computer graphics(unit2)

8/19/2019 Computer Graphics(unit2)

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UNIT II


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OPENGL API

• OpenGL’s structure is similar to that of

most modern APIs including Jaa!" and

"irect#$

• OpenGL is eas% to learn&compared 'ith

other API$

• It supports the simple (" and !"

programs$


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Graphics functions

Black box•our )asic model of a graphics pac*age is a black box$•This term is used to denote a s%stem 'hose properties aredescri)ed onl% )% its inputs and outputs$

•Graphics s%stem is a )o+ 'hose inputs are function callsfrom an application program, measurements from inputdeices&such as the mouse and *e%)oard and messagesfrom os.•Outputs are primaril% the graphics sent to our output

deices•E+ample• 'e can ta*e simplified ie' of inputs as function callsand outputs as primities$


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Graphics s%stem as a )lac* )o+

function calls output

• "ata Input

Application

program Graphics s%stemInput-output

deices


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• API contain hundreds of functions&so it is helpfulto diide them into seen ma.or groups$

/$Primitie functions

($Attri)ute functions!$0ie'ing functions

1$Transformation functions

2$Input functions3$4ontrol functions

5$6uer% functions$


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Primitive function

• "efine the lo' leel o).ects or atomic entities that our s%stem can

displa%$• "epending on the API&the primitives can include points, line,

segments, polygons, pixels, text , and arious t%pe of cures andsurfaces$

• E+ample gl7egin8GL9POINT:;,

gl0erte+(f8/


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Attri)ute function

• To perform operations ranging from choosingthe color 'ith 'hich 'e displa% a line segment$

= Eg gl4olor!f8/$


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0ie'ing and transformation

• The ie'ing functions allo's us to specif% ariousie's&although APIs differ in the degree of fle+i)ilit% the%proide in choosing a ie'$

= gl0ie'port 8+min& %min& p>idth& p?eight;,

= gluOrtho(" 8+'min& +'ma+& %'min& %'ma+;, = gluLoo*At8@;,

• Transformation function that allo's to carr% outtransformations of o).ects&such as rotation& translation and

scaling$ = glTranslatef 8t+& t%& t;,

= glBotatef 8theta& +& %& ;,

= gl:calef 8s+& s%& s;,


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Input function• Allo's us to deal 'ith the dierse forms of input

that characterie modern graphics s%stems$

= oid glutCe%)oardDunc8oid 8func; 8unsignedchar *e%& int +& int %;;,

Control function• Ena)le us to communicate 'ith the 'indo'

s%stem&to initialie our programs&and to deal'ith an% errors that ta*e place during thee+ecution of our programs$

• glutInit>indo':ie82


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Query function

• ho' man% color are supported or the sie

of the displa%$

• 4amera parameters or alues in the frame

)uffer$


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The graphics pipeline and state

machine• Entire graphics s%stem as a state machine$

• A )lac* )o+ that contains a finite state machine$

• This state machine has inputs that come from the

application program$

• These inputs ma% change the state of the machine

or can cause the machine to produce a isi)le

output$


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• T'o t%pes of graphics functionsF

= Those that define primities that flo' through a pipeline inside

the state machine

= those that either changes the state inside the machine or

return state information$

glerte+ first t%pe

Other t%pes =second t%pe

• In openGL most parameters are persistent$

• Their alues remain unchanged until 'e e+plicitl% change themthrough functions that alter the state$


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• Dor e+ample& once 'e set a color&that

color remains the current color until it is

changed through a coloraltering function


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OpenGL interface

• Three li)raries

= GL li)rar%

= GLU8OpenGL Utilit% li)rar%;

= GLUT8OpenGL Utilit% Tool*it;

G

functions in the GL li)rar% hae names that

)egin 'ith the letters gl and are stored in ali)rar% usuall% referred to as GL


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• GLU = This li)rar% uses onl% GL functions )ut

contains code for creating common o).ects

and simplif%ing ie'ing$ = Dunctions in the GLU li)rar% )egin 'ith the

letter glu$

G!"

