1. Basic of computer graphics with OpenGL

2. Handful graphics function  OpenGL :  by silicon graphics  PHIGS :  Programmer’s Hierarchical Graphics System  GKS :  Graphic Kernel System  JAVA-3D  By Sun micro-system  DirectX:Microsoft corp.

4. Former graphic model  Pen plotter model  Useful for drawing 2D large diagram  API ex. LOGO, GKS, and PostScript  Unsuitable for 3D model : need sophisticated math to user moveto(0,0); lineto(1,0); lineto(1,1); lineto(0,1); lineto(0,0); moveto(0,1); lineto(0.5,1.866); lineto(1.5,1.866); lineto(1.5, 0.866); lineto(1,0); moveto(1,1); lineto(1.5, 1.866);

5. Coordinate Systems  CG system is unable define exactly unit like cm, inch etc  CG is a device independent system  Current coordinate is user coordinate = world coordinate  It should be match with CRT coordinate system (Raster coordinate)

6. Graphic function properties  7 groups of function  Primitive: What is object ?  low level objects or atomic entities, ex. point, polygon etc,  Attribute  How the appear: fill, bold character  Viewing  How we saw the image  Transformation  Transform of object: rotate, move  Input  Deal with the devices: keyboard, mouse etc.  Control function  Multiwindow, multiprocessing environment handling.  Inquiry function  Information providing for different API

7. Pipeline and State Machine  Entire graphic system thinking as a state machine  There are 2 types of Graphic functions  thing that define primitives  thing that changes the state

8. The OpenGL Interface  Begin with “gl”  Stored in library and referred to as GL  There are  Graphics Utility Library (GLU)  GLU Toolkit (GLUT)  GLX or WGL : glue for GL to OS  Defined in standard header folder “GL” filename “glut.h”

9. Primitives and Attributes  API should contain small set of primitives that every hardware can be supported  Ex. Line, polygons, text  Variety of primitive such as circle, curves, surface and solids able to build sophisticated object but few hardware supported  OpenGL takes an intermediate  Support 2 classes of primitives  Geometric primitives : pass through a geometric pipeline  Raster primitives: pass through pixel pipeline

10.  Geometric  Able to manipulated  Raster  Lack of geometric properties

11. Let’s have a look at 2D Modeling  Special case of 3D  Suppose z=0, every point refer to (x, y,0)  Generally object created from set points  In graphics system, the word “vertex” more preferred that “point”  OpenGL function form glVertex*(); where *: nt or ntv, 2 or 3 characters form n : number of dimension ( 2, 3 or 4) t : data type (ingeter, float, double, v for pointer)  Ex. glVertex2i(); /* vertex for 2D integer type*/  The data type may change to GL type instead of C  Ex. GLfloat = float in C  Note:  All of them have already defined in header fine

12. OpenGL Object form  Defined object in glBegin- glEnd loop  2 kinds of primitives that is used to defined object  No interior, eg. points, line  have surface, eg. polygon glBegin(type); glVertex*(…);. glEnd(); Difference type of object form C command for defining object

13. Polygon Basics  Close object that has interior  Able to use as curve surface  Number of generated polygons per time is used as graphic performance  Display either only edges or fill  Correct properties should be simple, convex, and flat  3D polygon is unnecessarily flat Filled objects polygons displaying simple polygon nonsimple polygon convex property

14. Convex object properties  3D convex object: 3 vertices are not collinear  Safe for rendering if use triangle  Hardware and software often support

15. Types of Polygon  GL_POLYGONS  Edges are perform line loop and close  Edges has no with  define either fill or edges using glPolygonMode  If both, draw twice

16. Special types polygon  Triangles and Quadrilaterals (GL_TRIANGLES, GL_QUADS)  Strips and Fans (GL_TRIANGLE_STRIP, GL_QUAD_STRIP, GL_TRIANGLE_FAN)

17. Sample object: Generating a Sphere  assign to be polygons and used GL_QUAD_STRIP  Use longitude and latitude schemes for the middle body  For pole uses GL_TRIANGLE_FAN float C= PI/180.0; //degrees to radians, M_PI = 3.14159… for (float phi = -80.0; phi <= 80.0; phi += 20.0) { glBegin(GL_QUAD_STRIP); for (float theta = -180.0; theta <= 180.0; theta += 20.0) { float x=sin(c*theta)*cos(c*phi); float y=cos(c*theta)*cos(c*phi); float z=sin(c*phi); glVertex3d(x,y,z); x=sin(c*theta)*cos(c*(phi+20.0)); y=cos(c*theta)*cos(c*(phi+20.0)); z=sin(c*(phi+20.0)); glVertex3d(x,y,z); } glEnd(); }

