1.
Prog_2 course- 2014
2 bytes team
Kinan keshkeh
IT Engineering-Damascus University
3rd year

2.
GRAPH

3.
Introduction
In all programs we were using TXTmode (all outputs
were in Text).
In PASCAL there is a Graph Unit, which allow us
to change into Graphicmode and draw diagrams.

4.
Change into Graph mode
Uses Graph;
procedure my_initgraph;
var gd, gm, error,detect:integer; begin gd:=detect; initgraph(gd,gm,'c:evgrga.bgi'); error:=graphresult; if error<>grok then begin writeln('graphic error',GraphErrorMsg(error)); halt(1);
end;
end;

5.
1- Uses Graph : to include Graph library.
2- gd:=detect : detect ,to determine the kind of
display card .
3- initgraph(gd,gm,'c:evgrga.bgi')
that in (2)
display system : ex: gm=VGAHI , so the screen will be 2640*480*16 (16 number of colors ).
4- error:=graphresult : to insure if initgraph success in
changing to Graph mode, it return a value if success or error.
5-GraphErrorMsg(error) : display an error message , if an error happens when changing into graphic mode.
6-Halt: to exit the procedure.

6.
Note:
If we have this folder to save code file in it : C:MyFolderpro.pas
Go to (Turbo Pascal) folder , open ‘BGI’ folder
1)Copy this file EGAVGA.BGI and paste it in ‘C:MyFolder’ 2)Copy this fileGRAPH.TPU’ unit from ‘Units’ folder (in Turbo
Pascal folder).and paste it in the path ‘C:MyFolder’ too.
3)From pascal program , choose File -> Change dir ->
C:MyFolder .
* That to initialize Graph environment in pascal !

7.
How to paint a Normal function:
1) The function : Y= f(x) ex: (y=2x) .
2) X domain: ex: x in [ x0=-100, xn=100] .
4) Painting step dx : dx=(xn-x0)/n .
3) N number of points.
5) The Algorithm :
x1=x0; y1=F(x0);
For(i:=1) to (N) do
begin
x2 = x0+i*dx;
y2 = F(x2);
line(x1,y1,x2,y2);
x1:=x2; y1:=y2
end;

8.
Example :
paint ( Y=f(x) = x ) :
1- (f(x) = x ) 2- let x in [0,50] 3- n=100
4-dx=(50-0)/100 = 0.5 ;
5- Algorithm:
x1=x0; y1=x0;
For(i:=1) to (n) do
begin
x2 = x0+i*dx;
y2 = x2;
line(x1,y1,x2,y2);
x1:=x2; y1:=y2
end;
x1
y1
x2
y2
x2
y2

9.
How to paint a Polar function:
1) The function :R= F(u) ex: (y=cos(x) ) .
2) U domain: ex: U in [ u0=-100, un=100] .
4) Painting step du : du=(Un-U0)/n .
3) N number of points.
5) The Algorithm :
x1=F(u0)*cos(u0); y1=F(u0)*sin(u0);
For(i:=1) to (N) do
begin
U= u0+ i*du;
x2=F(u)*cos(u);
y2=F(u)*sin(u);
line(x1,y1,x2,y2);
x1:=x2; y1:=y2
end;
x
y
U

10.
the Coordinates
(wXb,wYb)
paper
bottom
(wXt,wYt)
top
(vXb,vYb)
screen
bottom
(vXt,vYt)
top

11.
Coordinates appropriate
- If you have On paper x in [0..460]
..it would be On Screen x in [0..230]
- So each two points on screen , one point on paper .
(6,0) paper -> (3,0) screen
- So the Ratio:
Sx = | vXb – vXt | / | wXt – wXb |
Sy = | vYb – vYt | / | wYt – wYb |
0
460
230
0
vXt
vXb
wXb
wXt
3
6
1)Increasing and decreasing coordinates:

12.
EX:
If the paper Coordinates are 640*320 , and the screen Coordinates are 1280*640 .
What are the coordinates on screen of the point (4,6) on paper ?
answer :
Sx=(1280-0) / (640-0) = 2
Sy=(640-0) / (320-0) = 2
the point on paper(4,6) -> (8,12) on screen

13.
Xv= (x-wXb)*Sx + vXt
2)Displacement coordinates:
0
200
vXt
vXb
-50
50
wXb
wXt
Ex: the point (50,0) -> Xv=(50+50)*2 + 0 = 200 (x on screen).
paper
Screen

14.
Yv= (y-wYb)*Sy + (GetMaxY – vYb)
0
0
paper
wYb
100
100
vYt
wYt
vYb
Screen
GetMaxY = 100
Ex: the point (0,100) -> Yv=(100-0)*1 +(100-100) = 100 (x on screen).