To interface 'ith the 'indo' s%stem and to getinput from e+ternal deices into ourprograms&'e need at least one more li)rar%$


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• G# $ %penG &xtension for the # 'indo( )ystem* = Dor the # (indo( system& this li)rar% is called G#

'G

for (indo(s, it is (gl = 'G or 'iggle is the 'indo'ing s%stem interface to the

Hicrosoft >indo's implementation of the OpenGL specification $

• +G = for the macintosh it is agl or+pple graphics library-.

• Bather than using a different li)rar% for each s%stem&'euse a readil% aaila)le li)rar% called the openGL utilit%Tool*it8GLUT;$

• GLUT proides minimum functionalit% that should )ee+pected in an% modern 'indo'ing s%stem$

http://www710.univ-lyon1.fr/~jciehl/Public/OpenGL_PG/apc.htmlhttp://en.wikipedia.org/wiki/Microsoft_Windowshttp://en.wikipedia.org/wiki/OpenGLhttp://en.wikipedia.org/wiki/OpenGLhttp://en.wikipedia.org/wiki/Microsoft_Windowshttp://www710.univ-lyon1.fr/~jciehl/Public/OpenGL_PG/apc.html


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Li)rar% organiation

OpenGL

Application

program

GLU

GL

GLUT

GL#

#li)t*

Drame

)uffer


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PBIHITI0E: AN"

ATTBI7UTE:


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• OpenGL supports t(o classes ofprimitiesF

= Geometric primities = Image 8or; raster primities

Geometric primitives

• Include points&line segments&pol%gons&curesand surfaces$

• These primities pass through a geometricpipeline$ 'here the% are su).ect to a series of

geometric operations that determine 'hethera primitie is isi)le$

• >here on the displa% it appears if it is isi)le$


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:implified OpenGL pipeline

OpenGL

application

program

Transform Pro.ect 4lip

Drame

)uffer Pi+el operations


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• Geometric Primities can )e used as )uilding )loc*s for othergeometric o).ects$

• Baster primities such as arra%s of pi+els pass through a separate

parallel pipeline$• The )asic OpenGL geometric primities are specified )% sets ofertices$ gl7egin8t%pe;,

gl0erte+8@;,

$

$ gl0erte+8@;,

glEnd8;,

• The alue of type specifies ho' OpenGL assem)les the ertices todefine geometric o).ects$

• Other code and OpenGL function calls can occur )et'een glBegin

and gl&nd$• Ha.or difference )et'een the geometric t%pes = >hether or not the% hae interiors$

All the )asic t%pes are defined )% sets of ertices$


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I& )&G/&")• Dinite sections of lines )et'een t'o

ertices called line segments.

!)&)• Use line segments to define appro+imations to

cures$• %ou can use a se6uence of line segments to

connect data alues for a graph$• ou can also use line segments for the edges of

closed o).ects& such as pol%gon&that haeinteriors$


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• The primitie and their type specification includethe follo'ingF

• PointsG0P%I")-$ = Each erte+ is displa%ed at a sie of at least onepi+el$

• ine segmentsG0I&)-$ = :uccessie pairs of ertices to )e interpreted as the

endpoints of indiidual segments$• PolylinesG0I&0)"1IP,G0I&0%%P-$

G0I&0)"1IP = If successie ertices are to )e connected&'e can use

the line strip&or pol%line form$G0I&0%%P

= 'ill dra' a line segment from the final erte+ to thefirst&thus creating a closed path$


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Pol%gon 7asics

• Polygon =has a )order and has a 'ell definedinterior$It can )e descri)ed )% line loop$

• Pol%gons pla% a special role in 4G$•

The performance of graphics s%stems ischaracteried )% the num)er of pol%gons persecond that can )e rendered$

