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H331: Computer Graphics

H331: Computer Graphics. Philip Dutré Department of Computer Science Wednesday, February 19. Today. Graphics programming Book: Chapters 3, 4, 10. Announcements. Pre-practicum available http://www.cs.kuleuven.ac.be/~graphics/H331/ SIGGRAPH student volunteers!

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H331: Computer Graphics

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  1. H331: Computer Graphics Philip Dutré Department of Computer Science Wednesday, February 19

  2. Today • Graphics programming • Book: Chapters 3, 4, 10

  3. Announcements • Pre-practicum available • http://www.cs.kuleuven.ac.be/~graphics/H331/ • SIGGRAPH student volunteers! • Deadline: Wednesday February 26

  4. Announcements • SIGGRAPH San Diego July 27 – 31 • http://www.siggraph.org/s2003/ • Student volunteers! (Deadline: February 26)

  5. 3D  2D • How to transform the 3D world to a 2D image? • 3 aspects: • Objects: exist in space, independent of viewer • Viewer: camera, human, …. • Lights: shading, shadows, …

  6. 3D  2D Objects (points, lines, polygons) Described by vertices Lights (e-m spectrum) (350-780 nm) Viewer = camera

  7. Pinhole camera

  8. Synthetic Camera Projection plane in front of center-of-projection:

  9. Synthetic Camera Clipping: looking through a window

  10. 3D APIs • Synthetic camera is basis of 3D API • OpenGL, PHIGS, Direct 3D, VRML,JAVA-3D, GKS, … • We need to functions to specify: • Objects: vertices that describe points, lines, polygons • Camera: position, orientation, width, height • Light sources: position, color • Materials: reflection characteristics

  11. 3D APIs glBegin(GL_POLYGON) glVertex3f(0.0, 0.0, 0.0); glVertex3f(0.0, 1.0, 0.0); glVertex3f(0.0, 0.0, 0.1); glEnd(); … gluLookAt(posx, posy, posz, atx, aty, atz, …); glPerspective(view_angle, …);

  12. 3D APIs • 3D API performs modeling + rendering • But … modeling can also be done ‘off-line’ • Write model to file • Read file in 3D API and transform to 3D API modeling commands • RenderMan (Pixar) • Prepares off-line model for rendering • Rendering takes ‘converted’ model

  13. Graphics hardware • 3D ‘world’ coordinates  2D ‘screen’ coordinates

  14. Graphics hardware • 3D vertex  2D pixel Transform to camera coordinate system Clip away things we don’t see in the camera window 3D coordinates  2D coordinates Transform to pixels in the frame buffer

  15. 2D Drawing • Little algorithm: • Pick 3 points V0, V1, V2 • P0 = random point • Pk = midpoint between Pk-1 and random(V0, V1, V2) • Plot all Pk

  16. How to draw things? • Given: window on the screen • Graphics API (e.g. OpenGL) has something of the form: plotPixel(int x, int y)

  17. window How to draw things? • plotPixel(289,190) • plotPixel(320,128) • plotPixel(239,67) • plotPixel(194,101) • plotPixel(129,83) • plotPixel(75,73) • plotPixel(74,74) • plotPixel(20,10)

  18. Y window y X x How to draw things? plotPixel(x,y) screen

  19. Why is this impractical? • Coordinates are expressed in screen space, but objects live in (3D) world space • Resizing window implies we have to change coordinates of objects to be drawn • We want to make a separation between: • values to describe geometrical objects • values needed to draw these objects on the screen

  20. How to draw things? • Specify points to OpenGL glVertex*( … ) glVertex2i( … ) glVertex3i( … ) glVertex2f( … ) glVErtex3f( … ) glBegin(GL_LINES); glVertex2f(x1, y1); glVertex2f(x2, y2); glEnd(); glBegin(GL_POINTS); glVertex2f(x1, y1); glVertex2f(x2, y2); glEnd();

  21. How to draw things? For (k=0; k<500; k++) { … // compute point k x = …; y = …; glBegin(GL_POINTS); glVertex2f(x, y); glEnd(); } glFlush();

