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Page 1: CS452 | COMPUTER GRAPHICS - Washington … | COMPUTER GRAPHICS Courtesy of Andries van DamScan Conversion - 10/15/13©} Point } Line } Circle } Ellipse } … } Woody 4 What is the

CS452 | COMPUTER GRAPHICS

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Scan ConversionCS452

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} EnrollyourselftoPiazza} Assignment0willbeduenextMonday} Testuploadingadummyfilenow} VisualStudioversion(onlyVS2013?NoVS2015)

} Officehourslocation(conferenceroominJolleyoruniversitylabs)?} Officehours(differenttime?)

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Logistics

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} Point} Line} Circle} Ellipse} …} Woody

4

What is the simplest possible thing to draw?

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LineDrawing} Firstproblemstatement:Drawalineonarasterscreenbetweentwopoints

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Scan Converting Lines

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Raster Screen

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LineDrawing} Firstproblemstatement:Drawalineonarasterscreenbetweentwopoints

} Whyisthisadifficultproblem?} Whatis“drawing”onarasterdisplay?} Whatisa“line”inrasterworld?} Efficiencyandappearancearebothimportant

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Scan Converting Lines

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LineDrawing} Firstproblemstatement:Drawalineonarasterscreenbetweentwopoints

} Whyisthisadifficultproblem?} Whatis“drawing”onarasterdisplay?} Whatisa“line”inrasterworld?} Efficiencyandappearancearebothimportant

ProblemStatement} GiventwopointsPandQinXYplane(integercoordinates),} determinewhichpixelsshouldbeon} tobestapproximateaunit-widthlinesegmentfromPtoQ.

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Scan Converting Lines

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Specialcases:} HorizontalLine:

} DrawpixelPandincrementxcoordinatevalueby1togetnextpixel.} VerticalLine:

} DrawpixelPandincrementycoordinatevalueby1togetnextpixel.} DiagonalLine:

} DrawpixelPandincrementbothxandycoordinateby1togetnextpixel.} Whatshouldwedoingeneralcase?

} Forslope<=1,incrementxcoordinateby1andchoosepixelonorclosesttoline.Slopesinotheroctantsbyreflection(e.g.,insecondoctant,incrementY)

} Buthowdowemeasure“closest”?

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Scan-converting a Line: Finding the next pixel:

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Strategy 1 – Incremental Algorithm (3/3) - issuesvoidLine(intx0,inty0,intx1,inty1){intx,y;floatdy=y1–y0;floatdx=x1–x0;floatm=dy/dx;

y=y0;for(x=x0;x<x1;++x){ WritePixel(x,Round(y)); y=y+m;}}

Roundingtakestime

Sinceslopeisfractional,needspecialcaseforverticallines(dx=0)

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voidMidpointLine(intx0,inty0,intx1,inty1){intdx=(x1-x0),dy=(y1-y0);intd=2*dy-dx;intincrE=2*dy;intincrNE=2*(dy-dx);intx=x0,y=y0;WritePixel(x,y);

while(x<x1){if(d<=0)d=d+incrE;//EastCaseelse{d=d+incrNE;++y;}//NortheastCase++x;WritePixel(x,y);} }

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Example Code

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}

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Incremental Computation (2/2)

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MidpointEighthCircle(R){/*1/8thofacirclew/radiusR*/intx=0,y=R;floatdecision=(x+1)*(x+1)+(y-0.5)*(y-0.5)–R*R;WritePixel(x,y);

while(y>x){if(decision<0){//MoveEastdecision+=2*x+3;x++;WritePixel(x,y);}else{//MoveSouthEastdecision+=2*x–2*y+5;y--;x++;WritePixel(x,y);}}}

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Midpoint Eighth Circle Algorithm (less optimized)

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MidpointEighthCircle(R){/*1/8thofacirclew/radiusR*/intx=0,y=R;intdeltaE=2*x+3;intdeltaSE=2*(x-y)+5;floatdecision=(x+1)*(x+1)+(y-0.5)*(y-0.5)–R*R;WritePixel(x,y);

while(y>x){if(decision<0){//MoveEastx++;WritePixel(x,y);decision+=deltaE;deltaE+=2;deltaSE+=2;//Updatedeltas}else{//MoveSouthEast y--;x++;WritePixel(x,y);decision+=deltaSE;deltaE+=2;deltaSE+=4;//Updatedeltas}}}

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Midpoint Eighth Circle Algorithm

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} AlignedEllipses

} Non-integerprimitives

} Generalconics

} Patternedprimitives

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Other Scan Conversion Problems

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