Polygon rendering• Bender onl% its edges$• Bender its interior 'ith a solid color or a

pattern$• 'e can render or not render the edges


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• "hree properties 'ill ensure that a

pol%gon 'ill )e displa%ed correctl%$

• It must )e simple,convex and flat$

)imple

in (" &as long as no t'o edges of a pol%gon

cross each other&'e hae a simple pol%gon$

>ell defined interiors$


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• a; :imple pol%gon

• 7; Nonsimple pol%gon


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Convex• An o).ect is cone+ if all points on the line

segment )et'een an% t'o points inside the

o).ect&or on its )oundar%&are inside the o).ect$• p/ and p( are ar)itrar% points inside a pol%gon

and the entire line segment connecting them isinside the pol%gon$

• 4one+ o).ects include triangle,tetrahedra,rectangles,circles,spheres,

parallepipeds.• )imple$ edges cannot cross• Convex$ All points on line segment )et'een

t'o points in a pol%gon are also in the pol%gon• 2lat$ all ertices are in the same plane


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• 4one+it%


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4one+ o).ects


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Pol%gon t%pes in OpenGL

• PolygonsG0P%3G%-$ = successie ertices define line segments$and a line

segment connects the final erte+ to the first$

= use the function glpolygon/ode to tell the rendererto generate onl% the edges or .ust points for theertices&instead of fill$

• "riangle and 4uadrilateralsG0"1I+G&),G0Q!+5)-$

= :uccessie groups of three and four ertices areinterpreted as triangles and 6uadrilaterals$


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• )trips and 2ansG0"1I+G&0)"1IP,G0Q!+50)"1IP, G0"1I+G&02+- = groups of triangles or 6uadrilaterals that share ertices and

edges$

"riangle strip = Each additional erte+ is com)ined 'ith the preious t'oertices to define a ne' triangle$

Quadstrip

= 4om)ine t'o ne' ertices 'ith the preious t'o ertices todefine a ne' 6uadrilateral$

"riangle fan

= Triangle fan is )ased on the one fi+ed point$The ne+t t'o pointsdetermine the first triangle& and su)se6uent triangles are formedfrom one ne' point&the preious point and the first point$


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Pol%gon t%pes


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Appro+imating a :phere

#8&K;sin cos K&8&K;cos cos K&

M8&K;sin K

Unit sphere$

Ceep theta fi+ and change phi&

'e get circles of constant

latitude

Ceep phi fi+ and change theta&

'e get circles of constantlongitude$

Poles are on the a+is of the

sphere$


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:phere

C hi fi d h th t D


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Ceep phi fi+ and change theta@Dor

Latitudesfor8float phi


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At Polesgl7egin8GL9TBIANGLE9DAN;,

gl0erte+!d8


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:tro*e te+t

• "efining a full /( or(23 character stro*e

font can )e comple+$

• It ta*es significantmemor% and

processing time$

• standard

postscript fonts


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Baster Te+t

1aster text

glut7itmap8GLUT97ITHAP9979/!& c;,

• simple and fast$

• 4haracters are defined as rectangles of )itcalled bit blocks$

• Each )loc* defines a single character )% thepattern of < and / )its in the )loc*$

• Bit6block6transfer = A raster character can )e placed in the frame )uffer

rapidl% )% a bit6block6transferbitblt- operation&'hich moes the )loc* of )its using a single call$


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• a;Baster te+t ); Baster character replication


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1eplicating

• %ou can increase the sie of raster

characters )% replicating or duplicating

pi+els&a process that gies larger

characters a )loc*% appearance$

• GLUT li)rar% proides a fe' predefined

)itmap and stro*e character sets $


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4ured o).ects

• T'o approaches

= >e can use the primities that 'e hae to

appro+imate cures and surfaces$

• a circle 'ith a regular pol%gon 'ith n sides

= mathematical definitions of cured o).ects

• supported )% GLU li)rar%

• 6uadric surfaces& parametric pol%nomial curesand surfaces


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Attri)utes

An Attri)utes is an% propert% that determines ho' a geometricprimitie is to )e rendered