15.
Some important functions and procedures :
Line(x1,y1,x2,y2) : draw a line between the two points.
Circle(x,y,radius) : draw a circle .
Rectangle(x1,y1,x2,y2): draw a rectangle between the two points .
Setcolor(color): change the color where the color is a number from [0..15] and each number is a color.
Setviewport(x1,y1,x2,y2,clipOn/clipOff): determine a specific display window
clipOn: inside it we can see, clipOff: outside it we can see.
TXTout(“Hello world”) or TXToutXY(50,20,“Hello world”) : print a text on screen with Graphicmode (at specific coordinate),
whereas at TXTmode we use writeln,write .

16.
Lets make it real :D !!
What u do in Exams

17.
Normal functions: F(x)=1+x2
س:ارسم الخط البياني للتابع:
2+x1
F(x)=
حيث x ضمن المجال ]100,+100-[
2000
N=
Program draw;
const n=2000; x0=-100; xm=100; dx=0.1 ; { (xm-x0)/n= [100-(-100)]/2000=0.1} uses graph; var x1,x2,y1,y2:real; nx1,nx2,ny1,ny2:real; maxx , maxy , i : integer; alpha , beta :real;

18.
procedure my_initgraph; {initialize screen for drawing} var gd,gm,error,detect :integer; begin gd:=detect; initgraph(gd,gm,'c:evgrga.bgi'); error:=graphresult; if error<>grok then begin writeln('graphic error',GraphErrorMsg(error) ); halt(1); end;
function f(x:real):real begin f:=x*x+1; end;

19.
Begin my_initgraph; x1:=x0; y1:=f(x0); maxx:=getmaxx; maxy:=getmaxy; alpha:=maxx/(xm-x0); beta:=maxy/abs( f(xm) - f(x0) );; line(0,maxy div 2,maxx,maxy div 2); line(maxx div 2,0,maxx div 2,maxy); for i:=1 to n do begin x2:=x0+i*dx; y2:=f(x2); nx1:=round(x1*alpha)+maxx div 2; nx2:=round(x2*alpha)+maxx div 2; ny1:= -round(y1*beta)+maxy div 2; ny2:= -round(y2*beta)+maxy div 2; line(nx1,ny1,nx2,ny2); x1:=x2; y1:=y2; end; close graph; End;
appropriate the coordinate
Displacement
Draw the axis

20.
Polar functions: F(u)=1+sin(u)
س:ارسم منحني التابع
+sin(u)1
F(u)=
0.02du=, 0 =0
U
Program draw;
const n=2500; u0=0; du=0.02;
uses graph; var x1,x2,y1,y2:real; nx1,nx2,ny1,ny2:real; maxx , maxy,i :integer; alpha ,beta :real;

21.
procedure my_initgraph; {initialize screen for drawing} var gd,gm,error,detect :integer; begin gd:=detect; initgraph(gd,gm,'c:evgrga.bgi'); error:=graphresult; if error<>grok then begin writeln('graphic error',GraphErrorMsg(error) ); halt(1); end;
function f(u:real):real begin f:=1+sin(u); end;

22.
Begin my_initgraph; x1:=f(u0)*cos(u0); y1:=f(u0)*sin(u0); maxx:=getmaxx; maxy:=getmaxy; alpha:=maxx/ ( n*du) beta:= maxy/abs( f(u0+n*du) - f(u0) ); line(0,maxy div 2,maxx,maxy div 2); line(maxx div 2,0,maxx div 2,maxy); for i:=1 to n do begin u:=u0+i*du; x2:=f(u)*cos(u); y2:=f(u)*sin(u); nx1:=round(x1*alpha)+maxx div 2; nx2:=round(x2*alpha)+maxx div 2; ny1:= -round(y1*beta)+maxy div 2; ny2:= -round(y2*beta)+maxy div 2; line(nx1,ny1,nx2,ny2); x1:=x2; y1:=y2; end; close graph; End;
Draw the axis

23.
The End of the course !!

24.
Group : group link
Mobile phone- Kinan : 0994385748
Facebook account : kinan’s account
2 bytes team