Subdivision for Line Drawings Bert Freudenberg - - PowerPoint PPT Presentation

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Subdivision for Line Drawings Bert Freudenberg - - PowerPoint PPT Presentation

Dec 12, 2022 286 likes •919 views

Subdivision for Line Drawings Bert Freudenberg Otto-von-Guericke-Universit at Magdeburg Overview Overview 1. Introduction 2. Subdivision 3. Silhouette Propagation 4. Drawing by Subdivision 5. Results 6. Conclusion 1 Introduction

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Subdivision for Line Drawings

Bert Freudenberg Otto-von-Guericke-Universit¨ at Magdeburg

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Overview Overview

  • 1. Introduction
  • 2. Subdivision
  • 3. Silhouette Propagation
  • 4. Drawing by Subdivision
  • 5. Results
  • 6. Conclusion

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Introduction Introduction

  • Subdivision surfaces

– general surfaces representation

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Introduction Introduction

  • Subdivision surfaces

– general surfaces representation

  • Non-photorealistic rendering

– here: line drawings

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Introduction Introduction

  • Subdivision surfaces

– general surfaces representation

  • Non-photorealistic rendering

– here: line drawings

  • no explicit connection yet

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Subdivision Subdivision

  • Geometry representation
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Subdivision Subdivision

  • Geometry representation
  • Interpolating or approximating
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Subdivision Subdivision

  • Geometry representation
  • Interpolating or approximating
  • Arbitrary mesh

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Subdivision: Modified Butterfly Subdivision: Modified Butterfly

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Subdivision: Modified Butterfly Subdivision: Modified Butterfly

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Subdivision: Control mesh Subdivision: Control mesh

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Subdivision: Subdivided once Subdivision: Subdivided once

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Subdivision: Subdivided twice Subdivision: Subdivided twice

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Subdivision: Subdivided three times Subdivision: Subdivided three times

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Subdivision: Line drawings Subdivision: Line drawings

  • Silhouettes

– border from a specific viewpoint – adjacent to front-facing and back-facing polygon

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Subdivision: Line drawings Subdivision: Line drawings

  • Silhouettes

– border from a specific viewpoint – adjacent to front-facing and back-facing polygon

  • Creases

– sharp features on surface – inherent to subdivision model

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Subdivision: Level 0 Subdivision: Level 0

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Subdivision: Level 1 Subdivision: Level 1

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Subdivision: Level 2 Subdivision: Level 2

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Subdivision: Level 3 Subdivision: Level 3

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Subdivision: Line drawings Subdivision: Line drawings

Problem: triangle count quadruples in each refinement step

  • Rapid determination of silhouettes
  • Fast drawing of silhouettes and creases

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Silhouette Propagation Silhouette Propagation

  • New method for determining silhouettes
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Silhouette Propagation Silhouette Propagation

  • New method for determining silhouettes
  • Idea: propagate silhouettes while refining the mesh

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Silhouette Propagation: silhouette triangles Silhouette Propagation: silhouette triangles

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Silhouette Propagation: triangles refined Silhouette Propagation: triangles refined

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Silhouette Propagation: refined again Silhouette Propagation: refined again

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Silhouette Propagation Silhouette Propagation

  • New method for determining silhouettes
  • Idea: propagate silhouettes while refining the mesh
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Silhouette Propagation Silhouette Propagation

  • New method for determining silhouettes
  • Idea: propagate silhouettes while refining the mesh

– silhouette band

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Silhouette Propagation Silhouette Propagation

  • New method for determining silhouettes
  • Idea: propagate silhouettes while refining the mesh

– silhouette band – update while subdividing

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Silhouette Propagation: before subdivision Silhouette Propagation: before subdivision

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Silhouette Propagation: subdivided Silhouette Propagation: subdivided

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Silhouette Propagation: new silhouette Silhouette Propagation: new silhouette

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Silhouette Propagation Silhouette Propagation

  • New method for determining silhouettes
  • Idea: propagate silhouettes while refining the mesh

