Upgrade to Pro — share decks privately, control downloads, hide ads and more …

Wil Yegelwel on The Rendering Equation

Wil Yegelwel on The Rendering Equation

Illumination in computer graphics deals with calculating the color of each pixel on the screen when trying to render a photorealistic scene. The problem is that generating increasingly realistic renderings requires a lot of processing and so a tradeoff must be made between compute time and image quality. We will first look at two foundational papers from the 70s that built “good enough” models that were fast to render. Finally, we look at The Rendering Equation that provides a single model to encompass many effects of lighting assuming you are willing to pay the processing cost.

Papers_We_Love

November 29, 2016
Tweet

More Decks by Papers_We_Love

Other Decks in Technology

Transcript

  1. Who am I? • Engineer at Two Sigma working on

    distributed systems problems • Studied computer graphics in school • Just got a kitten, she is adorable 2
  2. The views expressed herein are not necessarily the views of

    Two Sigma Investments, LP or any of its affiliates (collectively, “Two Sigma”). The information presented herein is only for informational and educational purposes and is not an offer to sell or the solicitation of an offer to buy any securities or other instruments. Additionally, the information is not intended to provide, and should not be relied upon for investment, accounting, legal or tax advice. Two Sigma makes no representations, express or implied, regarding the accuracy or completeness of this information, and you accept all risks in relying on the above information for any purpose whatsoever. Important Legal Information 3
  3. What we are trying to do By Gilles Tran -

    http://www.oyonale.com/modeles.php?lang=en&page=40, Public Domain, https://commons.wikimedia.org/w/index.php?curid=745313 4
  4. What we are going to talk about • Background •

    Continuous shading of curved surfaces – Henri Gouraud • An Improved Illumination Model for Shaded Display – Turner Whitted • The Rendering equation – James T. Kajiya 11
  5. Rendering Items first for each item for each pixel if

    pixel between eye and item draw something here Pixels first for each pixel for each item if ray from eye through pixel hits item draw something here 14
  6. Lighting models – Lambert cosine law Incoming light Outgoing light

    ∗ = cos ( ℎ ) Constant (viewer independent) 18
  7. 19

  8. Machbanding By The original uploader was Aliwiki at French Wikipedia

    - Transferred from fr.wikipedia to Commons by Korrigan using CommonsHelper., FAL, https://commons.wikimedia.org/w/index.php?curid=4770182 20
  9. for each triangle for each row in image for each

    col in row if pixel between eye and item draw something here Hidden surface removal problem 1-100 ~400 ~600 O(T*H*W) 24
  10. Hidden surface removal (simple) *Project triangles into screen space* for

    each row in image for each triangle if row intersects triangle line segments for col between intersected line segments draw something here* * Consider depth 25
  11. 29

  12. Refraction By JrPol - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/i

    ndex.php?curid=38535231 By Josell7 - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curi d=21670922 31
  13. 35

  14. 36

  15. 37

  16. 38

  17. The rendering equation , % = , % , %

    + N , %, %% %, %% ′′ Q 39
  18. The rendering equation , % = , % , %

    + N , %, %% %, %% ′′ Q 40
  19. , % = , % , % + N ,

    %, %% %, %% ′′ Q The rendering equation 41
  20. , % = , % , % + N ,

    %, %% %, %% ′′ Q The rendering equation 42
  21. The rendering equation , % = , % , %

    + N , %, %% %, %% ′′ Q 43
  22. The rendering equation , % = , % , %

    + N , %, %% %, %% ′′ Q 44
  23. Expectation = N ≈ 1 @ F W FXY ()

    = N ≈ 1 @ (F ) W FXY 51
  24. Monte Carlo integration N = N = () = N

    Where = () ≈ 1 @ F (F ) W FXY 56
  25. Summary 1. Continuous shading of curved surfaces – Henri Gouraud

    2. An Improved Illumination Model for Shaded Display – Turner Whitted 3. The Rendering equation – James T. Kajiya = < + ? @ A B B∈EFGHIJ , % = , % , % + N , %, %% %, %% ′′ Q = < + ? @ A B + J + I B∈EFGHIJ 62