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

University of Calgary Graphics Jungle PG 2001

Anemone-Starfish

page 2

Overview

IntroductionIntroduction

Related Works Related Works

Building the Hierarchical Model of Sea AnemoneBuilding the Hierarchical Model of Sea Anemone

Collision-based Tentacle Phyllotactic AlgorithmCollision-based Tentacle Phyllotactic Algorithm

Modeling the StarfishModeling the Starfish

Conclusions and Future WorkConclusions and Future Work

University of Calgary Graphics Jungle PG 2001

Anemone-Starfish

page 3

Objectives

Create realistic models for sea anemone and Create realistic models for sea anemone and sea starsea star

Visualize their structuresVisualize their structures

Animate their interactive behaviourAnimate their interactive behaviour

Provide visual tools for biological study.Provide visual tools for biological study.

University of Calgary Graphics Jungle PG 2001

Anemone-Starfish

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Introduction

Implicit SurfacesImplicit Surfaces

1

0

3

),,(),,(

}),,(,),,({

n

iii zyxFCzyxF

TzyxFRzyxPS

Wyvill Field Function

C1 = 1, C2 = 1 C1 = 1, C2 = 0.5 C1 = 1, C2 = -1

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Anemone-Starfish

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Introduction: BlobTree

Complexity Complexity Hierarchy Hierarchy

Affine Transformations - Affine Transformations - Instancing (Scene Graph)Instancing (Scene Graph)

CSGCSG

BlendBlend

Controlled BlendControlled Blend

WarpWarp

TextureTexture

Animation TracksAnimation Tracks

Precise contact modelingPrecise contact modeling

BlobTreeBlobTree

University of Calgary Graphics Jungle PG 2001

Anemone-Starfish

page 6

Overview

IntroductionIntroduction

Related WorksRelated Works

Building the Hierarchical Model of Sea AnemoneBuilding the Hierarchical Model of Sea Anemone

Collision-based Tentacle Phyllotactic AlgorithmCollision-based Tentacle Phyllotactic Algorithm

Modeling the StarfishModeling the Starfish

Conclusions and Future WorkConclusions and Future Work

University of Calgary Graphics Jungle PG 2001

Anemone-Starfish

page 7

Related Works

Rick M. Harbo. Rick M. Harbo. Whelks to Whales,Whelks to Whales, Coastal Coastal Marine Life of the Pacific NorthwestMarine Life of the Pacific Northwest. 1949. 1949

D.R.Fowler, P.Prusinkewicz, and J.Battjes. D.R.Fowler, P.Prusinkewicz, and J.Battjes. A A collision-based Model for Spiral Phyllotaxiscollision-based Model for Spiral Phyllotaxis. . SIGGRAPH 1992.SIGGRAPH 1992.

X. Liang and B.Wyvill. X. Liang and B.Wyvill. Hierarchical Implicit Surface Refinement. CGI 2001. CGI 2001

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Anemone-Starfish

page 8

Transform

Blend

Transform Transform

Bend

Transform

Blend

Transform Transform

Bend

Blend

Transform Transform Transform

Bending with the BlobTree:

Related Works

University of Calgary Graphics Jungle PG 2001

Anemone-Starfish

page 9

Related Works

Blend

Left wing Right wing

Column

Blend

Blend

Local Frame Local Frame

Blend

Left wing Right wing

Column

Blend

Blend

NewLocal Frame

NewLocal Frame

Y’

X’

Z’O’

Y’

X’

Z’O’

H-Bend

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Anemone-Starfish

page 10

Hierarchy Design:

Blend - super-elliptic blending

CBlend - controlled blending

CSG - CSG operations

PCM - precise contact modeling

Related Works

University of Calgary Graphics Jungle PG 2001

Anemone-Starfish

page 11

Overview

IntroductionIntroduction

Related WorksRelated Works

Building the Hierarchical Model of Sea AnemoneBuilding the Hierarchical Model of Sea Anemone

Collision-based Tentacle Phyllotactic AlgorithmCollision-based Tentacle Phyllotactic Algorithm

Modeling the StarfishModeling the Starfish

Conclusions and Future WorkConclusions and Future Work

University of Calgary Graphics Jungle PG 2001

Anemone-Starfish

page 12

Anemone Structure

• 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.

