1. CAP 4703 Computer Graphic Methods Prof. Roy Levow Lecture 2

2. 2-Dimensional Drawing with OpenGL  Two-dimensional objects are a special case of three-dimensional figures  The drawing is limited (by the programmer) to a plane  Viewing is normally an orthogonal view, perpendicular to the drawing plane

3. Sierpinski Gasket  A simple but interesting example  Start with any triangle 1. Pick an internal point at random 2. Pick a vertex at random 3. Find the midpoint between 1 and 2 4. Display this point 5. Replace initial point with this one 6. Repeat from step 2

4. Sierpinski Gasket Construction

5. OpenGL Program for Sierpinski Gasket main() { initialize_the_system(); for (some_number_of_points) { pt = generate_a_point(); display_the_point(pt); } cleanup(); return 0; }

6. Points or Vertices  Points are represented by vectors with an entry for each coordinate  p = (x, y, z) in 3 dimensions  p = (x, y, 0) gives 2 dimensions by always setting z to 0  OpenGL allows up to 4 dimensions  Internal representation is always the same

7. OpenGL Vertices  Vertex creating functions have general name glVertex*  The suffix is 2 or 3 characters –Number of dimensions: 2, 3, or 4 –Data type: i = integer, f = float, d = double –Optional v if pointer

8. Underlying Representation  OpenGL data types are defined in header file #define GLfloat float so a header might look like glVertex2i(GLint xi, GLint yi) or glVertex3f(GLfloat xf, GLfloat yf, GLfloat zf)

9. Representation (cont.)  For the vector form GLfloat vertex[3]; and then use glVertex3fv(vertex);

10. Defining Geometric Objects  Objects are defined by collections of point constructors bounded by calls to glBegin and glEnd  A line is defined by glBegin(GL_LINES); glVertex2f(x1, y1); glVertex2f(x2, y2); glEnd();

11. OpenGL Code for Sierpinski Gasket  See p. 41 of text  Code leaves many open questions by using default values 1.colors 2.image position 3.size 4.clipping? 5.persistence

12. A Resulting Image

13. Coordinate System  Early systems depended on specific device mapping  Device-independent graphics broke link  Use application or problem coordinate system to define image  Use device coordinates, raster coordinates, screen coordinates for device

14. Coordinates  Application coordinates can be integer or real and multi-dimensional  Screen or raster coordinates are always integer and essentially 2- dimensional  Graphics program maps application coordinates onto device coordinates

15. App to Device Mapping

16. Classes for OpenGL Functions 1. Primitives – draw points, line segments, polygons, text, curves, surfaces 2. Attributes – specify display characteristics of objects: color, fill, line width, font 3. Viewing – determine aspects of view: position and angle of camera, view port size, …

17. Function Classes (cont) 4. Transformations – change appearance or characteristics of objects: rotate, scale, translate 5. Input – handle keyboard, mouse, etc. 6. Control – communicate with window system 7. Inquiry – get display information: size, raster value, …

18. OpenGL Interface  Graphics Utility Interface (GLU) –Creates common objects like spheres  GL Utility Toolkit (GLUT) –Provides generic interface to window system  GLX for Unix/Linux and wgl for Microsoft Windows –provide low-level glue to window system

19. Library Organization

20. Using Libraries  Header files –#include –#include  On some systems the GL/ is not used

21. Primitives  OpenGL supports both geometric primitives and raster primitives

22. Geometric Primitives  Points = GL_POINTS –vertex displayed with size >= 1 pixel  Line segments = GL_LINES –defined by pairs of vertices as endpoints of segments  Polygons = GL_LINE_STRIPE or GL_LINE_LOOP –Loop is closed, stripe is not

23. Primitive Examples

24. Properties of Polygons  Defined by line loop border  Simple if no edges cross  Convex if every line segment connecting pair of points on boundary or inside lies completely inside

25. Polygon Types in OpenGL  Polygons are either filled regions (default) or boundaries  Set with glPolygonMode  To get polygon with boundary must draw twice, once as filled and once as boundary or line loop

26. Special Polygons  GL_TRIANGLES, GL_QUADS –Groups of 3 or 4 points are grouped as triangles or quadrilaterals

27. Special Polygons  GL_TRIANGLE_STRIPE, GL_QUAD_STRIPE, GL_TRIANGEL_FAN –Contiguous stripe or fan of triangles or quadrilaterals

28. Drawing a Sphere  Draw great circles  Fill between latitudes with quad strips  Fill caps with triangle fans  Code on p.52

29. Text  May be raster – from bit map –Fast –Does not scale well –Poor in rotation other than 90 o  Vector – from drawn curves –Slow to draw –Scales, rotates, etc. well

30. Raster text

31. Color  The physiology of vision leads to 3- color theory  Any color can be produced by a combination of red, green, and blue at intensities that produce the same response in the cones as the true color

32. Colors in OpenGL  Colors are stored using 4 attributes, RGBA  A = Alpha channel –Controls opacity or transparency  Color values can be integers in range from 0 to max component value –0 – 255 for 24-bit color  Real numbers between 0.0 and 1.0

33. Colors in OpenGL (cont)  Colors are set with glColor* functions –* is two characters, nt  n = 3 or 4 color values  t = date type: i, f, etc.

