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Robust Repair of Polygonal Models. Tao Ju Rice University. Polygonal Models. Not Closed. Closed. Not Closed. Closed. Closed Model. Partitions the space into disjoint inside and outside volumes Each polygon lies between inside and outside. Model Repair. Close polygonal models

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Robust Repair of Polygonal Models

Tao Ju

Rice University



Closed model

Not Closed

Closed

Not Closed

Closed

Closed Model

  • Partitions the space into disjoint inside and outside volumes

    • Each polygon lies between inside and outside


Model repair
Model Repair

  • Close polygonal models

    • Not just hole-filling

  • Challenges:

    • Models may contain complex errors

    • Models are often very big

    • Geometry features need to be preserved


Previous work
Previous Work

  • Mesh-based model repair

    • Zippering [Turk and Levoy 1994]

    • Stitching [Barequet and Kumar 1997]

    • Progressive boundary decimation [Borodin et al. 2002]

    • Hole filling with fairing [Liepa 2003]

  • Scattered data reconstruction

    • Tangent plane estimation [Hoppe et al. 1992]

    • Level sets [Zhao and Osher 2002]

    • Radial basis functions [Turk and O’Brien 2002]

    • Partition-of-unity methods [Ohtake et al. 2003]

    • Moving least squares surfaces [Shen et al. 2004]

    • Context-based completion [Sharf et al. 2004]


Previous work1
Previous Work

  • Volumetric model repair

  • How to determine signs ?

  • How to generate surface ?


Previous work2
Previous Work

  • Volumetric model repair – Sign generation

    • Adaptive signed distances [Frisken et al. 2000]

    • Flood-filling [Oomes et al. 1997][Andujar et al. 2002]

    • Space carving [Curless and Levoy 1996]

    • Volumetric diffusion [Davis et al. 2002]

    • Parity count and ray stabbing [Nooruddin and Turk 2003]

  • Volumetric model repair – Contouring

    • Marching Cubes [Lorensen and Cline 1987]

    • Extended Marching Cubes [Kobbelt et al. 2001]

    • Dual Contouring [Ju et al. 2002]


Robust model repair
Robust Model Repair

  • Robust

    • Closes arbitrary polygon soups

  • Efficient

    • Processes gigantic models on standard PCs

  • Accurate

    • Preserves surface quality

  • Simple !


Algorithm in a nutshell

Dual Surface”

Scan-convert

Patch

Contour

Closed Dual Surface

Algorithm in a Nutshell


Scan conversion
Scan-conversion

  • Octree grid

  • Edges intersected with model

  • Top-down creation

Memory-less octree construction

Reliable and fast intersection tests


Dual surface
Dual Surface

  • Each face dual to an intersected octree edge

Octree Edge

Dual Face


Finding holes
Finding Holes

  • Boundary edges

    • Odd-valence edges

    • Closed dual surface No boundary edge

  • Set of boundary edges partitioned into cycles

    • Each cycle encloses a “hole”


Building a patch
Building a Patch

  • Build one patch for each cycle

    • Each quad dual to an octree edge

    • Patch boundary is the cycle

  • Divide-and-conquer!

    • Using octree


Integrating a patch
Integrating a Patch

  • Add a quad

    • If does not exist on the dual surface

  • Remove a quad

    • If already exists on the dual surface

  • Key: parity of edge valence


Integrating a patch1
Integrating a Patch

  • Add a quad

    • If not already on the dual surface

  • Remove a quad

    • If already on the dual surface

  • Key: parity of edge valence


Sign generation
Sign Generation

  • Sign changes across dual surface

    • Flood-filling

Dual Face

Octree Signs


Contouring
Contouring

  • Marching Cubes

    • Edge intersections

    • Rounded corners

  • Dual Contouring

    • Hermite data

    • Sharp features




Examples cad model2
Examples – CAD Model

Closed Dual Surface


Examples cad model3
Examples – CAD Model

Output (Marching Cubes)


Examples cad model4
Examples – CAD Model

Output (Dual Contouring)


Examples bunny
Examples - Bunny

1. Input

2. DS

4. Output

3. DS Closed

Model Courtesy of the Stanford 3D Scanning Repository


Examples horse
Examples - Horse

1. Input

2. DS

4. Output

3. DS Closed

Model Courtesy of the Stanford 3D Scanning Repository


Examples david at 1mm

Output

Examples – David (at 1mm)

Input

Model Courtesy of the Digital Michelangelo Project


Performance
Performance

  • On PC with 1.5GHz CPU and 2GB memory


Conclusion
Conclusion

  • A simple, fast, and robust method to repair arbitrary polygon models

  • Future work

    • Remove topological noise

    • Improve the quality of hole filling

    • Repair using an adaptive grid

  • Special thanks to my advisor, Prof. Joe Warren, for his insights and support


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