= point 8color& sie;& line 8color&thic*ness& t%pe;& pol%gon 8patternt%pes& etc;$

= te+t 8height& 'idth& font& st%le 8)old& italic& underlined;;

immediate mode

primities are not stored in the displa% s%stem )ut ratherpassed through the s%stem for possi)le rendering as soon asthe% are defined$

no memor%

once erased from the displa%&it is lost$ display list

*eep o).ects in memor% so that these o).ects can )eredispla%ed$


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4OLOB

• A isi)le color can )e characteried )% afunction 48λ; that occupies 'aelengthsfrom a)out !2< to 5


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• Additie color model = Primar% colors add together to gie the

perceied color$

= The primaries are red&green&)lue8BG7; = E+ample of additie color include

4BT&pro.ectors

)ubractive color model

Primaries are complementar% colorsF 4%an&magenta& %ello'84H;

E+ampleF commercial printing and painting


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4olor formation

• Additie color :u)tractie color


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4olor solid


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4olor solid

• 4olor as a point in a color solid$

• "ra' :olid using a coordinate s%stem

corresponding to the three primaries$

• Principal diagonal of the cu)e connects

the origin8)lac*; 'ith 'hite$All colors along

this line hae shades of gra%$


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BG7 4olor


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BG7 4olor

• There are separate buffers for red,green, andblue images.

• Each pi+el has separate red&green and )luecomponents that correspond to locations in memor%$

• In a t%pical s%stem there might )e a /(< #/


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• 4olor components )et'een


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• Hust clear the 'indo' 'heneer 'e 'ant

to dra' a ne' frame$

• gl4lear4olor8/$


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Inde+ed 4olor

• Earl% graphics s%stems had frame )uffers that 'ere limitedin depth$

• Each pi+el 'as )its deep$• :maller group of pi+elassign to B&G&7$

• It gies less no of color$• Inde+ed color proide solution that allo'ed applications todispla% a 'ide range of color$

• Images are called indexed color )ecause the actual

image color data for each pi+el is the inde+ into thispalette $

• Analog% 'ith an artist 'ho paints in oil$


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• (23 entries in the

ta)le constitute the

user’s color palette$

• figFcolor loo*up ta)le


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Inde+ed color


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• :uppose that our frame has * )its per pi+el$

• Each pi+el alue or inde+ is an integer )et'een < and

(*/$

• >e can displa% colors 'ith precision of m )its$$'e canchoose from (m reds&(m greens&and (m )lues$

• >e can produce an% of (!m colors on the displa%&)ut theframe )uffer can specif% onl% (*of them$

• >e handle the specification through a user defined colorloo*up ta)le that is of sie (* !m$

• The user program fills the (*entries of the ta)le 'ith thedesired colors &using m )its for each of red &green and)lue$

• The first BG7 color in the ta)le is inde+


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• If 'e are in color inde+ mode the present

color is selected )% a function such as

= glIndexielement-:

That selects a particular color out of the ta)le$

GLUT allo's us to set the entries in a color

ta)le for each 'indo' through the follo'ing

functionF glut)etColorint color,Gfloat red,Gfloat

green,Gfloat blue-


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• Adantage

= Less memor%

= De'er other hard'are components$

• )it inde+ed images are still 'idel% used

to sae )and'idth and storage space$

• >hen earl% computer screens 'ere

commonl% limited to (23 colors& inde+ed

color methods 'ere essential$


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:etting of color attri)utes

• clear color

gl4lear4olor8/$


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0IE>ING


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0ie'ing

• The specification of the o).ects is completel%

independent of specification of the camera$

• 4amera forms an image )% e+posing a film$

• The computer s%stem forms an image )%carr%ing out a se6uence of operations in its

pipeline$

• The application program specifies parameters

for o).ect and the camera$


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0IE>INGOrthographic ie'

• OpenGL default ie' orthographic pro.ection

• Place the camera infinitel% far from o).ects$

• Image plane is fi+ed&moe camera far from this

plane$• All pro.ectors )ecome parallel and the center of

pro.ection is replaced )% direction of

pro


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• Pro.ectors that are parallel to the positie

a+is and the pro.ection plane at


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Orthographic Pro.ection

Pro.ectors are orthogonal to pro.ection surface


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• Dor orthographic ie'ing&specialorthographic camera resides in thepro.ection plane$

