Modeling the Structure of the Sea Anemone and Sea Star Using Hierarchical Implicit Surfaces by

1. Modeling the Structure of the Sea Anemone and Sea Star Using Hierarchical Implicit Surfaces by Xikun Liang, Mai Ali Nur and Brian Wyvill Department of Computer Science University of Calgary, Alberta, Canada

2. Overview Introduction Related Works Building the Hierarchical Model of Sea Anemone Collision-based Tentacle Phyllotactic Algorithm Modeling the Starfish Conclusions and Future Work

3. Objectives • Create realistic models for sea anemone and sea star • Visualize their structures • Animate their interactive behaviour • Provide visual tools for biological study.

4. Introduction • Implicit Surfaces Wyvill Field Function C1 = 1, C2 = 1 C1 = 1, C2 = 0.5 C1 = 1, C2 = -1

5. Introduction: BlobTree • BlobTree • Complexity - Hierarchy • Affine Transformations - Instancing (Scene Graph) • CSG • Blend • Controlled Blend • Warp • Texture • Animation Tracks • Precise contact modeling

6. Overview • Introduction • Related Works • Building the Hierarchical Model of Sea Anemone • Collision-based Tentacle Phyllotactic Algorithm • Modeling the Starfish • Conclusions and Future Work

7. Related Works • Rick M. Harbo. Whelks to Whales,Coastal Marine Life of the Pacific Northwest. 1949 • D.R.Fowler, P.Prusinkewicz, and J.Battjes. A collision-based Model for Spiral Phyllotaxis. SIGGRAPH 1992. • X. Liang and B.Wyvill. Hierarchical Implicit Surface Refinement. CGI 2001

8. Blend Bend Transform Transform Transform Blend Bend Blend Transform Transform Transform Transform Transform Transform Related Works Bending with the BlobTree:

9. Blend Column Local Frame Local Frame Blend Blend Y’ Z’ X’ O’ Left wing Right wing Y’ X’ O’ Z’ Related Works Blend Column New Local Frame New Local Frame H-Bend Blend Blend Left wing Right wing

10. Related Works • Hierarchy Design: • Blend - super-elliptic blending • CBlend - controlled blending • CSG - CSG operations • PCM - precise contact modeling

11. Overview • Introduction • Related Works • Building the Hierarchical Model of Sea Anemone • Collision-based Tentacle Phyllotactic Algorithm • Modeling the Starfish • Conclusions and Future Work

12. Base:Adhesive, wider than the column, used to attach the anemone to its environment • Column:cylindrical and divided into regions • Upper disk:circular and transparent • Mouth:a slit at the center of the upper disk • Tentacles:surround the mouth arranged in four or five cycles. Anemone Structure

13. CSG Mouth CBlend Main Body Blend Blend Tentacle Tentacle Anemone Hierarchy:3-level model

14. Anemone Hierarchy:5-level model Blend Base CSG Mouth Blend Column CBlend Upper Disk Blend Blend Tentacle Tentacle

15. Anemone Deformation Blend Base CSG Mouth Blend New Local Frame Column CBlend Upper Disk Blend Blend Tentacle Tentacle

16. Anemone Deformation

17. Anemone Hierarchy:6-level model PCM 5-Level Model Local Frame Base Blend Base CSG Mouth Blend Column CBlend Upper Disk Blend Blend Tentacle Tentacle

18. Overview • Introduction • Hierarchical Implicit Surfaces • Building the Hierarchical Model of Sea Anemone • Collision-based Tentacle Phyllotactic Algorithm • Modeling the Starfish • Conclusions and Future Work

19. Tentacle Patterns • typical number: 64, 72 • 4 cycles: 6,12,18,36 = 72 • or 6,10,16,32 = 64 • a few rings in a cycle cycle 1 rings cycle 4 cycle 3 cycle 2

20. 7 5 2 8 4 3 9 6 1 Collision Based Spiral Phyllotaxis primordium 137.50 receptacle Ref:D.R.Fowler, P.Prusinkewicz, and J.Battjes. A collision-based Model for Spiral Phyllotaxis. SIGGRAPH 1992.

21. Tentacle Phyllotaxis 0 = 0, r0 = D, radius of the upper disk (receptacle) n+1 = n +137.50 = (n+1)*137.50 rn+1 = x = rncos(n ), y = rnsin(n ), z = body height. 1  rn, same cycle,   rn - , new cycle 137.50 r0 0 D

22. Implicit Surface Searching R P  P’ or Q  Q’

23. Tentacle Deformations

24. Algorithm 1: Tentacle Spiral Phyllotaxis Begin Set the initial layer and ring; repeat Calculate an initial position on the receptacle; if (a collision occurs) then repeat Move the tentacle to the next inner ring; until (there is no collision or no more space is left) Shift the tentacle to the implicit surface; Add the tentacle to the hierarchy; if (current cycle is finished) then Change to the next inner cycle; until (all tentacles are added or no more space is left) end

25. Overview • Introduction • Hierarchical Implicit Surfaces • Building the Hierarchical Model of Sea Anemone • Collision-based Tentacle Phyllotactic Algorithm • Modeling the Starfish • Conclusions and Future Work

26. Starfish Structure • 5 arms that are up to 12 cm • Variety of colours • Mottled with reddish brown to orange blotches • Large, high disk at the centre of the body.

27. Modeling Starfish • Five implicit cones are used for the arms, • Initial positions: • x = rcos(n ), • y = rsin(n ), • z = body height. • Point primitives for small bumps, • Shifting bumps to the body surface, • Random offset applied to the bumps.

28. Overview • Introduction • Hierarchical Implicit Surfaces • Building the Hierarchical Model of Sea Anemone • Collision-based Tentacle Phyllotactic Algorithm • Modeling the Starfish • Conclusions and Future Work

29. Conclusions • A new method to model sea anemone and sea star using hierarchical implicit surfaces, • Implicit surface collision-based phyllotactic model which can be used to model other implicit objects, • Intuitive and easy control over the model through hierarchical local and global deformations, • Blending, controlled blending, CSG boolean operations, field warping, and PCM are useful tools for implicit modeling.

30. Future Works • Photo-realistic rendering these creatures, • Create realistic simulation of the behaviour of these marine creatures using physically based approaches.

31. Acknowledgements • Professors and students of Graphics Jungle at the University of Calgary, • MACI project at the University of Calgary, • National Science and Engineering Research Council (NSERC), • The anonymous reviewers.

33. Animated Escape Response from Starfish

34. Hierarchical Representation: Blend • Blending hierarchy: • A global surface • A set of sub-hierarchies Blend Blend Blend

35. CBlend Blend Blend Hierarchical Representation: CBlend • Controlled blending hierarchy: • A global surface • A set of sub-hierarchies Ref: A. Guy and B. Wyvill, IS’95.

36. CSG Blend Hierarchical Representation: CSG • CSG hierarchy: • A global surface • A sub-hierarchy

37. PCM Blend Hierarchical Representation: PCM • Precise contact modeling hierarchy: • A global surface • A sub-hierarchy Ref: M.P.Cani-Gascuel, SIGGRAPH’93.