– silhouette band – update while subdividing

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Silhouette Propagation Silhouette Propagation

  • New method for determining silhouettes
  • Idea: propagate silhouettes while refining the mesh

– silhouette band – update while subdividing

  • Problem: subdivision itself is expensive
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Silhouette Propagation Silhouette Propagation

  • New method for determining silhouettes
  • Idea: propagate silhouettes while refining the mesh

– silhouette band – update while subdividing

  • Problem: subdivision itself is expensive
  • Applications:

– dynamic subdivision – off-line rendering

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Drawing by Subdivision Drawing by Subdivision

  • New method for accelerating drawing
  • Idea: subdivide in 2D instead of 3D

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Drawing by Subdivision: Mesh Drawing by Subdivision: Mesh

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Drawing by Subdivision: One 2D subdivision Drawing by Subdivision: One 2D subdivision

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Drawing by Subdivision: No 2D subdivision Drawing by Subdivision: No 2D subdivision

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Drawing by Subdivision: Three 2D subdivisions Drawing by Subdivision: Three 2D subdivisions

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Drawing by Subdivision Drawing by Subdivision

  • New method for accelerating drawing
  • Idea: subdivide in 2D instead of 3D
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Drawing by Subdivision Drawing by Subdivision

  • New method for accelerating drawing
  • Idea: subdivide in 2D instead of 3D

– collect edges

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Drawing by Subdivision Drawing by Subdivision

  • New method for accelerating drawing
  • Idea: subdivide in 2D instead of 3D

– collect edges – make chains

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Drawing by Subdivision Drawing by Subdivision

  • New method for accelerating drawing
  • Idea: subdivide in 2D instead of 3D

– collect edges – make chains – sudivide chains

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Drawing by Subdivision Drawing by Subdivision

  • New method for accelerating drawing
  • Idea: subdivide in 2D instead of 3D

– collect edges – make chains – sudivide chains

  • Problem: accuracy
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Drawing by Subdivision Drawing by Subdivision

  • New method for accelerating drawing
  • Idea: subdivide in 2D instead of 3D

– collect edges – make chains – sudivide chains

  • Problem: accuracy
  • Solution: perform a few 3D refinement steps first

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Drawing by Subdivision: No 3D subdivision Drawing by Subdivision: No 3D subdivision

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Drawing by Subdivision: One 3D subdivision Drawing by Subdivision: One 3D subdivision

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Drawing by Subdivision: Two 3D subdivisions Drawing by Subdivision: Two 3D subdivisions

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Results Results

  • Implemented in Squeak
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Results Results

  • Implemented in Squeak

– open source Smalltalk system

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Results Results

  • Implemented in Squeak

– open source Smalltalk system – omni-platform, multi-media

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Results Results

  • Implemented in Squeak

– open source Smalltalk system – omni-platform, multi-media – interpreted (JIT coming)

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Results Results

  • Implemented in Squeak

– open source Smalltalk system – omni-platform, multi-media – interpreted (JIT coming)

  • factor 2–4 speedup for silhouette propagation over brute-force
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Results Results

  • Implemented in Squeak

– open source Smalltalk system – omni-platform, multi-media – interpreted (JIT coming)

  • factor 2–4 speedup for silhouette propagation over brute-force
  • factor 10 speedup for 2D over 3D subdivision

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Results Results

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Results Results

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Conclusion Conclusion

  • Subdivision is good for NPR
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Conclusion Conclusion

  • Subdivision is good for NPR
  • Exploit features of surface representations

⇒ silhouette propagation

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Conclusion Conclusion

  • Subdivision is good for NPR
  • Exploit features of surface representations

⇒ silhouette propagation

  • Simplify where possible

⇒ 2D subdivision for drawing

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Extensions Extensions

  • hidden line removal

⇒ visibility propagation

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Extensions Extensions

  • hidden line removal

⇒ visibility propagation

  • overshooting when drawing

⇒ chordal parametrization of curves

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The End The End

Questions?

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