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Imaging

Imaging. Modeling and Imaging. Picture. model. Reality. modeling. Imaging (visualisation). Projection. Mapping Φ : R n → R k n >k In case of 3D computer graphics Φ : R 3 → R 2 Projection ray The set of all pictures with the same image Projection ray is usually a line

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Imaging

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  1. Imaging

  2. Modeling and Imaging Picture model Reality modeling Imaging (visualisation)

  3. Projection • Mapping Φ: Rn→ Rk n>k • In case of 3D computer graphics Φ: R3→ R2 • Projection ray • The set of all pictures with the same image • Projection ray is usually a line • The image is in the intersection of the projection ray and the projection plane.

  4. Parallel projection • Intersection of projection rays (projection center) is in the infinity • Projection rays are parallel • Their direction is defined by two angels (azimuth,zenith)

  5. Parallel projection • Intersection of projection rays (projection center) is in the infinity • Projection rays are parallel • Their direction is defined by two angels (azimuth,zenith)

  6. Axonometry • Projection plane intersects coordinate axes dy dx dz

  7. Dimetry Projection triangle is isiscelles

  8. Izometry • Projection triangle is equilateral (dx=dy=dz) Often also azimuth=zenith=45o

  9. Perspective • Projection center is a point

  10. 1-vanishing point perpective

  11. 2-vanishing point perspective

  12. 3-vanishing point perspective

  13. Wireframe „model“

  14. Solving of edges visibility

  15. Solving of edges visibility

  16. Which faces are visible? The normal leads from the observer → the face is not visible The normal leads TO the observer → the face can (but must not) be visible

  17. Painter’s algorithm • Display the potentionaly visible faces from the back to the front

  18. Painter’s algorithm The face is not visible

  19. Painter’s algorithm The face can be visible

  20. Painter’s algorithm The face is not visible

  21. Painter’s algorithm The face can be visible

  22. Painter’s algorithm The face is not visible

  23. Painter’s algorithm The face can be visible

  24. Painter’s algorithm The face is not visible

  25. Painter’s algorithm The face is not visible

  26. Painter’s algorithm The face can be visible

  27. Painter’s algorithm The face can be visible

  28. Counter example of painter’s algorithm

  29. Simple imaging of all points of the solid

  30. Rendering observer Light source Projection plane Angleα

  31. Rendering

  32. Light source types • Point • Area (commonly approximated by a matrix of points) • Ambient

  33. Ray Tracing Mirror reflection Light sources Projection plane Diffuse reflection The ray goes through the solid

  34. Types of reflection on the solid • The ray is absorbed by a solid (solid color) • The ray is reflected • Mirror reflection (shine) • Diffuse reflection • Combinated reflection • The ray is going through the solid tělesem • Directly (transparent solid) • With a shift • With a diffusion (translucent solid)

  35. Ray Tracing

  36. Radiosity • e1 = z1 + o1 * ∑ jv1jej • e2 = z2 + o2 * ∑ jv2jej • ei = zi + oi * ∑ jvijej

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