Bresenham algorithm

Bresenham algorithm

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2. Name : Professor Dr. Md. Ismail Jabiullah Designation Professor   Department Department of Computer Science and Engineering SUBMITTED TO

3. Yasir Arefin Tusher 152-15-5944 MD Rubel 152-15-6037 MD A rifur Rahman 152-15-5830 Sk.Mehedi Hasan 161-15-7667 Raisa Tabassum 152-15-6022 Arafat Rahman 152-15-5983 SUBMITTED By

4. The representation and manipulation of image data by a computer INTRODUCTION TO COMPUTER GRAPHICS

5. INTRODUCTION DIU The term computer graphics refers to "almost everything on computers that is not text or sound” Refers to creation, Storage and manipulation of pictures and drawing using a digital computer. Effective tool for presenting information.

6. WHAT IS COMPUTER GRAPHICS? DIU Creation, Manipulation, and Storage of geometric objects (modelling) and their images (rendering). Display those images on screens or hardcopy devices Image processing

7. HISTORY OF COMPUTER GRAPHICS (1951–1959)s Data was displayed on printers. Used CRT and light pen for user interactive environment Design

8. HISTORY OF COMPUTER GRAPHICS 1960 – William Fetter  Introduced phrase “Computer Graphics”

9. HISTORY OF COMPUTER GRAPHICS 1970’s – powerful PCs to draw basic and complex shapes

10. HISTORY OF COMPUTER GRAPHICS 1980’s – artists and graphics designers preferred to use Macintosh and PCs Late 1980’s – 3-D computer graphics with SGI (Silicon Graphics) computers

11. HISTORY OF COMPUTER GRAPHICS 1990’s onwards – 3D graphics in gaming, multi media and animation, GUI

12. HISTORY OF COMPUTER GRAPHICS 3D rendering capabilities became a standard feature after in 2000 ’s

13. APPLICATIONS OF COMPUTER GRAPHICS DIU COMPUTER AIDED DESIGN (CAD) ANIMATION COMPUTER GAMES VISUALIZATION GRAPHICAL PRESENTATION

14. COMPUTER AIDED DESIGN DIU Computer Aided Design(CAD) is the Use of Computer System to Assist in the Creation , Modification , Analysis or Optimization of Design.

15. VISUALIZATIN DIU Visualization is any Technique For Creating Images , Diagrams or Animations To Communicate A Message.

16. ANIMATION DIU Animation is the process of creating a continuous motion & shape change illusion by means of rapid display of a sequence of static images that minimally differ from each other

17. COMPUTER GAMES DIU Computer games are video games played on a general purpose personal computer

18. DISPLAY OF INFORMATION: Graphics for Scientific, Engineering, and medical Data Nebula Medical Image

19. Entertainment: Computer Graphics methods are used in making music videos ,games ,cartoon movies ,television shows etc. Graphics for Movie, cartoon etc movie cartoon

20. LINE DRAWING ALGORITHMS DIU There are two basic line drawing algorithm…. DDA line drawing algorithm Bresenham’s Line Drawing Algorithm

21. REFERENCES TOOTHLESS GEAR https://en.wikipedia.org/wiki/Computer_graphics iu.edu.jo/files/ FacultyIT / slides_it / ComputerGraphics /DrJamalLecture01.pdf https://www.civilsimplified.com/resources/What-is-computer-aided-design https://en.wikipedia.org/wiki/Visualization_(graphics) https://en.wikiquote.org/wiki/Animation

22. Bresenham's Line Algorithm

23. DESCRIPTIONS DIU Bresenham’s line algorithm is an algorithm,that determines the points of an n -dimensional raster that should be selected in order to form a close approximation to a straight line between two points. The Bresenham’s algorithm is another incremental scan conversion algorithm . The big advantage of this algorithm is that it uses only integer calculations

24. FIGURE ANALYSIS DIU

25. ANALYSIS DIU

26. ANALYSIS DIU

27. ALGORITHM DIU

28. Working Process Bresenham’s algorithm for scan-converting a line from P 1 (x 1 , y 1 ) to P 2 (x 2 , y 2 ) with x 1 ’<x 2 ’ and o<m<1 can be stated as follows: int x = x 1 , y =y 1 ; int dx = x 2 - x 1 , dy = y 2 - y 1 , dT = 2( dy - dx), dS = 2dy; int d = 2dy – dx; setPixel ( x,y ); while(x<x 2 ){ x ++ ; if(d<0) d = d + dS ; else{ y ++ ; d = d + dT ; } setPixel (x, y); }

29. Plot a Line whose Slope is between 0 to 45 using Bresenham’s Line Algorithm Algorithm: Step 1: Compute the initial values: dx = x 2 – x 1 , Inc 2 = 2( dy – dx ) dy = y 2 – y 1 , d = Inc 1 – dx Inc 1 = 2dy Step 2: Set (x, y) equal to the lower left-hand end-point and set x end equal to the largest value of x. If dx < 0, then x = x 2 , y = y 2 and x end = x 1 . If dx > 0, then x = x 1 , y = y 1 and x end = x 2 . Step 3: Plot a point at current (x, y) position. Step 4: Test to see whether the entire line has been drawn. If x> x end , Stop. Step 5: Compute the location of the next pixel. If d<0, then d = d+ inc 1 . If d>=0, then d = d + Inc 2 , and y = y + 1. Step 6: Increment x: x = x+1. Step 7: Plot a point at current (x, y) position. Step 8: Go to Step 4.

30. Bresenham’s Line Algorithm: Scan- conerting a Line from (1, 1) to (8, 5) Algorithm: Step 1: Find the starting values. Step 2: In this case, dx = x 2 – x 1 = 8 – 1 = 7, dy = y2 – y1 = 5 – 1 = 4. Step 3: Therefore, Inc 1 = 2, dy = 2 x 4 = 8. Inc2 = 2( dy –dx) = 2(4 - 7) = - 6, d= Inc 1 – dx = 8 – 7 = 1. The following table indicates the values computed by the algorithm:

31. Applications of Bresenham Algorithm Wire-frame Modeling 

32. Applications of Bresenham Algorithm

33. EXAMPLE

34. Advantages of Bresenham Algorithm Uses fixed points Easy to calculate (only addition & subtraction) Fast execution compare to DDA More accurate and efficient

35. Disadvantages of Bresenham’s Algorithm Drift away from actual line path Causes stair-case pattern

36. REFERENCES TOOTHLESS GEAR https://en.wikipedia.org/wiki/Computer_graphics iu.edu.jo/files/ FacultyIT / slides_it / ComputerGraphics /DrJamalLecture01.pdf https://www.civilsimplified.com/resources/What-is-computer-aided-design https://en.wikipedia.org/wiki/Visualization_(graphics) https://en.wikiquote.org/wiki/Animation

37. REFERENCES TOOTHLESS GEAR https://en.wikipedia.org/wiki/Computer_graphics https://www.thecrazyprogrammer.com/2017/01/bresenhams-line-drawing-algorithm-c-c.html https://en.wikipedia.org/wiki/Visualization_(graphics) https://en.wikiquote.org/wiki/Animation

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