Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics...

Manuel Mesters - Subdivision Surfaces Manuel Mesters - Subdivision Surfaces

computer graphics & computer graphics & visualizationvisualization

Seminar Computer GraphicsSeminar Computer Graphics

Geometric representation and processing:Geometric representation and processing: Subdivision SurfacesSubdivision Surfaces


Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces

At a glanceAt a glance

Refinement 1 Refinement 2

Refinement ∞



At a glanceAt a glance



OutlineOutline

- Motivation: Geri’s Game Motivation: Geri’s Game

- Introduction: Subdivision BasicsIntroduction: Subdivision Basics

- Loop Subdivision SurfacesLoop Subdivision Surfaces

- Catmull-Clark Subdivision SurfacesCatmull-Clark Subdivision Surfaces

- SummarySummary



OutlineOutline

- Motivation: Geri’s GameMotivation: Geri’s Game




- SummarySummary



Making of Geri‘s GameMaking of Geri‘s Game

Zur Anzeige wird der QuickTime™ Dekompressor „TIFF (LZW)“

benötigt.



Geri’s GameGeri’s Game

- 1st animation using Subdivision Surfaces1st animation using Subdivision Surfaces

- Playground for new technologiesPlayground for new technologies

- Best Animated Short (1997)Best Animated Short (1997)



DraftDraft

- 1000s of drawings- 1000s of drawings


benötigt.



Clay ModelsClay Models

- Double Life Size Model:Double Life Size Model:- HeadHead

- HandsHands


benötigt.



DigitizingDigitizing

- Laserscanner -> Point CloudLaserscanner -> Point Cloud



MeshMesh

- Point Cloud -> MeshPoint Cloud -> Mesh

- Controls for facial movements (manual insertion)Controls for facial movements (manual insertion)


benötigt.



Animation ProcessAnimation Process

- Using Pixar’s RenderMan:Using Pixar’s RenderMan:- Animate MeshAnimate Mesh

- Call Controls / SubdivideCall Controls / Subdivide


benötigt.



Cloth DynamicsCloth Dynamics


benötigt.

- Dynamic flexible meshDynamic flexible mesh

- Energy functionsEnergy functions

- Many equations ...Many equations ...



Watch Geri’s GameWatch Geri’s Game



OutlineOutline





- SummarySummary



Subdivision - DefinitionSubdivision - Definition

Subdivision defines a smooth curve or surface asSubdivision defines a smooth curve or surface as

the limit of a sequence of successive refinementsthe limit of a sequence of successive refinements



Subdivision - DefinitionSubdivision - Definition

Subdivision defines a smooth curve or surface asSubdivision defines a smooth curve or surface as


- Start: Start: Control MeshControl Mesh

- Process: Process: Apply refinement rules (many times)Apply refinement rules (many times)

- Result: Result: Smooth curve/surfaceSmooth curve/surface



Subdivision CurveSubdivision Curve

Start: Polygon

Apply refinement rule



Result: Smooth curve



Subdivision Curve - RulesSubdivision Curve - Rules

€

P0

€

P2

€

P3

€

P1

€

P neu =1

16−P0

alt + 9P1alt + 9P2

alt − P3alt

( )



Subdivision CurveSubdivision Curve



Different Algorithms - Different ResultsDifferent Algorithms - Different Results

Loop Catmull-Clark

Butterfly Doo-Sabin



OutlineOutline





- SummarySummary



Loop SubdivisionLoop Subdivision




original vertexoriginal vertexv3

v1 v2

v4




8

3

8

1

8

3

8

1

edge point (ep): constructed on each edgeedge point (ep): constructed on each edge

original vertexoriginal vertexv3

v1 v2

v4

ep

( ) ( )438

121

8

3vvvvep +++=



vertex point vertex point constructed for each old (original) vertex constructed for each old (original) vertex


edge pointedge point

original vertexoriginal vertex



vertex point: constructed for each old (original) vertexvertex point: constructed for each old (original) vertex


A given vertex has A given vertex has nn neighbor vertices. neighbor vertices.

The new vertex point: The new vertex point:

For For nn = 3 = 3

For For nn > 3 > 3 ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛+−=2

2cos4

1

8

3

8

51

nns

π

16

3=s

( ) ⎟⎠

⎞⎜⎝

⎛∗+∗−= ∑

nivsvsnvp *)1(

vv

vv



Loop - Local SubdivisionLoop - Local Subdivision

- Exclude some edges from SubdivisionExclude some edges from Subdivision

- More details later ...More details later ...



OutlineOutline





- SummarySummary



Catmull-Clark SubdivisionCatmull-Clark Subdivision




∑=n

ivnf

1

1FACE

42121 ffvv

e+++

=

EDGE




∑=n

ivnf

1

1FACE

42121 ffvv

e+++

=

EDGE

VERTEX

∑∑ ++−

=+j

jj

jii fn

en

vn

nv

221

112



Sharp creasesSharp creases

- Subdivision produces smooth surfacesSubdivision produces smooth surfaces

1. Tag Edges as “sharp” or “not-sharp”

During Subdivision,

2. if an edge is “sharp”, use sharp subdivision rules.

3. If an edge is “not-sharp”, use normal smooth subdivision rules.



Infinitely Sharp CreasesInfinitely Sharp Creases

- Tag Control vertices and edges as sharpTag Control vertices and edges as sharp

- Face points: same as smooth ruleFace points: same as smooth rule

- Edge points: place at midpoint of edgeEdge points: place at midpoint of edge

- Vertex pointsVertex points- One sharp incident edge (dart): same as smooth ruleOne sharp incident edge (dart): same as smooth rule

- Two sharp edges (crease): (eTwo sharp edges (crease): (e11 + 6v + 6vii + e + e22) / 8) / 8

- Three or more sharp edges (corner): do not modify pointThree or more sharp edges (corner): do not modify point



Sharp rulesSharp rules

∑=n

ivnf

1

1FACE (unchanged)

221 vv

e+

=EDGE

VERTEX

ii vv =+1

8

6 211

evev ii

++=+

crease

dart

corner ∑∑ ++−

=+j

jj

jii fn

en

vn

nv

221

112

>2

2

0,1

# adj. Sharp edges



Semi-sharp creasesSemi-sharp creases

1. Tag Edges as “sharp” or “not-sharp”

• n = 0 : “not sharp”

• n > 0 : sharp

During Subdivision,

1. if an edge is “sharp”, use sharp subdivision rules. Newly created edges, are assigned a sharpness of n-1.

2. If an edge is “not-sharp”, use normal smooth subdivision rules.



Subdivision Subdivision

- Sharpness!Sharpness!



OutlineOutline





- SummarySummary



SummarySummary

Take home messageTake home message



SummarySummarySubdivision defines a smooth curve or surface asSubdivision defines a smooth curve or surface as




SummarySummary



SummarySummary

- There are different AlgorithmsThere are different Algorithms- Mesh TypeMesh Type

- RulesRules



SummarySummary

- LoopLoop

- Catmull-ClarkCatmull-Clark



SummarySummary

- SubdivisionSubdivision- Standard rules -> smoothnessStandard rules -> smoothness

- Additional rules -> sharpnessAdditional rules -> sharpness

- Sharpness parameter -> flexibilitySharpness parameter -> flexibility



The EndThe End

Thank you for your attentionThank you for your attention

Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics...

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