Sketching Freeform Surfaces Using Network of Curves

1
Sketching Free-form Surfaces Using Network of
Curves

• Koel Das
• Pablo Diaz-Gutierrez
• M. Gopi
• University of California, Irvine

2
Motivation
www-ui.is.s.u-tokyo.ac.jp/takeo

• We have tools for sketching rotund objects
• Teddy!
• Round and symmetric objects
• We have sketch-based CAD tools
• SketchUp
• Boxy, rectilinear shapes
• What about something intermediate?
• Requirements for artists
• Free-form shapes
• Easy to learn interface
• Artists can draw!

www.sketchup.com
graphics.cs.brown.edu
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Problem description

• Generation of networks of free-form curves
• Simple sketching interface
• Surface interpolation for networks of curves
• Flexible
• Capable of large variety of shapes
• Simple
• Few parameters

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Talk outline

• Problem description
• Networks of Curves
• Depth interpolation
• Surface Generation
• Normals
• Topological triangulation
• Vertex relocation
• Results
• Demo
• Conclusion, Future Work and Q/A

5
Networks of curves

• Whats a network of curves?
• A set of 3D vertices and polylines
• All locations are known
• Not necessarily planar
• How is it different from a 2D sketch?
• 2D sketch is a flat drawing
• Networks of curves have (explicit) depth
• What are the implications?
• Better clues on the intention of the user
• Better usage of computing capabilities
• Less ambiguity
• One step less to solve

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Networks of curves2D/3D ambiguities
?
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Networks of curvesGranularity of 2D/3D

• Sketch Thick grain 2D-3D conversion
• Network of curves Fine grain conversion

Input Complete sketch
Global sketch interpretation
2D
Input Sketch segments
3D
Produced shape
2D
3D
Network of curves
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Networks of curves

• What are the challenges in its creation?
• Allow transformations without complicating
  interface
• Early 2D to 3D conversion
• Depth interpolation

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Networks of curves From 2D to 3D

• 3 types of curves
• Both endpoints free
• Constant, arbitrary depth
• One endpoint fixed, one free
• Constant depth given by fixed endpoint
• Both endpoints fixed
• Depth interpolation

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Networks of curves Depth interpolation

• Underconstrained problem
• No solution is always better than other
• Our choice minimize curvature
• Informal lab study showed most users find these
  curves to be the natural interpolation
• 3D Bezier curve with control points of uniformly
  increasing depth minimizes curvature

2D
?
3D
3D
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Networks of curves Depth interpolation

• We know
• Projection parameters
• X,Y screen coordinates along curve
• Depth at endpoints of curve (Z0,Z1)
• Need to find intermediate Z
• Our approximation
• Find extremal deviation points
• These will be our control points
• Uniformly distribute Z values
• Split segment at those points
• Recursively repeat until curve segment is close
  to straight line
• Similar to Casteljau subdivision

Z0
Z0(Z1-Z0)0.25
Z0(Z1-Z0)0.75
Z0(Z1-Z0)0.5
Z1
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Talk outline

• Problem description
• Networks of Curves
• Depth interpolation
• Surface Generation
• Normals
• Topological triangulation
• Vertex relocation
• Results
• Demo
• Conclusion, Future Work and Q/A

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Surface generation

• Two steps problem
• Identification of surface patches
• Surface generation (skinning)
• We focus on skinning
• Manifolds without boundaries

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Surface generationNormals

• Normals are crucial for surface generation
• Meaning of a vertex normal
• Perpendicular direction to surface
• Why is it a problem?
• Need to calculate normal without knowing the
  surface
• In current implementation, we guess and let the
  user fix (flip/rotate)
• More work should go on this
• SLERP (quaternions) for normal interpolation
  along curves

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Surface generationTopological triangulation

• Why the name?
• The location doesnt matter
• Just the connectivity
• How is it done?
• Layers of triangles reducing boundary complexity
• Finish with triangle fan
• Enough for convex, planar faces w/ sharp edges
• Split non-convex polygons

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Surface generationVertex relocation (2D diagram)

• What if we want round edges?
• No sharp features
• Need to relocate generated vertices
• To minimize surface distortion
• Repeat as desired
• Quadric error for each non-fixed vertex
• Relocate vertices to minimize error
• Recalculate normals
• The order of these updates is crucial
• Vertex dependencies from boundary to center

Etc
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Talk outline

• Problem description
• Networks of Curves
• Depth interpolation
• Surface Generation
• Normals
• Topological triangulation
• Vertex relocation
• Results
• Demo
• Conclusion, Future Work and Q/A

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Results
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Talk outline

• Problem description
• Networks of Curves
• Depth interpolation
• Surface Generation
• Normals
• Topological triangulation
• Vertex relocation
• Results
• Demo
• Conclusion, Future Work and Q/A

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Demo

• Disclaimer
• Normal calculations
• Patch identification
• Numerical stability of the surface generation
• Cross your fingers

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Talk outline

• Problem description
• Networks of Curves
• Depth interpolation
• Surface Generation
• Normals
• Topological triangulation
• Vertex relocation
• Results
• Demo
• Conclusion

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Summary

• Curvature minimizing depth interpolation
• Simple surface generation scheme
• Still work in progress!

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Future work

• Automatic identification of surface patches
• Fix numerical stability issues
• Gesture recognition to simplify GUI
• Selectively highlight and fade out regions of the
  sketch
• Reduce the overlapping webs effect
• Automatic pre-visualization
• Better user feedback

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Acknowledgements

• ICS Computer Graphics Lab _at_ UCI
• http//graphics.ics.uci.edu
• Google Summer of Code program
• http//code.google.com
• Blender Foundation
• http//blender3d.org

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The End

• Thank you!
• Questions?
• Comments?
• Suggestions?