Adventures with the GPU Roice Nelson GE Aviation, Austin TX My - - PowerPoint PPT Presentation

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Adventures with the GPU Roice Nelson GE Aviation, Austin TX My - - PowerPoint PPT Presentation

Nov 21, 2022 128 likes β€’642 views

Adventures with the GPU Roice Nelson GE Aviation, Austin TX My goals for this talk Provide resources and motivation to get started with shader programming roice3.org/icerm A few mathematical detours Share fun with @TilingBot and a

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Adventures with the GPU

Roice Nelson

GE Aviation, Austin TX

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  • Provide resources and motivation to get started

with shader programming roice3.org/icerm

  • A few mathematical detours
  • Share fun with @TilingBot

and a resulting art piece

  • Tons and tons of pictures and animations! Maybe too many

My goals for this talk

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What is a shader?

Shaders are little programs that run on the GPU. These programs run at certain points of the graphics pipeline.

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From primitives to shaders

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From primitives to shaders

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From primitives to shaders

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From primitives to shaders

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β€œFolding”

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www.shadertoy.com

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Shader #2: Isometry classes of hyperbolic space 𝐺 𝑨 = 𝑏𝑨 + 𝑐 𝑑𝑨 + 𝑒 𝑄𝑇𝑀(2, 𝑫) β‰… 𝑄𝐻𝑀(2, 𝑫) ΰ·‘ 𝑫 = 𝑫 βˆͺ ∞

Group of MΓΆbius Transformations

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This is not a cone

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It’s a cylinder in UHS model: Elliptic Isometry

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Hyperbolic Isometry

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Hyperbolic Isometry

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Loxodromic Isometry

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Loxodromic Isometry

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This is not a plane

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It’s a horosphere: Parabolic Isometry

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Raymarching

See β€œRay Marching and Signed Distance Functions” by Jamie Wong

Credit: GPU Gems 2: Chapter 8

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Quaternions! 𝑨 ↦ 𝑏𝑨 + 𝑐 𝑑𝑨 + 𝑒 π‘₯ ↦ 𝑏π‘₯ + 𝑐 𝑑π‘₯ + 𝑒 π‘₯ = 𝑨 + π‘§π’Œ , 𝑧 ∈ 𝑺+ , 𝑨 ∈ ΰ·‘ 𝑫

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Shader #3: Spherical Images

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Shader #4: Hyperbolic VR using Raymarching

Folding AND Raymarching, see Henry’s NSF video!

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Utilities

  • Shadertoy-render
  • ffmpeg
  • Pov-Ray
  • LinqToTwitter

Again, links (and scripts) at: roice3.org/icerm

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In my experience…

Advantages

  • Fast!
  • Motion
  • Quality
  • Fractals
  • WebGL
  • Lots of Examples

Disadvantages

  • Hardware
  • Debugging
  • Optimization
  • Low-level
  • Code libraries
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β€œThe explorer who will not come back or send back his ships to tell his tale is not an explorer,

  • nly an adventurer.”
  • Ursula K. Le Guin, The Dispossessed: An Ambiguous Utopia
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@Tilingbot

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The Real Shader #1: Hyperbolic Wythoff explorer

by Matt Zucker, mzucker.github.io

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Regular and Rectified

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Uniform Tilings

Truncation

5 7

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Uniform Tilings

Bitruncation

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Uniform Tilings

Cantellation

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Uniform Tilings

Omnitruncation

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Duals to Uniform (Catalan Tilings)

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The Same But Different

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Rotating in a conformal square

Snub {8,8}

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In a rotating conformal square

Omnitruncated {6,9}

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Omnitruncated {6,9}

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Omnitruncated {6,9}

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Rotating in the band model

Truncated {6,4}

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In a rotating band model

Truncated {8,4}

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Limit Rotations

Omnitruncated {4,∞} Truncated {3,∞}

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Joukowsky projection 𝑨 =

1 2 πœ‚ + 1 πœ‚

named after Nikoli Zhukovsky

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The best internal representation?

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Thank you!

roice3.org/icerm