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Ray Marching Explained

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MΓ₯rten RΓ₯nge
MΓ₯rten RΓ₯nge

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.

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Ray Marching Explained MΓ₯rten RΓ₯nge
www.shadertoy.com https://www.shadertoy.com/view/ldyGWm
GLSL + Basic linear algebra
r d p 𝑑 = 𝑝 βˆ’ π‘Ÿ
Show us the code
Lighting
π‘›π‘œπ‘Ÿπ‘šπ‘Žπ‘™
π‘›π‘œπ‘Ÿπ‘šπ‘Žπ‘™
10 51520
𝑛: π‘›π‘œπ‘Ÿπ‘šπ‘Žπ‘™π‘–π‘§π‘’(𝑑 𝑝 + 𝑒π‘₯ βˆ’ 𝑑 𝑝 βˆ’ 𝑒π‘₯ , 𝑑 𝑝 + 𝑒𝑦 βˆ’ 𝑑 𝑝 βˆ’ 𝑒𝑦 , 𝑑 𝑝 + 𝑒𝑧 βˆ’ 𝑑 𝑝 βˆ’ 𝑒𝑧 ) 𝑒𝑧: (0, 0, π‘’π‘π‘ π‘–π‘™π‘œπ‘›) 𝑒𝑦: (0, π‘’π‘π‘ π‘–π‘™π‘œπ‘›, 0) 𝑒π‘₯: (π‘’π‘π‘ π‘–π‘™π‘œπ‘›, 0, 0) 𝑝: π‘π‘œπ‘–π‘›π‘‘π‘‚π‘›π‘†π‘’π‘Ÿπ‘“π‘Žπ‘π‘’ 𝑑: π‘‘π‘–π‘ π‘‘π‘Žπ‘›π‘π‘’π‘‡π‘œπ‘†π‘’π‘Ÿπ‘“π‘Žπ‘π‘’
𝑑𝑖𝑓𝑓𝑒𝑠𝑒 a
𝑑𝑖𝑓𝑓𝑒𝑠𝑒: π‘šπ‘Žπ‘₯(π‘‘π‘œπ‘‘ π‘›π‘œπ‘Ÿπ‘šπ‘Žπ‘™, π‘™π‘–π‘”β„Žπ‘‘π·π‘–π‘Ÿπ‘’π‘π‘‘π‘–π‘œπ‘› , 0)
π‘ π‘π‘’π‘π‘’π‘™π‘Žπ‘Ÿ a a b
π‘ π‘π‘’π‘π‘’π‘™π‘Žπ‘Ÿ: π‘šπ‘Žπ‘₯ π‘‘π‘œπ‘‘ π‘Ÿπ‘’π‘“π‘™π‘’π‘π‘‘ π‘™π‘–π‘”β„Žπ‘‘π·π‘–π‘Ÿπ‘’π‘π‘‘π‘–π‘œπ‘›, π‘›π‘œπ‘Ÿπ‘šπ‘Žπ‘™ , π‘’π‘¦π‘’π·π‘–π‘Ÿπ‘’π‘π‘‘π‘–π‘œπ‘› , 0 π‘“π‘œπ‘π‘’π‘ 
Show us the code
Creating complex geometries
π‘’π‘›π‘–π‘œπ‘›: π‘šπ‘–π‘›(𝑑1, 𝑑2) π‘–π‘›π‘‘π‘’π‘Ÿπ‘ π‘’π‘π‘‘π‘–π‘œπ‘›: π‘šπ‘Žπ‘₯(𝑑1, 𝑑2) π‘ π‘’π‘π‘‘π‘Ÿπ‘Žπ‘π‘‘π‘–π‘œπ‘›: π‘šπ‘Žπ‘₯(𝑑1, βˆ’π‘‘2) π‘π‘œπ‘œπ‘™π‘’π‘Žπ‘› π‘œπ‘π‘’π‘Ÿπ‘Žπ‘‘π‘œπ‘Ÿπ‘ 
π‘ π‘π‘Žπ‘™π‘’: 𝑑(𝑝 βˆ— 𝑠)/𝑠 π‘Ÿπ‘’π‘π‘’π‘‘π‘–π‘‘π‘–π‘œπ‘›: 𝑑(π‘šπ‘œπ‘‘ 𝑝, π‘Ÿ βˆ’ 0.5π‘Ÿ) π‘‘π‘Ÿπ‘Žπ‘›π‘ π‘™π‘Žπ‘‘π‘–π‘œπ‘›: 𝑑(𝑝 βˆ’ 𝑑) π‘‘π‘œπ‘šπ‘Žπ‘–π‘› π‘œπ‘π‘’π‘Ÿπ‘Žπ‘‘π‘œπ‘Ÿπ‘ 
Show us the code
Shadows
π‘ π‘œπ‘“π‘‘ π‘ β„Žπ‘Žπ‘‘π‘œπ‘€π‘ 
π‘Žπ‘šπ‘π‘–π‘’π‘›π‘‘ π‘œπ‘π‘π‘™π‘’π‘ π‘–π‘œπ‘›
Show us the code
All together now
Cool shadertoy examples β€’ Graphics + Music β€’ https://www.shadertoy.com/view/4tc3zf β€’ 460 lines! β€’ https://www.shadertoy.com/view/4sjSW1 β€’ https://www.shadertoy.com/view/XlBGz3 β€’ Retro! β€’ Mandel bulb β€’ https://www.shadertoy.com/view/ltfSWn β€’ Advanced modeling β€’ https://www.shadertoy.com/view/ld3Gz2 β€’ Terrains β€’ https://www.shadertoy.com/view/MdlGW7 β€’ https://www.shadertoy.com/view/4ttSWf β€’ https://www.shadertoy.com/view/XslGRr
Links β€’ Raymarching explanined β€’ http://9bitscience.blogspot.com/2013/07/raymarching-distance-fields_14.html β€’ Links other useful resources as well β€’ Advanced operators β€’ http://mercury.sexy/hg_sdf/ β€’ NNUG Demos β€’ https://www.shadertoy.com/view/4t3cDl β€’ https://www.shadertoy.com/view/Xl3cDl β€’ https://www.shadertoy.com/view/Xl3cDs β€’ https://www.shadertoy.com/view/MtcyWl β€’ https://www.shadertoy.com/view/ltccD2
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