18. x=y=0; // North pole modeling z = 1; glBegin(GL_TRIANGLE_FAN); glVertex3d(x,y,z); c=M_Pi/180.0; z=sin(c*80.0); for (theta=-180.0; theta<=180.0;theta+=20.0) { x=sin(c*theta)*cos(c*80.0); y=cos(c*theta)*cos(c*80.0); glVertex3d(x,y,z); } glEnd(); x=y=0; // South pole modeling z=-1: glBegin(GL_TRIANGLE_FAN); glVertex3d(x,y,z); z = -sin(c*80.0); for(theta = -180.0; theta <= 180.0; theta=20.0) { x=sin(c*theta)*cos(c*80.0); y=cos(c*theta)*cos(c*80.0); glVertex3d(x,y,z); } glEnd();

19. Today topic  fonts  attributes  color system  drawing a graphic with OpenGL

20. Text 2 types of text  Stroke Text  Constructed via using graphic primitives  Able to transform like other primitives  Raster Text  Character are defined as rectangle of bits block

21.  Stroke text  Consume a lot of memories  Postscript as an example  Raster text  Rapidly be placed in buffer by using bit-block-transfer (bitblt) operation  Operate only character sizing  Often store in ROM (hardware)  Portability is limited by particular font  GLUT provide 8x8 pixels function  glutBitmapCharacter(GLUT_BITMAP_8_BY_13, C) C: ASCII character number  Character is placed in the present position of screen

22. Curved Objects  Create by using 2 approach  Use the primitive except points  n side polygon instead of circle  Approximate sphere with polyhedron  Curved surface by a mesh of convex polygon  Use mathematical definition  Quadric surfaces and parametric polynomial curved and surfaces  example:  Define sphere by center and a point on surface  Cubic Polynomial is defined by 4 points  OpenGL able to do both

23. Attributes  About how primitive display  Line : display color, type of line (dash, solid)  Concern with immediate mode: display as soon as they are defined

24. Color  Most interesting of perception and computer graphics  Base on three color theory  If using additive color model - c = T 1 R+T 2 G+T 3 B  C: color that we trying to match  T1, T2, T3: strength of intensity, the tristimulus value

25. Human Visual System  Our visual system do a continuous perception  Depends on 3 types of cone cell  Visually indistinguishable if they have the same tristimulus value  CRT is an example of additive color system A i : brain perception value S i : cone cell sensitivity Viewing a point as a color solid cube

26. Subtractive color model  The complementary of additive color model  Start with white surface  If white light hit the surface, color will be absorb except the object color which are reflect  Ex. painting and printing  Complementary color: cyan, magenta, yellow additive color model subtractive color model

27. RGB-color model  Use separate buffer for each color  Each pixel has 3 bytes (24 bits) for each color  16 Million shade of color  OpenGL function  glColor3f(r, g, b);  ex. Red  glColor3f(1.0, 0.0, 0.0);

28. RGBA, the 4 color model  A: Alpha channel  Store in frame buffer like RGB  For creating effect ex. fog, combining images.  OpenGL treat as opacity or transparency  Ex. OpenGL command for 4 color model  glClearColor(1.0, 1.0, 1.0, 1.0);  White color and opaque

29. Indexed Color  Difficult to support in hardware  Higher memory requirements but now memory is cheaper  Use color tray of artist as principle  Infinite color can be produced from different quantity of primary colors

30. OpenGL indexed color function glIndex(element);  Select color out of table glutSetcolor(int color, GLfloat red, GLfloat blue, GLfloat green);  Set color entry to map the color table

31. Color Attributes  For RGB mode glClearColorglClearColor(1.0, 1.0, 1.0); /* clear to white */ glColor3f(1.0, 0.0, 0.0); /* setting point to red */ glPointSize(2.0); /* 2 pixel wide */ Note: If 2 display differ in pixel size, rendered images may appear slightly different

32. Viewing  Method for objects appear on screen  Use synthetic camera concept  Fix lens and fix location  Picture would be distort like real world  If we need to take an elephant picture, camera should far enough to take all information

33. 2D Viewing  Base on the 2D rectangular area  Know as viewing rectangle or clipping rectangle  Be a special case of 3D viewing ex. plane at z=0  Default in 2x2x2 volume, origin in the center and bottom-left corner is at (-1.0, -1.0)

34. Orthographic View  2D view the orthographic projection of 3D  Function void glOrtho(GLdouble left, GLdouble right, GLdouble bottom, GLdouble top, GLdouble near, GLdouble far); // near, far: distance which are measured from camera /* orthographic projection from 3D */ void gluOrtho2D(GLdouble left, GLdouble right, GLdouble bottom, GLdouble top); /* 2D equivalent to glOrtho but near and far set to -1.0, 1.0 */  Unlike camera, it is able to view behind object

35. Matrix Modes  Between graphic pipeline state, any transformation  2 important matrices:  model-view  Projection glMatrixMode(GL_PROJECTION); glLoadIdentity(); gluOrtho2d(0.0, 500.0, 0.0, 500.0); glMatrixMode(GL_MODELVIEW);

36. Control function  Concern about software environment between software and platform  Different platform will have different interfacing  GLUT also provide the utility : see further

37. Windows interfacing  Window : a rectangular area of our display, max = CRT screen  Window default origin: (0,0) at lower-left corner like CRT but mouse at top-left  OpenGL function (GLUT function) for window glutInit (int *argcp, char **argv); glutCreateWindow(char *title); /* given the window title */

38. Change the display setup glutInitDisplayMode(GLUT_RGB| GLUT_DEPTH | GLUT_DOUBLE); GLUT_RGB: define RGB color mode GLUT_DEPTH: a depth buffer for hidden-surface removal GLUT_DOUBLE: number of buffer Double/Single default: RGB color, no hidden surface removal, single buffering glutInitWindowSize(480, 640); glutInitWindowPosition(0,0)

39. Aspect ratio  Ratio of rectangle’s width to its height  If glOrtho and glutInitWindowSize are not specified the same size, object are distort.

