This document provides an overview of ray marching techniques for rendering 3D scenes using shaders. It explains basic linear algebra concepts used in ray marching like position, distance to surface, and normals. It also covers lighting models including diffuse and specular lighting. Advanced techniques like boolean operations allow for creating complex geometries. Additional effects covered include soft shadows, ambient occlusion, and examples of shadertoy implementations. Links to further resources on raymarching and distance fields are also provided.

1. Ray Marching Explained
Mårten Rånge

8. www.shadertoy.com
https://www.shadertoy.com/view/ldyGWm

9. GLSL
+
Basic linear algebra

13. r
d
p
𝑑 = 𝑝 − 𝑟

14. Show us the code

15. Lighting

16. 𝑛𝑜𝑟𝑚𝑎𝑙

17. 𝑛𝑜𝑟𝑚𝑎𝑙

18. 10 51520

19. 𝑛: 𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒(𝑑 𝑝 + 𝑒𝑥 − 𝑑 𝑝 − 𝑒𝑥 , 𝑑 𝑝 + 𝑒𝑦 − 𝑑 𝑝 − 𝑒𝑦 , 𝑑 𝑝 + 𝑒𝑧 − 𝑑 𝑝 − 𝑒𝑧 )
𝑒𝑧: (0, 0, 𝑒𝑝𝑠𝑖𝑙𝑜𝑛)
𝑒𝑦: (0, 𝑒𝑝𝑠𝑖𝑙𝑜𝑛, 0)
𝑒𝑥: (𝑒𝑝𝑠𝑖𝑙𝑜𝑛, 0, 0)
𝑝: 𝑝𝑜𝑖𝑛𝑡𝑂𝑛𝑆𝑢𝑟𝑓𝑎𝑐𝑒
𝑑: 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑇𝑜𝑆𝑢𝑟𝑓𝑎𝑐𝑒

20. 𝑑𝑖𝑓𝑓𝑢𝑠𝑒
a

21. 𝑑𝑖𝑓𝑓𝑢𝑠𝑒: 𝑚𝑎𝑥(𝑑𝑜𝑡 𝑛𝑜𝑟𝑚𝑎𝑙, 𝑙𝑖𝑔ℎ𝑡𝐷𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 , 0)

22. 𝑠𝑝𝑒𝑐𝑢𝑙𝑎𝑟
a
a
b

23. 𝑠𝑝𝑒𝑐𝑢𝑙𝑎𝑟: 𝑚𝑎𝑥 𝑑𝑜𝑡 𝑟𝑒𝑓𝑙𝑒𝑐𝑡 𝑙𝑖𝑔ℎ𝑡𝐷𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛, 𝑛𝑜𝑟𝑚𝑎𝑙 , 𝑒𝑦𝑒𝐷𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 , 0 𝑓𝑜𝑐𝑢𝑠

24. Show us the code

25. Creating complex
geometries

26. 𝑢𝑛𝑖𝑜𝑛: 𝑚𝑖𝑛(𝑑1, 𝑑2)
𝑖𝑛𝑡𝑒𝑟𝑠𝑒𝑐𝑡𝑖𝑜𝑛: 𝑚𝑎𝑥(𝑑1, 𝑑2)
𝑠𝑢𝑏𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛: 𝑚𝑎𝑥(𝑑1, −𝑑2)
𝑏𝑜𝑜𝑙𝑒𝑎𝑛 𝑜𝑝𝑒𝑟𝑎𝑡𝑜𝑟𝑠

27. 𝑠𝑐𝑎𝑙𝑒: 𝑑(𝑝 ∗ 𝑠)/𝑠
𝑟𝑒𝑝𝑒𝑡𝑖𝑡𝑖𝑜𝑛: 𝑑(𝑚𝑜𝑑 𝑝, 𝑟 − 0.5𝑟)
𝑡𝑟𝑎𝑛𝑠𝑙𝑎𝑡𝑖𝑜𝑛: 𝑑(𝑝 − 𝑡)
𝑑𝑜𝑚𝑎𝑖𝑛 𝑜𝑝𝑒𝑟𝑎𝑡𝑜𝑟𝑠

28. Show us the code

29. Shadows

30. 𝑠𝑜𝑓𝑡 𝑠ℎ𝑎𝑑𝑜𝑤𝑠

31. 𝑎𝑚𝑏𝑖𝑒𝑛𝑡 𝑜𝑐𝑐𝑙𝑢𝑠𝑖𝑜𝑛

32. Show us the code

33. All together now

34. Cool shadertoy examples
• Graphics + Music
• https://www.shadertoy.com/view/4tc3zf
• 460 lines!
• https://www.shadertoy.com/view/4sjSW1
• https://www.shadertoy.com/view/XlBGz3
• Retro!
• Mandel bulb
• https://www.shadertoy.com/view/ltfSWn
• Advanced modeling
• https://www.shadertoy.com/view/ld3Gz2
• Terrains
• https://www.shadertoy.com/view/MdlGW7
• https://www.shadertoy.com/view/4ttSWf
• https://www.shadertoy.com/view/XslGRr

35. Links
• Raymarching explanined
• http://9bitscience.blogspot.com/2013/07/raymarching-distance-fields_14.html
• Links other useful resources as well
• Advanced operators
• http://mercury.sexy/hg_sdf/
• NNUG Demos
• https://www.shadertoy.com/view/4t3cDl
• https://www.shadertoy.com/view/Xl3cDl
• https://www.shadertoy.com/view/Xl3cDs
• https://www.shadertoy.com/view/MtcyWl
• https://www.shadertoy.com/view/ltccD2

37. Questions?