Computer Graphics

1. Computer Graphics Rendering Geometric Primitives Reading: HB4, HB8-1 to HB8-6, HK9.7, 11 Last updated on 06-02-2012

2. Rendering • Goal • transform computer models into images • may or may not be photo-realistic • interactive rendering • fast, but limited quality • roughly follows a fixed patterns of operations • rendering pipeline • offline rendering • ray tracing • global illumination

3. Rendering • Tasks that need to be performed • project all 3D geometry onto the image plane • geometric transformations • determine which primitives or parts of primitives are visible • hidden surface removal • determine which pixels a geometric primitive covers • scan conversion • compute the color of every visible surface point • lighting, shading, texture mapping

4. Rendering Pipeline • What is the pipeline? • abstract model for sequence of operations to transform geometric model into digital image • abstraction of the way graphics hardware works • underlying model for application programming interfaces (APIs) that allow programming of graphics hardware • OpenGL • Direct 3D • Actual implementation details of rendering pipeline will vary

5. Geometry Database Model/View Transform. Perspective Transform. Lighting Clipping Frame- Buffer Texturing Scan Conversion Depth Test Blending Rendering Pipeline

6. Geometry Database • Geometry database • Application-specific data structure for holding geometric information • Depends on specific needs of application • triangle, points, mesh with connectivity information, curved surface Geometry Database

7. Model/View Transformation • Modeling Transformation • Map all geometric objects from local coordinate system into world coordinates • Viewing transformation • Map all geometry from world coordinates into camera coordinates Geometry Database Model/View Transform.

8. Lighting • Lighting • Compute brightness based on property of material and light position(s) • Computation is performed per-vertex Geometry Database Model/View Transform. Lighting

9. Perspective Transformation • Perspective Transformation • Projecting the geometry onto the image plane • Projective transformations and model/view transformations can all be expressed with 4x4 matrix operations Geometry Database Model/View Transform. Perspective Transform. Lighting

10. Clipping • Clipping • Removal of parts of the geometry that fall outside the visible screen or window region • May require re-tessellation of geometry Geometry Database Model/View Transform. Perspective Transform. Lighting Clipping

11. Scan Conversion • Scan Conversion • Turn 2D drawing primitives (lines, polygons etc.) into individual pixels • Interpolate color across primitive • Generate discrete fragments Geometry Database Model/View Transform. Perspective Transform. Lighting Clipping Scan Conversion

12. Texture Mapping • Texture Mapping • “Gluing images onto geometry” • Color of every fragment is altered by looking up a new color value from an image Geometry Database Model/View Transform. Perspective Transform. Lighting Clipping Texturing Scan Conversion

13. Depth Test Geometry Database Model/View Transform. Perspective Transform. Lighting Clipping Texturing Scan Conversion Depth Test • Depth Test • Remove parts of geometry hidden behind other geometric objects • Perform on every individual fragment

14. Blending Geometry Database Model/View Transform. Perspective Transform. Lighting Clipping Texturing Scan Conversion Depth Test Blending • Blending • Final image: write fragments to pixels • Draw from farthest to nearest • No blending – replace previous color • Blending: combine new & old values with arithmetic operations

15. Geometry Database Model/View Transform. Perspective Transform. Lighting Clipping Frame- Buffer Texturing Scan Conversion Depth Test Blending Frame Buffer • Frame Buffer • Video memory on graphics board that holds image • Double-buffering: two separate buffers • Draw into one while displaying other, then swap to avoid flicker

16. Pipeline Advantages • Modularity: logical separation of different components • Easy to parallelize • Earlier stages can already work on new data while later stages still work with previous data • Similar to pipelining in modern CPUs • But much more aggressive parallelization possible (special purpose hardware!) • Important for hardware implementations • Only local knowledge of the scene is necessary

17. Pipeline Disadvantages • Limited flexibility • Some algorithms would require different ordering of pipeline stages • hard to achieve while still preserving compatibility • Only local knowledge of scene is available • shadows, global illumination difficult

18. 3D Scene Representation • Scene is usually approximated by 3D primitives • Point • Line segment • Polygon • Polyhedron • Cylinder • Curved surface • Solid object • etc.

19. OpenGLAttributes of Graphics Primitives • Color, antialiasing, … • Point attributes, • Line attributes, • Curve attributes, • Character attributes

20. OpenGLAttributes of Graphics Primitives • Attributes are any parameters that affect the way graphic primitives are displayed. • Basic attributes • Color • Size • Style • Fill patterns

21. OpenGLAttributes of Graphics Primitives • Attribute parameter • A parameter that affects the way a primitive is to be displayed, ex: color, size. • State system / State machine • A graphics system that maintains a list for the current values of attributes

22. OpenGLState Variables • All OpenGL state parameters have default values. • Set the state once, remains until overwritten • Changing the attribute settings • Only affects those primitives that are specified after the OpenGL state is changed • Lines: blue or orange, dotted or dashed, and fat or thin. • State parameters can have more than two states, e.g., colors, styles, etc.

