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Viewing

Dive into the fundamentals of Computer Graphics, focusing on Normalized Device Coordinates (NDC) in the [-1, 1] range. Learn the concepts of scaling, mapping in 1D and 2D spaces, NDC to screen space conversions, and viewport transformations. Understand how OpenGL automates certain processes, such as setting glViewport values. Explore Orthographic view volume and camera transformations to map objects effectively. Uncover the significance of z-coordinate for depth buffering. Discover how to convert coordinates through rotation matrices and achieve Isometric drawing with Orthographic projection.

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Viewing

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  1. Viewing CPSC 453 - Fundamentals of Computer Graphics

  2. Normalized Device Coordinates (NDC) : [-1,1]3

  3. Normalized Device Coordinates (NDC) : [-1,1]3

  4. Scaling in 1D

  5. Mapping in 1D

  6. Mapping in 2D

  7. Mapping in 2D

  8. 2D mapping NDC to screen space [-1,1]2 [-0.5, -nx – 0.5] x [-0.5, -ny – 0.5]

  9. 2D mapping NDC to screen space

  10. 3D mapping: Viewport transformation

  11. 3D mapping: Viewport transformation OpenGL does this automatically with the values set in glViewport(x, y, width, height)

  12. NDC volume Orthographic view volume

  13. Orthographic view volume Volume is along z-axis ( i.e. n > f )

  14. Orthographic view volume

  15. Mapping one box to another… NDC volume Orthographic view volume

  16. Mapping one box to another… NDC volume Orthographic view volume

  17. NDC volume Orthographic view volume

  18. NDC volume Orthographic view volume The z-coordinate is in [-1,1], and will be used for depth buffering later.

  19. Camera transformation Orthographic view volume Arbitrary view transform

  20. Camera transformation Orthographic view volume Arbitrary view transform

  21. 2D change of coordinates

  22. 2D change of coordinates

  23. 2D change of coordinates

  24. 2D change of coordinates A matrix with columns that are mutually orthonormal, is a rotation matrix

  25. Camera transformation

  26. Camera transformation Orthographic view volume

  27. World space to Screen space

  28. Isometric drawing (using Orthographic projection)

  29. Next Week

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