40. View port  A rectangular area of the display window  Setting a view port void glViewport(GLint x, GLint y, GLsizei w, GLsizei h);

41. The function: main, display and myinit  glutMainLoop(); /* begin an event-processing loop, let the window waiting for kill process */  void glutDisplayFunc(void *(func)(void)); /* call to the redisplay function name func */ #include void main(int argc, char **argv){ glutInit(&argc, argv); glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB ); glutInitWindowSize(500, 500); glutInitWindowPosition(0, 0); glutCreateWindow("Simple OpenGL example"); glutDisplayFunc(display); myinit(); glutMainLoop(); } Program template

42. Program structure consisting  myinit : setup user options to state variables dealing with viewing and attributes-parameters

43. Example program: Sierspinski Gasket Proceeding of Sierspinski 1. Pick an random initial point in triangle 2. Select vertex 3. Finding the halfway point between initial point and random vertex 4. Mark and display new point 5. Replace the initial point with this new point 6. Return to step 2

44. Pseudo code main() { Initialize_the_system(); Initialize_the_system(); for(some_number_of_points) { pt = generate_a_point(); display_the_point(pt);}cleanup();} Sierpinski gasket

45. Using array with OpenGL // For 3D vertex, 2D is a special case GLfloat vertex[3]; /* define array */ // Then we can use glVertex3fv(vertex);/* pass by reference */ // Defining geometric object in Begin and End fn. statement glBegin(GL_LINES); glVertex2f(x1, y1); glVertex2f(x2, y2); glEnd();

46. The same data able to define another object // define a pair of points glBegin(GL_POINTS); glVertex2f(x1, y1); glVertex2f(x2, y2); geEnd();

47. Using a 2 element array to carry a point // By defining new data type with 2 element array typedef GLfloat point2[2]; // point2[0] carry x data // point2[1] carry y data when use point2 vertices[3] ; // the members are vertices[0][0], vertices[1][0], vertices[2][0] // carry x value vertices[0][1], vertices[1][1], vertices[2][1] // carry y value point2 vertices[3] = {{0.0, 0.0}, {250.0, 500.0}, {500,0}}

48.  Thing need to do  Coloring  Locate the image  Define size  Window creating  Image clipping  Image duration 5000 random point 2D Sierspinski

49. Triangular gasket  There is no point in the middle triangle  The same observation can be applied to the other 3 triangles and so on  Another method to fill the area is use triangle polygon instead of point  Strategy  Start with a triangle which subdivide the area to 4 triangles  Remove the middle one  Repeat to other triangles until the size of the removing triangle is small enough. Let say 1 pixel  This is the recursive program  See program

50. typedef float point2[2];/* initial triangle */ point2 v[]={{-1.0, -0.58}, {1.0, -0.58}, {0.0, 1.15}}; void triangle( point2 a, point2 b, point2 c) { /* display one triangle */ glBegin(GL_TRIANGLES); glVertex2fv(a); glVertex2fv(b); glVertex2fv(c); glEnd(); } void divide_triangle(point2 a, point2 b, point2 c, int m) { /* triangle subdivision using vertex numbers */ point2 v0, v1, v2; int j; if (m>0) { for(j=0; j<2; j++) v0[j]=(a[j]+b[j])/2; for(j=0; j<2; j++) v1[j]=(a[j]+c[j])/2; for(j=0; j<2; j++) v2[j]=(b[j]+c[j])/2; divide_triangle(a, v0, v1, m-1); divide_triangle(c, v1, v2, m-1); divide_triangle(b, v2, v0, m-1); } else /* draw triangle at end of recursion */ triangle(a,b,c); }

51. void display(void) { glClear(GL_COLOR_BUFFER_BIT); divide_triangle(v[0], v[1], v[2], n); glFlush(); } with 4 level recursionwith 5 level recursion

52. 3D Sierspinski gasket  Begin with tetrahedron instead triangle  Use 3D point point v[]={ { 0.0, 0.0, 1.0}, { 0.0, 0.942809, -0.33333}, {-0.816497, -0.471405, -0.333333}, { 0.816497, -0.471405, -0.333333} };

53. The hidden surface removal  Problem may happen if there is no relation between surface  Close opaque object should mask the far object  The part of far object which overlap with close object should remove  Z-buffer algorithm is a method to manipulate.

54. Exercises  Write a part of C program to define a unit circle object at position (1,1) using OpenGL command Hint: you may use primitive such as TRIANGLE_FANS, or others