3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling...
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Transcript of 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling...
![Page 1: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/1.jpg)
3D Modeling Topics
Gerald FarinComputer Science
PRISM: Partnership for Research In Spatial ModelingASU
![Page 2: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/2.jpg)
PRISM’sexpertises
are well-suited tointerdisciplinary
research
Data Acquisition
GeometricModeling
Analysis
Visualization
Data Archiving
RapidPrototyping
![Page 3: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/3.jpg)
Overview
• History• Curvature• Surface analysis• Ruled surfaces• Coons surfaces• Continuity• NURBS• Subdivision surfaces
![Page 4: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/4.jpg)
Lofting
![Page 5: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/5.jpg)
before fairing
![Page 6: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/6.jpg)
after fairing
![Page 7: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/7.jpg)
History
• 1962 C. de Boor: bicubic splines• 1972 J. Ferguson, Boeing: cubic splines• 1974 W. Gordon, R. Riesenfeld: B-splines• 1964 S. Coons: Coons patches, conics• 1975 K. Vesprille: NURBS
![Page 8: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/8.jpg)
History
• 1958 P. de Casteljau, Citroen: de Casteljau algorithm
• 1965 P. Bezier, Renault: Bezier curves
![Page 9: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/9.jpg)
Overview
• History• Curvature• Surface analysis• Ruled surfaces• Coons surfaces• Continuity• NURBS• Subdivision surfaces
![Page 10: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/10.jpg)
Osculating circle
![Page 11: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/11.jpg)
Frenet frame
Interactive demo
![Page 12: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/12.jpg)
Helix curve fitcubic quintic
![Page 13: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/13.jpg)
Helix curvature plotcubic quintic
![Page 14: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/14.jpg)
Curvature plot, cubic B-spline
![Page 15: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/15.jpg)
B-spline curve operations
redundancy creation processes:
• Knot insertion• Degree raising
![Page 16: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/16.jpg)
Knot insertion
quintic
cubic
![Page 17: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/17.jpg)
B-spline curve fairing
“Invert” redundancy creation processes:
• Knot removal• Degree lowering
![Page 18: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/18.jpg)
Cubic spline
Before fairing
After fairing
![Page 19: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/19.jpg)
Curvature & Beauty
![Page 20: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/20.jpg)
Curvature & Cars
![Page 21: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/21.jpg)
Overview
• History• Curvature• Surface analysis• Ruled surfaces• Coons surfaces• Continuity• NURBS• Subdivision surfaces
![Page 22: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/22.jpg)
Surface curvatures
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Surface curvatures
![Page 24: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/24.jpg)
Lines of curvature
![Page 25: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/25.jpg)
Surface curvatures
• Gaussian = min curvature x max curvature• Gaussian = 0: developable surface
Gaussian curvature signs
![Page 26: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/26.jpg)
First Gaussian image
![Page 27: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/27.jpg)
Gaussian application
![Page 28: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/28.jpg)
Gaussian curvature
![Page 29: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/29.jpg)
Mean curvature
![Page 30: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/30.jpg)
Max curvature
![Page 31: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/31.jpg)
Reflection lines
![Page 32: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/32.jpg)
Reflection lines
![Page 33: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/33.jpg)
Overview
• History• Curvature• Surface analysis• Ruled surfaces• Coons surfaces• Continuity• NURBS• Subdivision surfaces
![Page 34: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/34.jpg)
Ruled surface
![Page 35: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/35.jpg)
Ruled, bilinear surface
![Page 36: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/36.jpg)
Ruled surfaces
![Page 37: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/37.jpg)
Overview
• History• Curvature• Surface analysis• Ruled surfaces• Coons surfaces• Continuity• NURBS• Subdivision surfaces
![Page 38: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/38.jpg)
Coons surface
![Page 39: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/39.jpg)
+ Ruled in u
![Page 40: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/40.jpg)
+ Ruled in v
![Page 41: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/41.jpg)
- Bilinear
![Page 42: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/42.jpg)
Coons surfaces
![Page 43: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/43.jpg)
Overview
• History• Curvature• Surface analysis• Ruled surfaces• Coons surfaces• Continuity• NURBS• Subdivision surfaces
![Page 44: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/44.jpg)
G1 vs C1 surfaces
• C1: differentiable across common boundary of two surfaces; requires a common domain.
• G1: common tangent plane along common boundary; no common domain required.
![Page 45: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/45.jpg)
Tangent ribbon
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G1 condition
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T-splines
![Page 48: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/48.jpg)
T-splines
![Page 49: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/49.jpg)
G1 mixed patch types
![Page 50: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/50.jpg)
• History• Curvature• Surface analysis• Ruled surfaces• Coons surfaces• Continuity• NURBS• Subdivision surfaces
![Page 51: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/51.jpg)
NURBS
![Page 52: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/52.jpg)
Conics: Pascal’s theorem
![Page 53: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/53.jpg)
Homogeneous coordinates
![Page 54: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/54.jpg)
Polynomial vs rational
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Conics: ellipse; 0<w<1
![Page 56: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/56.jpg)
Conics: parabola; w=1
![Page 57: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/57.jpg)
Conics: hyperbola; w>1
![Page 58: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/58.jpg)
NURB curve, all weights = 1
![Page 59: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/59.jpg)
NURB curve, one weight = 0.2
![Page 60: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/60.jpg)
NURB curve, one weight = 3
![Page 61: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/61.jpg)
B-spline curves
![Page 62: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/62.jpg)
Bicubic NURB surface
![Page 63: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/63.jpg)
One weight changed
![Page 64: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/64.jpg)
NURBS: torus
![Page 65: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/65.jpg)
NURB hierarchies
• Conics: subset of rational Bezier• Rational Bezier: subset of NURB curves• Conics: not subset of splines • Parabolas: subset of splines• Quadrics: subset of NURB surfaces
• Conic lofted surfaces: not subset of NURB surfaces
![Page 66: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/66.jpg)
• History• Curvature• Surface analysis• Ruled surfaces• Coons surfaces• Continuity• NURBS• Subdivision surfaces
![Page 67: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/67.jpg)
Subdivision
• Movie introducing Catmull-Clark subdivision
![Page 68: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/68.jpg)
Viking ships
![Page 69: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/69.jpg)
Symmetry Analysis
![Page 70: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/70.jpg)
Whole body scanner from Cyberware
Art Meets Engineering
Twister, Dan Collins 1995 Rendering in 3D Studio Max
![Page 71: 3D Modeling Topics Gerald Farin Computer Science PRISM: Partnership for Research In Spatial Modeling ASU.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649d095503460f949dafc7/html5/thumbnails/71.jpg)
Water Table & Pop Growth (1900 - 2000)