• There is reference point in the pro.ectionplane from 'hich 'e can ma*emeasurements of a ie' olume and adirection of pro.ection$

• 1eference point origin$ camera points inthe negatie direction$

The default camera and an


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The default camera and an

orthographic ie' olume


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0ie'ing olume


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• It ta*es a point8+&%&; and pro.ects it into the point8+&%&


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• The orthographic pro.ection sees onl%those o).ects in the olume specified )%ie'ing olume$

• If 'e do not specif% a ie'ingolume&openGL uses its default& ( + ( + (cu)e&'ith the origin in the center$

• In (" t'o dimensional plane&the )ottomleft corner is at 8/$


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(" ie'ing

• =oid glu%rtho>5Gdouble left,Gdouble

right,Gdouble bottom,Gdouble top-

• Near and far set to /$< and /$< respectiel%$

• Ta*e a rectangular area of our t'o dimensional'orld and transfering its contents to the displa%$

• The area of the 'orld that 'e image is *no'n as

vie(ing rectangle or clipping rectangle$

• O).ects inside the rectangle are in the

image$o).ects outside are clipped out$


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(" ie'ing

• a; o).ects )eforeclipping$

• ); o).ects after

clipping


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HATBI# HO"E

• Using gl/atrix/ode function %ou chose 'hich matri+ %ou 'ant tochange$

• OpenGL 'or*s 'ith ! matricesF G0/%5&=I&'F this one is usedto moe erte+ to model space$

• 7% default& the matri+ mode is GL9HO"EL0IE>& 'hich assumeseer%thing %ou dra' 'ill )e in one !d space$

• G0P1%?&C"I%F this one is used to conert !d coordinate to (dcoordinate for final pi+el position$

• A computer monitor is a (" surface$ >e need to transform !" sceneinto (" image in order to displa% it$ GL9PBOJE4TION matri+ is forthis pro.ection transformation

• G0""!1&F this one is used to alter te+ture coordinates$

http://www.songho.ca/opengl/gl_transform.htmlhttp://www.songho.ca/opengl/gl_transform.html


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Hatri+ mode

• Pipeline graphics s%stem depends on multipl%ingtogether or Concatenating a num)er of transformationmatrices to achiee the desired image of a primitie

• T'o important matricesF

= /odel6vie( = Prohich are initiall% set to identit% matri+$

= The usual se6uence is to modif% the initial identit% matri+ )%appl%ing se6uence of transformations$

= :elect the matri+ to 'hich the operations appl% )% first settingthe matri+ mode&a aria)le that is set to one t%pe of matri+ that isalso part of the state$


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• Once %ou set the matri+ mode& each su)se6uentoperation is applied to that particular matri+ mode and)elo' it $

glHatri+Hode8GL9PBOJE4TION;,

glLoadIdentit%8;,

glOrtho8/$


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4ONTBOL DUN4TION


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Interaction 'ith the 'indo' s%stem

• GLUT is a li)rar% of function that proidesa simple interface )et'een s%stems$

• 'indo( or screen (indo( denote a

rectangular area of our displa%$• 'indo(

= has height and 'idth

= it displa%s the contents of the frame )uffer$ = Positions in the 'indo' measured in terms

pixels.

• >e can displa% man% t%pe of 'indo's on


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>e can displa% man% t%pe of 'indo's on

monitor$

• The 'indo' in 'hich the graphics output

appears is one of the 'indo's managed )% the

'indo' s%stem$

• In science and engglo'er left corner is the

origin$• All raster s%stem top left corner is origin$

• openGL )ottom left corner is origin$

• :creen resolution/(< +/


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• Interaction )et'een 'indo'ing s%stem and OpenGL isinitialied )% the follo'ing function$• glutInitint @argc,char @@argv-