23. Stored Color Values in Frame Buffer Displayed Color Red GREEN Blue Black Blue Green Cyan Red Magenta Yellow White 0 1 2 3 4 5 6 7 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 OpenGLColor & Gray Scale • Color is a common attribute for all primitives • Color information can be stored in two ways 1. RGB color codes 2. Color table

24. OpenGLColor & Gray Scale • Color is a common attribute for all primitives • Color information can be stored in two ways • 1. RGB color codes • 2. Color table

25. OpenGLColor Functions Set color display mode 1. OpenGL RGB and RGBA mode 2. OpenGL Color-Index Mode glutInitDisplayMode ( GLUT_SINGLE | GLUT_RGB ) GLUT_RGBA GLUT_INDEX glColor* (colorComponents); // Select current color glIndexi(196); glutSetColor (index, red, green, blue); // Select current color // Specify color into a table

26. Source OpenGLColor Functions OpenGL color blending • Combining the color of overlapping objects • Blending an object with the background Color-blending function Destination object: Current object in the frame buffer • Source object: Other object in the frame buffer glEnable(GL_BLEND); glDisable(GL_BLEND); Destination  Blending methods can be performed only in RGB or RGBA mode.

27. Source OpenGLColor Functions Blending Factors • glColor4f(R, G, B, A), A is a blending factor • Source color components are (Rs, Gs, Bs, As) • Destination color components are (Rd, Gd, Bd, Ad) • Source blending factors are (Sr, Sg, Sb, Sa) • Destination blending factors are (Dr, Dg, Db, Da) • The new blending color that is then loaded into the frame buffer is calculated as: • (SrRs+DrRd, SrGs+DgGd, SbBs+DbBd, SaAs+DaAd) Destination

28. Source OpenGLColor Functions glBlendFunc (sFactor, dFactor); Default: GL_ONE GL_ZERO (1.0, 1.0, 1.0, 1.0) (0.0, 0.0, 0.0, 0.0) Ex. glBlendFunc(GL_SRC_ALPHA,GL_ONE); Ex: implement it by using glColor4f (0.8, 0.2, 0.2, 0.4); Destination

29. OpenGLExample: Blending 1/3 #include <GL/glut.h> void init (void) { glEnable(GL_BLEND); glBlendFunc (GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA); // (sFactor, dFactor) glClearColor (1.0, 1.0, 1.0, 0.0); //(red, green, blue, alpha) }

30. OpenGLExample: Blending 2/3 void display(void) { glClear (GL_COLOR_BUFFER_BIT); glBegin(GL_TRIANGLES); // Draw triangle glColor4f(1.0, 0.0, 0.0, 0.75); glVertex3f(0, -0.5, 0.0); glVertex3f(0.5, -0.5, 0.0); glVertex3f(0, 1, 0.0); glEnd(); glBegin(GL_POLYGON); // Draw rectangle glColor4f(0.0, 0.0, 1.0, 0.75); glVertex3f (-0.6, -0.6, 0); glVertex3f (0.6, -0.6, 0); glVertex3f (0.6, 0.6, 0); glVertex3f (-0.6, 0.6, 0); glEnd(); glFlush (); }

31. OpenGLExample: Blending 3/3 int main(intargc, char** argv) { glutInit(&argc, argv); glutInitDisplayMode (GLUT_SINGLE | GLUT_RGB); glutInitWindowSize (600, 400); glutInitWindowPosition (200, 100); glutCreateWindow ("Hello Students"); init(); glutDisplayFunc(display); glutMainLoop(); return 0; }

32. OpenGLHome Work Plot red, green & blue circles overlapping as shown in figure. Reading: HB4, RB

33. OpenGLPoint Attributes & Functions • Basic attributes • Color • Size • A multiple of the pixel size (a square) • glPointSize (size); // size is the number of pixels

34. OpenGLLine Attributes & Functions • Basic attributes • Color • Width • glLineWidth(width); • Style • glEnable(GL_LINE_STIPPLE); • glLineStippel(repeatFactor, pattern); • Other attributes • Shade • glShadeModel(GL_SMOOTH); How many times each bit is to be repeat 16-bit integer Default: 0xFFFF Solid line Lower-order bits are applied first

35. dashed line Inter-dash spacing OpenGLLine Attributes & Functions Pixel mask • A pattern of binary digits • For example, 11111000

36. OpenGLFill-Area Attribute Functions • OpenGL fill-area routines for convex polygons only. • Four steps: • Define a fill pattern • Invoke the polygon-fill routine • Activate the polygon-fill feature • Describe the polygons to be filled.

