2,y2);

//20 to the left , 10 down

x1+=20; x2+=20;

y1+= 10; y2+=10;

g.drawLine(x1,y1,x2,y2);

(0,0) Increasing x

Increasing y

(30,40)

(60,80)

(50,50)

(80,90)

ScaleScale/*Sizing an object multiplication */

int x1,y1,x2,y2;

x1=30; y1=40; x2=60; y2=80;

g.drawLine(x1,y1,x2,y2);

//double the size

x1*=2; x2*=2;

y1*= 2; y2*=2;

g.drawLine(x1,y1,x2,y2);

// NOT “in place”

(0,0) Increasing x

Increasing y

(30,40)

(60,80)

(60,80)

(120,160)

QuestionQuestion

Given “scale” and “translation” as above:

How would you do “translation in place”?

(ie : keep center of line in place, alter size)

(30,40)

(60,80)

(15,20)

(75,100)

Scale in placeScale in place

int x1,y1,x2,y2;x1=30; y1=40; x2=60; y2=80;g.drawLine(x1,y1,x2,y2);

//center pointint averageX = (x1+x2)/2;Int averageY = (y1+y2)/2;

//put center @ originx1-=averageX; x2-=averageX;y1-=averageY; y2-=averageY;

//scale as beforex1*=2; x2*=2;y1*= 2; y2*=2;

//center is still at center//so, return center to same//put center @ originx1+=averageX; x2+=averageX;x1+=averageY; y2+=averageY;

g.drawLine(x1,y1,x2,y2);

Scale in placeScale in place

int x1,y1,x2,y2;x1=30; y1=40; x2=60; y2=80;g.drawLine(x1,y1,x2,y2);

//center pointint averageX = (x1+x2)/2; //45Int averageY = (y1+y2)/2; //60

//put center @ originx1-=averageX; // 30-45 = = -15x2-=averageX; // 60-45 = = 15y1-=averageY; // 40-60 = = -20y2-=averageY; // 80-60 = = 20

//scale as beforex1*=2; // -15 * 2 = = -30x2*=2; // 15 * 2 = = 30y1*= 2; // -20 * 2 = = -40y2*=2; // 20 * 2 = = 40

//center is still at center//so, return center to same//put center @ originx1+=averageX; // -30 + 45 = =15x2+=averageX; // 30+45 = = 75x1+=averageY; // -40+60 = =20y2+=averageY; // 40+60 = =100

g.drawLine(x1,y1,x2,y2);

Rotation Rotation So, we can translateScale, in place

What about rotation– Rotation involves “angles”– Angles involve math

In computer science math is used for application as well as analysis

A little trigonometryA little trigonometry

Recall:

On the unit circle,

Give the angle x=cos()

y=sin()(x,y)

x=cos()

y=sin()

(1,0)(-1,0)

(0,1)

(0,-1)

y

x

Any point in the planeAny point in the plane

x=r*cos()

y=r*sin()

Rotation about the origin is going from one point on the circle to another

(adding an angle) (x,y)

x=r*cos()

y=r*sin()

y

x

(0,r)

(0,-r)

(r,0)(-r,0)

Angle AdditionAngle AdditionGoing from (x1,y1)

add to is like finding the sum

Remember:

cos(+) ==

cos*cos-sin*sin

sin(+) ==

sin*cos+cos*sin

(x1,y1)

(x2,y2)

Angle AdditionAngle Additionx1=r*cos()y1=r*sin()

x2 = r*cos(+) ==r* (cos*cos-sin*sin

x1*cos-y1*sin

y2= r* sin(+) ==

r*(sin*cos+cos*sinx1*siny1*cos

(x1,y1)

(x2,y2)

Rotation about the originRotation about the originx2 x1*cos-y1*sin

y2 x1*sin+y1*cos

(x1,y1)

(x2,y2)

Rotation as a Matrix operationRotation as a Matrix operation

x2 x1*cos-y1*sin

y2 x1*sin+y1*cos

1

1

)cos()sin(

)sin()cos(

2

2

y

x

y

x

Rotation by 90 degreesRotation by 90 degreesint x1,y1,x2,y2;

x1=30; y1=40; x2=60; y2=80;

g.drawLine(x1,y1,x2,y2);

int x1p,y1p,x2p,y2p

//sin(90) == 1

//cos(90) == 0

//what happens??

