Subdivision for Line Drawings Bert Freudenberg - PowerPoint PPT Presentation

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 Introduction • Subdivision surfaces – general surfaces representation

Introduction Introduction • Subdivision surfaces – general surfaces representation • Non-photorealistic rendering – here: line drawings

Introduction Introduction • Subdivision surfaces – general surfaces representation • Non-photorealistic rendering – here: line drawings • no explicit connection yet 2

Subdivision Subdivision • Geometry representation

Subdivision Subdivision • Geometry representation • Interpolating or approximating

Subdivision Subdivision • Geometry representation • Interpolating or approximating • Arbitrary mesh 3

Subdivision: Modified Butterfly Subdivision: Modified Butterfly

Subdivision: Modified Butterfly Subdivision: Modified Butterfly 4

Subdivision: Control mesh Subdivision: Control mesh 5

Subdivision: Subdivided once Subdivision: Subdivided once 6

Subdivision: Subdivided twice Subdivision: Subdivided twice 7

Subdivision: Subdivided three times Subdivision: Subdivided three times 8

Subdivision: Line drawings Subdivision: Line drawings • Silhouettes – border from a specific viewpoint – adjacent to front-facing and back-facing polygon

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 9

Subdivision: Level 0 Subdivision: Level 0 10

Subdivision: Level 1 Subdivision: Level 1 11

Subdivision: Level 2 Subdivision: Level 2 12

Subdivision: Level 3 Subdivision: Level 3 13

Subdivision: Line drawings Subdivision: Line drawings Problem: triangle count quadruples in each refinement step • Rapid determination of silhouettes • Fast drawing of silhouettes and creases 14

Silhouette Propagation Silhouette Propagation • New method for determining silhouettes

Silhouette Propagation Silhouette Propagation • New method for determining silhouettes • Idea: propagate silhouettes while refining the mesh 15

Silhouette Propagation: silhouette triangles Silhouette Propagation: silhouette triangles 16

Silhouette Propagation: triangles refined Silhouette Propagation: triangles refined 17

Silhouette Propagation: refined again Silhouette Propagation: refined again 18

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

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

Silhouette Propagation Silhouette Propagation • New method for determining silhouettes • Idea: propagate silhouettes while refining the mesh – silhouette band – update while subdividing 19

Silhouette Propagation: before subdivision Silhouette Propagation: before subdivision 20

Silhouette Propagation: subdivided Silhouette Propagation: subdivided 21

Silhouette Propagation: new silhouette Silhouette Propagation: new silhouette 22

Silhouette Propagation Silhouette Propagation • New method for determining silhouettes • Idea: propagate silhouettes while refining the mesh – silhouette band – update while subdividing

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

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 23

Drawing by Subdivision Drawing by Subdivision • New method for accelerating drawing • Idea: subdivide in 2D instead of 3D 24

Drawing by Subdivision: Mesh Drawing by Subdivision: Mesh 25

Drawing by Subdivision: One 2D subdivision Drawing by Subdivision: One 2D subdivision 26

Drawing by Subdivision: No 2D subdivision Drawing by Subdivision: No 2D subdivision 27

Drawing by Subdivision: Three 2D subdivisions Drawing by Subdivision: Three 2D subdivisions 28

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

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

Drawing by Subdivision Drawing by Subdivision • New method for accelerating drawing • Idea: subdivide in 2D instead of 3D – collect edges – make chains

Drawing by Subdivision Drawing by Subdivision • New method for accelerating drawing • Idea: subdivide in 2D instead of 3D – collect edges – make chains – sudivide chains

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

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 29

Drawing by Subdivision: No 3D subdivision Drawing by Subdivision: No 3D subdivision 30

Drawing by Subdivision: One 3D subdivision Drawing by Subdivision: One 3D subdivision 31

Drawing by Subdivision: Two 3D subdivisions Drawing by Subdivision: Two 3D subdivisions 32

Results Results • Implemented in Squeak

Results Results • Implemented in Squeak – open source Smalltalk system

Results Results • Implemented in Squeak – open source Smalltalk system – omni-platform, multi-media

Results Results • Implemented in Squeak – open source Smalltalk system – omni-platform, multi-media – interpreted (JIT coming)

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

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 33

Results Results 34

Results Results 35

Conclusion Conclusion • Subdivision is good for NPR

Conclusion Conclusion • Subdivision is good for NPR • Exploit features of surface representations ⇒ silhouette propagation

Conclusion Conclusion • Subdivision is good for NPR • Exploit features of surface representations ⇒ silhouette propagation • Simplify where possible ⇒ 2D subdivision for drawing 36

Extensions Extensions • hidden line removal ⇒ visibility propagation

Extensions Extensions • hidden line removal ⇒ visibility propagation • overshooting when drawing ⇒ chordal parametrization of curves 37

The End The End Questions? 38