• Argument is same as main$• Open OpenGL 'indo' using GLUT function

glutCreate'indo(char @title-

• >here the Title at the top of the 'indo' is gien )% string

title$• Use follo'ing GLUT functions )efore 'indo' creation to

specif% these parameters$• glutInit5isplay/odeG!"01GB A G!"05&P" A

G!"05%!B&-:

• glutInit'indo()i;eD8,DE8-:• glutInit'indo(Position8,8 ;,

• :pecifies a 1< + 31< 'indo' in the topleft corner of thedispla%$

A t ti d i t


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Aspect ratio and ie'ports

• The aspect ratio of a rectangle is the ratio of therectangle’s 'idth to its height$

• If alues in gl%rtho and glutInit'indo()i;e

differ = undesira)le side effects• If the% differ& o).ects are distorted on the

screen$

• To aoid this distortion if 'e ensure that the

clipping rectangle and displa% 'indo' hae the

same aspect ratio$

A t ti i t h


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Aspect ratio mismatch

• a; ie'ing

• rectangle

• );displa%

• 'indo'

A i t th i t


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A mapping to the ie'port


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• Another method = =ie(port

• A ie'port is a rectangular area of the displa%'indo'$)% default it is entire 'indo'$

• It can )e set to an% smaller sie in pi+els ia thefunction$

• void gl=ie(portGint x,Glint y,Gsi;ei

(,Gsi;ei h-• #&%lo'er left corner of the 'indo'$

• '&h gie height and 'idth$

The main&displa% and m%init


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The main&displa% and m%init

Dunctions = =oid glut/ainoop-:

• >hose e+ecution 'ill cause the program to )egin aneentprocessing loop$If there are no eents toprocess&the program 'ill sit in a 'ait state&until 'eterminate the program$

• The graphics are sent to the screen through a functioncalled the display callback$ this function is namedthrough the GLUT function$

• void glut5isplay2uncdisplay-• And registered 'ith the 'indo' s%stem$ function named

display 'ill )e called 'heneer the 'indo'ing s%stemdetermines that the OpenGL 'indo' needs to )eredispla%ed$

• A displa% call)ac* also occurs &'hen the 'indo' ismoed from one location on the screen to another$

0oid main8int argc&char arg;


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Q

glutInit8Vargc& arg;,

glutInit"ispla%Hode8GLUT9:INGLEWGLUT9BG7;, glutInit>indo':ie82


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Program structure

• Eer% program hae same structure$

• Al'a%s use the GLUT tool*it$

• The main function 'ill consists of calls to GLUT

functions to set up our 'indo'$• Eer% program must hae displa% call)ac*$

• H%init function set up user operations$

• In ma.orit% of programs&the graphics output 'ill)e generated in the displa% call)ac*

:i i *i G * t 8(";


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:ierpins*i Gas*et 8(";

• :tart 'ith a triangle

• 4onnect )isectors of sides and remoe centraltriangle

• Bepeat


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• If 'e dra' line segments connecting themidpoints of the sides of the original triangle&then'e diide the original triangle into fourtriangles&the middle one containing no points$

• >e can appl% the same o)eration to each ofthem$• It uses polygons instead of points and does

not re6uire the use of a random num)ergenerator$

• The adantages of using pol%gon is that 'e getsolid areas on our display.

G * t P


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Gas*et Program

#include

/* initial triangle */

GLfloat v[3][2]={{-.!" -!.$%"{.!" -!.$%" {!.!" .%%&

int n& /* nu'(er of recur)ive )te) */

" t i l


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"ra' one triangle

void triangle+ GLfloat *a" GLfloat *("GLfloat *c,

/* di)la one triangle */

{ gl7egin8GL9TBIANGLE:;,

gl0erte+(f8a;,

gl0erte+(f8);,

gl0erte+(f8c;,

glEnd8;,

S


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displa% and init Dunctions


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displa% and init Dunctions

void di)la+,{ gllear+GL4L456788956:;,&dividetriangle+v[!]" v[]" v[2]" n,&

gl8lu)h+,&%

void 'init+,{

glu4rtho2+-2.!" 2.!" -2.!" 2.!,& gllearolor +.!" .!" .!".!, glolor3f+!.!"!.!"!.!,&%