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Anemone-Starfish

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Anemone Hierarchy: 3-level model

CSG

Mouth CBlend

Main Body Blend Blend

Tentacle Tentacle

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CSG

Blend

Base

BlendMouth

CBlendColumn

Blend BlendUpper Disk

Tentacle Tentacle

Anemone Hierarchy: 5-level model

University of Calgary Graphics Jungle PG 2001

Anemone-Starfish

page 15

Anemone Deformation

CSG

Blend

Base

BlendMouth

CBlend

Column

Blend BlendUpper Disk

Tentacle Tentacle

NewLocal Frame

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Anemone-Starfish

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Anemone Deformation

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Anemone Hierarchy: 6-level model

PCM

Base

5-Level Model

Local Frame

CSG

Blend

Base

BlendMouth

CBlendColumn

Blend BlendUpper Disk

Tentacle Tentacle

University of Calgary Graphics Jungle PG 2001

Anemone-Starfish

page 18

Overview

IntroductionIntroduction

Hierarchical Implicit SurfacesHierarchical Implicit Surfaces

Building the Hierarchical Model of Sea AnemoneBuilding the Hierarchical Model of Sea Anemone

Collision-based Tentacle Phyllotactic AlgorithmCollision-based Tentacle Phyllotactic Algorithm

Modeling the StarfishModeling the Starfish

Conclusions and Future WorkConclusions and Future Work

University of Calgary Graphics Jungle PG 2001

Anemone-Starfish

page 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 4 cycle 3 cycle 2cycle 1

rings

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Anemone-Starfish

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Collision Based Spiral Phyllotaxis

1

2

3

4

5

6

78

9

137.50

Ref: D.R.Fowler, P.Prusinkewicz, and J.Battjes. D.R.Fowler, P.Prusinkewicz, and J.Battjes. A collision-A collision-based Model for Spiral Phyllotaxisbased Model for Spiral Phyllotaxis. SIGGRAPH 1992.. SIGGRAPH 1992.

primordium

receptacle

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Anemone-Starfish

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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.

rn, same cycle,

rn - , new cycle

D

137.50

0

1

r0

University of Calgary Graphics Jungle PG 2001

Anemone-Starfish

page 22

Implicit Surface Searching

P P’ or Q Q’

R

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Tentacle Deformations

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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

University of Calgary Graphics Jungle PG 2001

Anemone-Starfish

page 25

Overview

IntroductionIntroduction

Hierarchical Implicit SurfacesHierarchical Implicit Surfaces

Building the Hierarchical Model of Sea AnemoneBuilding the Hierarchical Model of Sea Anemone

Collision-based Tentacle Phyllotactic AlgorithmCollision-based Tentacle Phyllotactic Algorithm

Modeling the StarfishModeling the Starfish

Conclusions and Future WorkConclusions and Future Work

University of Calgary Graphics Jungle PG 2001

Anemone-Starfish

page 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.

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Anemone-Starfish

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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.

Modeling Starfish

University of Calgary Graphics Jungle PG 2001

Anemone-Starfish

page 28

Overview

IntroductionIntroduction

Hierarchical Implicit SurfacesHierarchical Implicit Surfaces

Building the Hierarchical Model of Sea AnemoneBuilding the Hierarchical Model of Sea Anemone

Collision-based Tentacle Phyllotactic AlgorithmCollision-based Tentacle Phyllotactic Algorithm

Modeling the StarfishModeling the Starfish

Conclusions and Future WorkConclusions and Future Work

University of Calgary Graphics Jungle PG 2001

Anemone-Starfish

page 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.

University of Calgary Graphics Jungle PG 2001

Anemone-Starfish

page 30

Future Works

Photo-realistic rendering these creatures,

Create realistic simulation of the behaviour of these marine creatures using physically based approaches.

University of Calgary Graphics Jungle PG 2001

Anemone-Starfish

page 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.

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Animated Escape Response from Starfish

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Hierarchical Representation: Blend

Blending hierarchy:

A global surface

A set of sub-hierarchies

1isub

iglobal

isurface FFF

Blend

BlendBlend

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Anemone-Starfish

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Hierarchical Representation: CBlend

Controlled blending hierarchy:

A global surface

A set of sub-hierarchies

)( 1isub

iglobal

isurface FctFF

Ref: A. Guy and B. Wyvill, IS’95.

CBlend

BlendBlend

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page 36

Hierarchical Representation: CSG

CSG hierarchy:

A global surface

A sub-hierarchy

for

FF

FF

FF

Fi

globali

sub

iglobal

isub

iglobal

isub

isurface

),min(

),max(

),min(

CSG

Blend

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Anemone-Starfish

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Hierarchical Representation: PCM

Precise contact modeling hierarchy:

A global surface

A sub-hierarchy

Ref: M.P.Cani-Gascuel, SIGGRAPH’93.

PCM

Blendisub

isub

isurfacesub

iglobal

iglobal

isurface

gFF

gFF

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