manuel mesters - subdivision surfaces computer graphics & visualization seminar computer...
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![Page 1: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/1.jpg)
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
![Page 2: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/2.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
At a glanceAt a glance
Refinement 1 Refinement 2
Refinement ∞
![Page 3: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/3.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
At a glanceAt a glance
![Page 4: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/4.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
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
![Page 5: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/5.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
OutlineOutline
- Motivation: Geri’s GameMotivation: Geri’s Game
- Introduction: Subdivision BasicsIntroduction: Subdivision Basics
- Loop Subdivision SurfacesLoop Subdivision Surfaces
- Catmull-Clark Subdivision SurfacesCatmull-Clark Subdivision Surfaces
- SummarySummary
![Page 6: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/6.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
Making of Geri‘s GameMaking of Geri‘s Game
Zur Anzeige wird der QuickTime™ Dekompressor „TIFF (LZW)“
benötigt.
![Page 7: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/7.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
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)
![Page 8: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/8.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
DraftDraft
- 1000s of drawings- 1000s of drawings
Zur Anzeige wird der QuickTime™ Dekompressor „TIFF (LZW)“
benötigt.
![Page 9: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/9.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
Clay ModelsClay Models
- Double Life Size Model:Double Life Size Model:- HeadHead
- HandsHands
Zur Anzeige wird der QuickTime™ Dekompressor „TIFF (LZW)“
benötigt.
![Page 10: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/10.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
DigitizingDigitizing
- Laserscanner -> Point CloudLaserscanner -> Point Cloud
![Page 11: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/11.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
MeshMesh
- Point Cloud -> MeshPoint Cloud -> Mesh
- Controls for facial movements (manual insertion)Controls for facial movements (manual insertion)
Zur Anzeige wird der QuickTime™ Dekompressor „TIFF (LZW)“
benötigt.
![Page 12: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/12.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
Animation ProcessAnimation Process
- Using Pixar’s RenderMan:Using Pixar’s RenderMan:- Animate MeshAnimate Mesh
- Call Controls / SubdivideCall Controls / Subdivide
Zur Anzeige wird der QuickTime™ Dekompressor „TIFF (LZW)“
benötigt.
![Page 13: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/13.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
Cloth DynamicsCloth Dynamics
Zur Anzeige wird der QuickTime™ Dekompressor „TIFF (LZW)“
benötigt.
- Dynamic flexible meshDynamic flexible mesh
- Energy functionsEnergy functions
- Many equations ...Many equations ...
![Page 14: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/14.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
Watch Geri’s GameWatch Geri’s Game
![Page 15: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/15.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
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
![Page 16: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/16.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
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
![Page 17: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/17.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
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
- Start: Start: Control MeshControl Mesh
- Process: Process: Apply refinement rules (many times)Apply refinement rules (many times)
- Result: Result: Smooth curve/surfaceSmooth curve/surface
![Page 18: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/18.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
Subdivision CurveSubdivision Curve
Start: Polygon
Apply refinement rule
Apply refinement rule
Apply refinement rule
Result: Smooth curve
![Page 19: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/19.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
Subdivision Curve - RulesSubdivision Curve - Rules
€
P0
€
P2
€
P3
€
P1
€
P neu =1
16−P0
alt + 9P1alt + 9P2
alt − P3alt
( )
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computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
Subdivision CurveSubdivision Curve
![Page 21: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/21.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
Different Algorithms - Different ResultsDifferent Algorithms - Different Results
Loop Catmull-Clark
Butterfly Doo-Sabin
![Page 22: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/22.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
Different Algorithms - Different ResultsDifferent Algorithms - Different Results
Loop Catmull-Clark
Butterfly Doo-Sabin
![Page 23: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/23.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
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
![Page 24: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/24.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
Loop SubdivisionLoop Subdivision
![Page 25: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/25.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
Loop SubdivisionLoop Subdivision
original vertexoriginal vertexv3
v1 v2
v4
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computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
Loop SubdivisionLoop Subdivision
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 +++=
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computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
vertex point vertex point constructed for each old (original) vertex constructed for each old (original) vertex
Loop SubdivisionLoop Subdivision
edge pointedge point
original vertexoriginal vertex
![Page 28: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/28.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
vertex point: constructed for each old (original) vertexvertex point: constructed for each old (original) vertex
Loop SubdivisionLoop Subdivision
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
![Page 29: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/29.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
Loop - Local SubdivisionLoop - Local Subdivision
- Exclude some edges from SubdivisionExclude some edges from Subdivision
- More details later ...More details later ...
![Page 30: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/30.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
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
![Page 31: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/31.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
Catmull-Clark SubdivisionCatmull-Clark Subdivision
![Page 32: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/32.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
Catmull-Clark SubdivisionCatmull-Clark Subdivision
∑=n
ivnf
1
1FACE
42121 ffvv
e+++
=
EDGE
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computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
Catmull-Clark SubdivisionCatmull-Clark Subdivision
∑=n
ivnf
1
1FACE
42121 ffvv
e+++
=
EDGE
![Page 34: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/34.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
Catmull-Clark SubdivisionCatmull-Clark Subdivision
∑=n
ivnf
1
1FACE
42121 ffvv
e+++
=
EDGE
VERTEX
∑∑ ++−
=+j
jj
jii fn
en
vn
nv
221
112
![Page 35: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/35.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
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.
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computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
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
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computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
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
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computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
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.
![Page 39: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/39.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
Subdivision Subdivision
- Sharpness!Sharpness!
![Page 40: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/40.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
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
![Page 41: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/41.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
SummarySummary
Take home messageTake home message
![Page 42: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/42.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
SummarySummarySubdivision 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
![Page 43: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/43.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
SummarySummary
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computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
SummarySummary
- There are different AlgorithmsThere are different Algorithms- Mesh TypeMesh Type
- RulesRules
![Page 45: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/45.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
SummarySummary
- LoopLoop
- Catmull-ClarkCatmull-Clark
![Page 46: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/46.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
SummarySummary
- SubdivisionSubdivision- Standard rules -> smoothnessStandard rules -> smoothness
- Additional rules -> sharpnessAdditional rules -> sharpness
- Sharpness parameter -> flexibilitySharpness parameter -> flexibility
![Page 47: Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision](https://reader035.vdocuments.net/reader035/viewer/2022062314/56649e615503460f94b5d5b8/html5/thumbnails/47.jpg)
computer graphics & computer graphics & visualizationvisualization
Manuel Mesters - Subdivision SurfacesManuel Mesters - Subdivision Surfaces
The EndThe End
Thank you for your attentionThank you for your attention