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Mid Point Line Drawing Algorithm

Mid Point Line Drawing Algorithm. Assist. Prof. Dr. Ahmet Sayar Computer Engineering Department Computer Graphics Course Kocaeli University Fall 2013. How to Improve It?. Question: if we draw the current pixel, where is the next pixel? Next column, E or NE direction.

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Mid Point Line Drawing Algorithm

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  1. Mid Point Line Drawing Algorithm Assist. Prof. Dr. Ahmet Sayar Computer Engineering Department Computer Graphics Course Kocaeli University Fall 2013

  2. How to Improve It? Question: if we draw the current pixel, where is the next pixel? Next column, E or NE direction

  3. Midpoint Algorithm • Given a point just drawn, determine whether we move E or NE on next step • Is the line above or below ? Below: move E Above: move NE

  4. Above/Below the Line?

  5. Two Issues • How to evaluate if the midpoint is above or below the line? • How to incrementally evaluate this?

  6. Midpoint Algorithm – Implicit Forms • How do we tell if a point is above or below the line?

  7. Midpoint Algorithm – Implicit Forms • How do we tell if a point is above or below the line?

  8. Midpoint Algorithm – Implicit Forms • How do we tell if a point is above or below the line? Properties f(x,y)=0 (x,y) on the line f(x,y)<0 (x,y) below the line f(x,y)>0 (x,y) above the line

  9. Midpoint Algorithm – Implicit Forms

  10. Two Issues • How to evaluate if the midpoint is above or below the line? • How to incrementally evaluate this? What about starting value? What is the middle point? (xL+1,yL+1/2)

  11. Midpoint Algorithm What about starting value? (xL+1,yL+1/2) is on the line!

  12. Midpoint Algorithm What about starting value? Multiplying coefficients by 2 doesn’t change sign of f

  13. Midpoint Algorithm • Need value of to determine E or NE • Build incremental algorithm • Assume we have value of • Find value of if E chosen

  14. Midpoint Algorithm Need value of to determine E or NE Build incremental algorithm Assume we have value of Find value of if E chosen Find value of if NE chosen 14/110

  15. Midpoint Algorithm If E was chosen, find

  16. Midpoint Algorithm If NE was chosen, find

  17. Midpoint Algorithm – Summary x=xLy=yL d=xH - xL c=yL - yH sum=2c+d //initial value draw(x,y) while ( x < xH) // iterate until reaching the end point if ( sum < 0 ) // below the line and choose NE sum+= 2d y++ x++ sum += 2c draw(x,y)

  18. Midpoint Algorithm – Summary x=xLy=yL d=xH - xL c=yL - yH sum=2c+d //initial value draw(x,y) while ( x < xH) // iterate until reaching the end point if ( sum < 0 ) // below the line and choose NE sum+= 2d y++ x++ sum += 2c draw(x,y) - Update the current pixel - Update the function value of midpoint 18/110

  19. Midpoint Algorithm – Summary x=xLy=yL d=xH - xL c=yL - yH sum=2c+d //initial value draw(x,y) while ( x < xH) // iterate until reaching the end point if ( sum < 0 ) // below the line and choose NE sum+= 2d y++ x++ sum += 2c draw(x,y) - Draw the pixel based on the function value of midpoint 19/110

  20. Midpoint Algorithm – Example x=xLy=yL d=xH - xL c=yL - yH sum=2c+d draw(x,y) while ( x < xH) if ( sum < 0 ) sum+= 2d y++ x++ sum += 2c draw(x,y) d =6 c = -2

  21. Midpoint Algorithm – Example x=xLy=yL d=xH - xL c=yL - yH sum=2c+d draw(x,y) while ( x < xH) if ( sum < 0 ) sum+= 2d y++ x++ sum += 2c draw(x,y) d =6 c = -2

  22. Midpoint Algorithm – Example x=xLy=yL d=xH - xL c=yL - yH sum=2c+d draw(x,y) while ( x < xH) if ( sum < 0 ) sum+= 2d y++ x++ sum += 2c draw(x,y) d =6 c = -2

  23. Midpoint Algorithm – Example x=xLy=yL d=xH - xL c=yL - yH sum=2c+d draw(x,y) while ( x < xH) if ( sum < 0 ) sum+= 2d y++ x++ sum += 2c draw(x,y) d =6 c = -2

  24. Midpoint Algorithm – Example x=xLy=yL d=xH - xL c=yL - yH sum=2c+d draw(x,y) while ( x < xH) if ( sum < 0 ) sum+= 2d y++ x++ sum += 2c draw(x,y) d =6 c = -2

  25. Midpoint Algorithm – Example x=xLy=yL d=xH - xL c=yL - yH sum=2c+d draw(x,y) while ( x < xH) if ( sum < 0 ) sum+= 2d y++ x++ sum += 2c draw(x,y) d =6 c = -2

  26. Midpoint Algorithm – Example x=xLy=yL d=xH - xL c=yL - yH sum=2c+d draw(x,y) while ( x < xH) if ( sum < 0 ) sum+= 2d y++ x++ sum += 2c draw(x,y) d =6 c = -2

  27. Midpoint Algorithm – Example x=xLy=yL d=xH - xL c=yL - yH sum=2c+d draw(x,y) while ( x < xH) if ( sum < 0 ) sum+= 2d y++ x++ sum += 2c draw(x,y) d =6 c = -2

  28. Midpoint Algorithm • Only integer operations • Exactly the same as the more commonly found Bresenham’s line drawing algorithm • Extends to other types of shapes (circles)

  29. Midpoint Algorithm – Example x=xmin y=ymin d=xmax- xmin c=ymin- ymax sum=2c+d draw(x,y) while ( x < xmax) if ( sum < 0 ) sum += 2d y++ x++ sum += 2c draw(x,y)

  30. Midpoint Algorithm – Example x=xmin y=ymin d=xmax- xmin c=ymin- ymax sum=2c+d draw(x,y) while ( x < xmax) if ( sum < 0 ) sum += 2d y++ x++ sum += 2c draw(x,y)

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