34. Clearing Frame Buffer  To get predictable results a program must first clear the frame buffer glClearColor(1.0, 1.0, 1.0, 1.0) –sets color to white

35. Indexed Color  OpenGL also supports indexed color –Saves space when only a limited number of distince colors are used

36. Indexed Color (cont)  Set color in table with glutSetColor(int color, GLfloat red, GLfloat blue, GLfloat green) GLfloat blue, GLfloat green)  Access color in table with glIndexi(element)

37. Viewing  Based on synthetic camera model  If nothing is specified, there are default viewing parameters –Rarely used –Would force us to fit model world to camera  Prefer flexibility of setting viewing parameters

38. Two-Dimensional Viewing  Selected rectangle from 2- dimensional world is displayed  Called viewing rectangle or clipping rectangle

39. Viewing Volume  2-dimensional viewing is special case of 3-dimensional viewing –viewing volume  Default is 2 x 2 x 2 cube centered cube centered at (0,0,0)

40. Orthographic Projection  Projects point (x,y,z) onto (x,y,0)  View is perpendicular to plane x=0  Set viewing rectagle with void glOrtho(GLdouble left, GLdouble right, GLdouble bottom, GLdouble top) GLdouble top)

41. Matrix Modes  Graphic pipelines perform matrix transformations on images at each stage  Most important matrices are –model-view –projection  State includes both

42. Manipulating Mode Matrices  Matrix mode operations operate on matrix for currently selected mode –Model-view is default  Mode is set with glMatrixMode(mode) mode = GL_PROJECTION, GL_MODELVIEW, etc.  Always return to model-view to insure consistency

43. Control Functions  Depend on particular window system  GLUT provides standard set of basic operations –We will consider only these

44. Window Control  Operations only on display window for the program  Initialization – glutInit  Creation – glutCreateWindow  Display mode –glutInitDisplayMode –RGB or indexed –hidden-surface removal –singer or double buffering

45. Example Code glutInit(&argc, argv); glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB | GLUT_DEPTH); glutInitWindowSize(480, 480); glutWindowPosition(0, 0); glutCreateWindow(“sample");

46. Aspect Ratio and Viewports  Ratio of width to length is aspect ratio  If aspect ratio of viewing rectangle and window differ, image will be stretched and distorted  Viewport defines region of screen in which to display image –Can eliminate distortion

47. Distortion

48. Viewport  Set viewport with void glViewport(GLint x, GLint y, GLsizei w, GLsizei h)

49. GLUT Main Loop  If we simply run an OpenGL program it will display the image and exit –may not allow time to see it –could sleep program to keep window open but this is limited solution  GLUT provides controls to avoid this  Keep program running waiting for event void glutMainLoop(void)

50. Glut Display  To display an image, code a function to create the image and have GLUT call it  image drawing function takes no arguments and returns no result –Any parameters must be passed through global variables void glutDisplayFunc(void (*func)(void))

51. Simple Main Program #include void main(int argc, char **argv) { glutInit(&argc, argv); glutInitDisplayMode (GLUT_SINGLE | GLUT_RGB); glutInitWindowSize(500, 500); glutWindowPosition(0, 0);

52. Simple Main Program (cont) glutCreateWindow(“My Image"); glutDisplayFunc(display); myinit(); glutMainLoop(); }

53. Program Structure  Key components –initialization –display callback function –main  Gasket Program..\code\gasket.c..\code\gasket.c – 2-d..\code\gasket.c..\code\gasket2.c..\code\gasket2.c – 3-d with colors..\code\gasket2.c../code/gasket3.c../code/gasket3.c – 3-d with polygons../code/gasket3.c

54. Hidden Surface Removal  Z-buffer algorithm  Z coordinate determines depth  Point nearer camera obscures one with greater depth  Steps –Init with GLUT_DEPTH –glEnable(GL_DEPTH_TEST  can also disable –clear before redrawing

55. Sample HSR Program void display() { glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT) tetrahedron(n) glFlush(); }