Graohics

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Graohics

• CSC 171 FALL 2001
• LECTURE 16

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History 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.

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Coordinate System

• Origin in upper left
• X increases to right
• Y increases down

Increasing x
(0,0)
Increasing y
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Coordinate System

• So
• g.drawLine(30,40,50,70)

Increasing x
(0,0)
(30,40)
(50,70)
Increasing y
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Basic Graphics Operations

• Translation
• Change the position
• Scale
• Change the size
• Rotation
• Change the angle

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Translation

• /Moving an object is addition /
• int x1,y1,x2,y2
• x130 y140 x260 y280
• g.drawLine(x1,y1,x2,y2)
• //20 to the left , 10 down
• x120 x220
• y1 10 y210
• g.drawLine(x1,y1,x2,y2)

Increasing x
(0,0)
(30,40)
(50,50)
(80,90)
(60,80)
Increasing y
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Scale

• /Sizing an object multiplication /
• int x1,y1,x2,y2
• x130 y140 x260 y280
• g.drawLine(x1,y1,x2,y2)
• //double the size
• x12 x22
• y1 2 y22
• g.drawLine(x1,y1,x2,y2)
• // NOT in place

Increasing x
(0,0)
(30,40)
(60,80)
(60,80)
Increasing y
(120,160)
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Question

• Given scale and translation as above
• How would you do translation in place?
• (ie keep center of line in place, alter size)

(15,20)
(30,40)
(60,80)
(75,100)
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Scale in place

• int x1,y1,x2,y2
• x130 y140 x260 y280
• g.drawLine(x1,y1,x2,y2)
• //center point
• int averageX (x1x2)/2
• Int averageY (y1y2)/2
• //put center _at_ origin
• x1-averageX
• x2-averageX
• y1-averageY
• y2-averageY

• //scale as before
• x12 x22
• y1 2 y22
• //center is still at center
• //so, return center to same
• //put center _at_ origin
• x1averageX
• x2averageX
• x1averageY
• y2averageY
• g.drawLine(x1,y1,x2,y2)

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Scale in place

• //scale as before
• x12 // -15 2 -30
• x22 // 15 2 30
• y1 2 // -20 2 -40
• y22 // 20 2 40
• //center is still at center
• //so, return center to same
• //put center _at_ origin
• x1averageX // -30 45 15
• x2averageX // 3045 75
• x1averageY // -4060 20
• y2averageY // 4060 100
• g.drawLine(x1,y1,x2,y2)

• int x1,y1,x2,y2
• x130 y140 x260 y280
• g.drawLine(x1,y1,x2,y2)
• //center point
• int averageX (x1x2)/2 //45
• Int averageY (y1y2)/2 //60
• //put center _at_ origin
• x1-averageX // 30-45 -15
• x2-averageX // 60-45 15
• y1-averageY // 40-60 -20
• y2-averageY // 80-60 20

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Rotation

• So, we can translate
• Scale, in place
• What about rotation
• Rotation involves angles
• Angles involve math
• In computer science math is used for application
  as well as analysis

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A little trigonometry

• Recall
• On the unit circle,
• Give the angle F
• xcos(F)
• ysin(F)

(0,-1)
x
F
(1,0)
(-1,0)
y
(x,y)
(0,1)
ysin(F)
xcos(F)
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Any point in the plane

• xrcos(F)
• yrsin(F)
• Rotation about the origin is going from one point
  on the circle to another
• (adding an angle)

(0,-r)
x
F
(r,0)
(-r,0)
y
(x,y)
(0,r)
yrsin(F)
xrcos(F)
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Angle Addition

• Going from (x1,y1)
• add f to a
• is like finding the sum
• Remember
• cos(af)
• cosacosf-sinasinf
• sin(af)
• sinacosfcosasinf

a
f
(x1,y1)
(x2,y2)
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Angle Addition

• x1rcos(a)
• y1rsin(a)
• x2 rcos(af)
• r (cosacosf-sinasinf)
• x1cosf-y1sinf
• y2 r sin(af)
• r(sinacosfcosasinf) x1sinfy1cosf

a
f
(x1,y1)
(x2,y2)
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Rotation about the origin

• x2 x1cosf-y1sinf
• y2 x1sinay1cosf

a
f
(x1,y1)
(x2,y2)
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Rotation as a Matrix operation

• x2 x1cosf-y1sinf
• y2 x1sinay1cosf

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Rotation by 90 degrees

• int x1,y1,x2,y2
• x130 y140 x260 y280
• 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)
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Rotation by 90 degrees

• x1p x10-y11 // -40
• y1p y10x11// 30
• x2p x20-y21 //-80
• y2p y20x21 //60

(0,0)
(-40,30)
(30,40)
(-80,60)
(60,80)
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Rotation about the Origin

• Not In Place
• How do we do in place?

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Rotation about the Origin

• Not 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

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FILE IO

• FileReader class
• read() method gets a character
• FileWriter class
• write() method writes a character

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The Caesar Cipher
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Program Crypt.java import java.io.FileReader imp
ort 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 lt 2
args.length gt 4) usage() // gather
command line arguments and open files
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try for(int i 0 i lt args.length i)
if (argsi.substring(0, 1).equals("-")) //
it is a command line option String
option argsi.substring(1, 2) if
(option.equals("d")) decrypt true
else if (option.equals("k"))
key Integer.parseInt
(argsi.substring(2)) if (key lt 1
key gt NLETTERS) usage()
else if (infile
null) infile new FileReader(argsi)
else if (outfile null)
outfile new FileWriter(argsi)
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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()
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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)
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/ Encrypts a character with the Caesar
cipher. Only upper- and lowercase letters are
encrypted. _at_param c the character to encrypt
_at_param k the encryption key _at_return the
encrypted character / public static char
encrypt(char c, int k) if ('a lt c c lt
'z') return (char)('a (c - 'a k)
NLETTERS) if ('A lt c c lt 'Z')
return (char)('A (c - 'A k) NLETTERS)
return c
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/ Encrypts all characters in a file.
_at_param in the plaintext file _at_param out the
file to store the encrypted characters _at_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
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Whole class
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Passing class
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All exams projects in 73/134
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All exam projects in 73/134