  22. More about OpenGL… • OpenGl = set of libraries

  23. More about OpenGL… • OpenGl supports geometric primitives and raster primitives

  24. Geometric Primitives in OpenGL • Geometric primitives are defined by vertices • GL_POINTS • GL_LINES • GL_LINE_STRIP, GL_LINE_LOOP

  25. Geometric Primitives in OpenGL • Closed loops = polygons • Polygons: describe surfaces

  26. Geometric Primitives in OpenGL • GL_POLYGON, GL_QUADS, …

  27. Viewing in OpenGL • Scene is independent of camera • gluOrtho2D(left, tight, bottom, top)

  28. 3D primitives void triangle(point3 a, point3 b, point3 c) { glBegin(GL_POLYGON) glVertex3fv(a); glVertex3fv(b); glVertex3fv(c); glEnd(); } void tetrahedron () { glColor3f(1.0,0.0,0.0); triangle(v[0], v[1], v[2]); … }

  29. 3D primitives • Hidden surfaces? • Z-buffer • Keep depth for each pixel • Initialize! • glClear(GL_COLOR_BUFFER_BIT); • glClear(GL_DEPTH_BUFFER_BIT); • … • glFlush();

  30. World window & viewport • World window:specifies what part of the world should be drawn • Viewport:rectangular area in the screen window in which we will draw

  31. window World window & viewport screen window world window viewport

  32. window Mapping: world window to viewport Vt Wt Wb Vb Vl Vr Wl Wr

  33. window Mapping: world window to viewport Maintain proportions! Vt Wt Wb Vb Vl Vr Wl Wr

  34. Mapping: world window to viewport x sx Vl Vr Wl Wr

  35. Mapping: world window to viewport • If x = Wl, then sx = Vl • If x = Wr, then sx = Vr • If x = f*(Wr-Wl), then sx = f*(Vr-Vl) • If x < Wl, then sx < Vl • If x > Wr, then sx > Vr • … also for y and sy

  36. World window • Pick size automatically world window

  37. window Automatic setting to preserve aspect ratio & center H Aspect ratio R W R > W/H

  38. window Automatic setting to preserve aspect ratio & center H Aspect ratio R W R < W/H

  39. Clipping • Lines outside of world window are not to be drawn. • Graphics API clips them automatically. • But clipping is a general tool in graphics!

  40. Clipping

  41. Clipping A B clipSegment(…): • Return 1 if line within window • Return 0 if line outside window • If line partially inside, partially outside: clip and return 1 C E D

  42. Cohen-Sutherland clipping • Trivial accept/reject test! Trivial reject Trivial accept

  43. Cohen-Sutherland region outcodes • 4 bits: TTFF Left of window? Above window? Right of window? Below window?

  44. Cohen-Sutherland region outcodes • Trivial accept: both endpoints are FFFF • Trivial reject: both endpoints have T in the same position TTFF FTFF FTTF TFFF FFFF FFTF TFFT FFFT FFTT

  45. Cohen-Sutherland: chopping • If segment is neither trivial accept or reject: • Clip against edges of window in turn

  46. Cohen-Sutherland: chopping Trivial accept

  47. Cohen-Sutherland line clipper • int clipSegment (point p1, point p2) Do { If (trivial accept) return (1) If (trivial reject) return (0) If (p1 is outside) if (p1 is left) chop left else if (p1 is right) chop right … If (p2 is outside) … } while (1)

  48. Raster Graphics • What is an image? • Array of pixels • How to convert lines and polygons to pixels? • Continuous to discrete • Scan conversion

  49. Displays • Early displays were vector displays • Electron beam traces lines • Image is sequence of endpoints • Wireframes, no solid fills

  50. Displays • Raster displays • Electron beam traces regular pattern • Image is 2D array of pixels • Fast, but discretisation errors • Every pixel has b bits for color • B&W: 1 bit • Basic colors: 8, 15, 16, 24 bits • High-end: 96 bits

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