37. OpenGLExample void init(void) { glClearColor (0.0, 0.0, 0.0, 0.0); glShadeModel (GL_SMOOTH)} void triangle(void) { glBegin (GL_TRIANGLES); glColor3f (1.0, 0.0, 0.0); glVertex2f (5.0, 5.0); glColor3f (0.0, 1.0, 0.0); glVertex2f (25.0, 5.0); glColor3f (0.0, 0.0, 1.0); glVertex2f (5.0, 25.0); glEnd(); }

38. OpenGLPolygon Stippling

39. OpenGLPolygon Stippling byte fly[] = { (byte) 0x00, (byte) 0x00, (byte) 0x00, (byte) 0x00, (byte) 0x00, (byte) 0x00, (byte) 0x00, (byte) 0x00, (byte) 0x03, (byte) 0x80, (byte) 0x01, (byte) 0xC0, (byte) 0x06, (byte) 0xC0, (byte) 0x03, (byte) 0x60, (byte) 0x04, (byte) 0x60, (byte) 0x06, (byte) 0x20, (byte) 0x04, (byte) 0x30, (byte) 0x0C, (byte) 0x20, (byte) 0x04, (byte) 0x18, (byte) 0x18, (byte) 0x20, (byte) 0x04, (byte) 0x0C, (byte) 0x30, (byte) 0x20, (byte) 0x04, (byte) 0x06, (byte) 0x60, (byte) 0x20, (byte) 0x44, (byte) 0x03, (byte) 0xC0, (byte) 0x22, (byte) 0x44, (byte) 0x01, (byte) 0x80, (byte) 0x22, (byte) 0x44, (byte) 0x01, (byte) 0x80, (byte) 0x22, (byte) 0x44, (byte) 0x01, (byte) 0x80, (byte) 0x22, (byte) 0x44, (byte) 0x01, (byte) 0x80, (byte) 0x22, (byte) 0x44, (byte) 0x01, (byte) 0x80, (byte) 0x22, (byte) 0x44, (byte) 0x01, (byte) 0x80, (byte) 0x22, (byte) 0x66, (byte) 0x01, (byte) 0x80, (byte) 0x66, (byte) 0x33, (byte) 0x01, (byte) 0x80, (byte) 0xCC, (byte) 0x19, (byte) 0x81, (byte) 0x81, (byte) 0x98, (byte) 0x0C, (byte) 0xC1, (byte) 0x83, (byte) 0x30, (byte) 0x07, (byte) 0xe1, (byte) 0x87, (byte) 0xe0, (byte) 0x03, (byte) 0x3f, (byte) 0xfc, (byte) 0xc0, (byte) 0x03, (byte) 0x31, (byte) 0x8c, (byte) 0xc0, (byte) 0x03, (byte) 0x33, (byte) 0xcc, (byte) 0xc0, (byte) 0x06, (byte) 0x64, (byte) 0x26, (byte) 0x60, (byte) 0x0c, (byte) 0xcc, (byte) 0x33, (byte) 0x30, (byte) 0x18, (byte) 0xcc, (byte) 0x33, (byte) 0x18, (byte) 0x10, (byte) 0xc4, (byte) 0x23, (byte) 0x08, (byte) 0x10, (byte) 0x63, (byte) 0xC6, (byte) 0x08, (byte) 0x10, (byte) 0x30, (byte) 0x0c, (byte) 0x08, (byte) 0x10, (byte) 0x18, (byte) 0x18, (byte) 0x08, (byte) 0x10, (byte) 0x00, (byte) 0x00, (byte) 0x08 };

40. 3D Geometric Primitives

41. Rendering • Generate an image from geometric primitives Rendering Geometric Primitives Raster Image

42. 3D Rendering Example What issues must be addressed by a 3D rendering system?

43. 3D Object RepresentationPolyhedra

44. OpenGL 3D Primitives (GLUT Support)

45. OpenGL 3D Primitives • Cube • glutWireCube(GLdouble size) • size = length of a side • Sphere • glutWireSphere(GLdouble radius, GLintnSlices, GLintnStacks) • Approximated by polygonal faces • nSlices = # of polygons around z-axis • nStacks = # of bands along z-axis There are solid counterparts of the wire objects

46. OpenGL 3D Primitives • Regular Polyhedron • Tetrahedron (4 sided) • glutWireTetrahedron() • Hexahedron (6 sided) • glutWireHexahedron() • Octahedron (8 sided) • glutWireOctahedron() • Dodecahedron (12 sided) • glutWireDodecahedron() • Icosahedron (20 sided) • glutWireIcosahedron() Display with center at the origin and with radius (distance from the center of polyhedron to any vertex) equal to Sqrt(3)

47. OpenGL 3D Primitives • Cone • glutWireCone(GLdoublebaseRad, GLdouble height, GLintnSlices, GLintnStacks) • Axis coincides with the z-axis • Base rests on xy-plane and extends to +ve z = height • baseRad: radius at z = 0 • nSlices: The number of subdivisions around the z axis. • nStacks: The number of subdivisions along the z axis.

48. OpenGL 3D Primitives • Torus • glutWireTorus(GLdoubleinRad, GLdoubleoutRad, GLintnSlices, GLintnStacks) • Approximated by polygonal faces • Teapots • glutWireTeapot(GLdouble size)

49. Things to do OpenGL practice: HB 2.9

50. References • http://www.ugrad.cs.ubc.ca/~cs314/ • http://faculty.cs.tamu.edu/schaefer/teaching/441_Spring2012/index.html • http://faculty.cs.tamu.edu/schaefer/teaching/441_Spring2012/index.html • http://www.ugrad.cs.ubc.ca/~cs314/Vjan2007/