main Dunction


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main Dunction

int 'ain+int argc" char **argv,{ n=& glut:nit+argc" argv,&

glut:niti)la?ode+GL7;@:AGL9BGL7;5G6,& glut:nitCindo@iDe+!!" !!,& glutreateCindo+E2 Ga)Fet,&

gluti)la8unc+di)la,& 'init+,& glut?ainLoo+,&%

E+ample


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E+ample

•Die su)diisions


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!" GA:CET

• A tetrahedron 8pluralF tetrahedra; is a pol%hedron

composed of four triangular faces three of 'hich meet at

http://en.wikipedia.org/wiki/Polyhedronhttp://en.wikipedia.org/wiki/Trianglehttp://en.wikipedia.org/wiki/Trianglehttp://en.wikipedia.org/wiki/Polyhedron


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composed of four triangular faces& three of 'hich meet at

each erte+$

• The tetrahedron is the onl% cone+ pol%hedron that hasfour faces$

•>e can su)diide each of the four faces$

!" Gas*et Use of !" points

http://en.wikipedia.org/wiki/Trianglehttp://en.wikipedia.org/wiki/Vertex_(geometry)http://en.wikipedia.org/wiki/Vertex_(geometry)http://en.wikipedia.org/wiki/Triangle


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!" Gas*et Use of !" points

• Eer% tetrahedron is cone+& the midpoint of a linesegment )et'een a erte+ and an% point inside atetrahedron is also inside the tetrahedron$

• >e need initial four ertices to define a tetrahedron$

• >e define and initialie an arra% to hold the ertices asfollo's$

• GLfloat erticesZ1[Z![ QQ


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Q

Int i,

fork78:kF888:kHH-Q

Jrand8;\1,

pZ


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dimensions

• :u)diision of a tetrahedron into smaller tetrahedron$• :tart 'ith a tetrahedron and find 'ith midpoints of its six

edges and connect these midpoints.• There are four smaller tetrahedrons& one for each of the

original ertices& and another area in the middle that 'e 'ill

discard$• "riangle function

0oid triangle8GLfloat a&GLfloat )&GLfloat c;

Q

gl0erte+!f8a;,

gl0erte+!f8);,

gl0erte+!f8c;

S


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• >e dra' each tetrahedron&coloring each face 'ith a different color)% using the follo'ing function$

0oid tetra8GLfloat a& &GLfloat )&GLfloat c&GLfloat d;

Q

gl4olor!f8colorsZ


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Q

GLfloat midZ3[Z![,

int .,

if8mY


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p %8;

Q

gl4lear8GL94OLOB97UDDEB97IT;,

gl7egin8GL9TBIANGLE:;,

diide9tetra8Z


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?idden surface remoal• Drom the ie'er’s position&6uadrilateral A

is seen clearl%&)ut triangle is )loc*ed fromie'&and triangle 4 is onl% partiall% isi)le$

• Algorithms for ordering o).ects so that the%are dra'n correctl% are called visiblesurface algorithms or hidden surface

removal algorithms.

• ;6buffer algorithm is used for hiddensurface remoal&that is supported )%openGL$

• "his algorithm can be turnedonenabled- and offdisabled- easily.

• >e re6uest the au+iliar% storage&a ; depth- buffer & )%


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6 % g & p - & %modif%ing the initialiation of the displa% mode to thefollo'ing$

glutInit5isplay/odeG!"0)IG& A G!"01GB AG!"05&P"-:

• >e ena)le the algorithm )% the function call gl&nableG05&P"0"&)"-

either in main or in an initialiation function such asm%init$

• >e modif% the clear procedure in the displa% functionFgl4lear8GL94OLOB97UDDEB97IT W

GL9"EPT?97UDDEB97IT;,


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0oid displa%8;Q

gl4lear8GL94OLOB97UDDEB97ITWGL9"EPT?97IT;,

gl7egin8GL9TBIANGLE:;, diide9tetra8Z

computer graphics(unit2)

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