(0,0)

(30,40)

(60,80)

Rotation by 90 degreesRotation by 90 degreesx1p =x1*0-y1*1 // -40

y1p = y1*0+x1*1// 30

x2p = x2*0-y2*1 //-80

y2p = y2*0+x2*1 //60

(0,0)

(30,40)

(60,80)

(-40,30)

(-80,60)

Rotation about the OriginRotation about the OriginNot “In Place”

How do we do “in place”?

Rotation about the OriginRotation about the OriginNot “In Place”

How do we do “in place”?

The same way as scale “in place”– Translate center of object to origin– Rotate around origin– Translate back

FILE IOFILE IO

FileReader class– read() method gets a character

FileWriter class – write() method writes a character

The Caesar Cipher

Program Crypt.java

import java.io.FileReader;import java.io.FileWriter;import java.io.IOException;

public class Crypt{ public static void main(String[] args) { boolean decrypt = false; int key = DEFAULT_KEY; FileReader infile = null; FileWriter outfile = null;

if (args.length < 2 || args.length > 4) usage();

// gather command line arguments and open files

try{ for(int i = 0; i < args.length; i++) { if (args[i].substring(0, 1).equals("-")) // it is a command line option { String option = args[i].substring(1, 2); if (option.equals("d")) decrypt = true; else if (option.equals("k")) { key = Integer.parseInt (args[i].substring(2)); if (key < 1 || key >= NLETTERS) usage(); } } else { if (infile == null) infile = new FileReader(args[i]); else if (outfile == null) outfile = new FileWriter(args[i]);

} }}catch(IOException e){ System.out.println("Error opening file"); System.exit(0);}

if (infile == null || outfile == null) usage();

// encrypt or decrypt the input

if (decrypt) key = NLETTERS - key;

try{ encryptFile(infile, outfile, key); infile.close(); outfile.close();}

catch(IOException e) { System.out.println("Error processing file"); System.exit(0); }}

/** Prints a message describing proper usage and exits.*/public static void usage(){ System.out.println ("Usage: java Crypt [-d] [-kn] infile outfile"); System.exit(1);}

/** Encrypts a character with the Caesar cipher. Only upper- and lowercase letters are encrypted. @param c the character to encrypt @param k the encryption key @return the encrypted character*/public static char encrypt(char c, int k){ if ('a’ <= c && c <= 'z') return (char)('a’ + (c - 'a’ + k) % NLETTERS); if ('A’ <= c && c <= 'Z') return (char)('A’ + (c - 'A’ + k) % NLETTERS);

return c;}

/** Encrypts all characters in a file. @param in the plaintext file @param out the file to store the encrypted characters @param k the encryption key*/ public static void encryptFile(FileReader in, FileWriter out, int k) throws IOException { while (true) { int next = in.read(); if (next == -1)return; // end of file char c = (char)next; out.write(encrypt(c, k)); } }

public static final int DEFAULT_KEY = 3; public static final int NLETTERS = 'z’ - 'a’ + 1;}

CSC 171 GRADES FALL 2001

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CSC 171 GRADES FALL 2001

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All exams & projects in 73/134All exams & projects in 73/134CSC 171 GRADES FALL 2001

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E 0.00% 5 6.85% 100.00%D- 60.00% 3 4.11% 93.15%D 63.00% 6 8.22% 89.04%D+ 67.00% 3 4.11% 80.82%C- 70.00% 5 6.85% 76.71%C 73.00% 10 13.70% 69.86%C+ 77.00% 10 13.70% 56.16%B- 80.00% 7 9.59% 42.47%B 83.00% 7 9.59% 32.88%B+ 87.00% 6 8.22% 23.29%A- 90.00% 4 5.48% 15.07%A 93.00% 7 9.59% 9.59%