meshgit diffing and merging meshes for polygonal modeling jonathan - - PowerPoint PPT Presentation

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meshgit diffing and merging meshes for polygonal modeling jonathan - - PowerPoint PPT Presentation

Jun 09, 2023 439 likes •1.1k views

meshgit diffing and merging meshes for polygonal modeling jonathan d. denning + , fabio pellacini + + dartmouth college, sapienza university of rome original derivative original derivative original derivative original

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meshgit

diffing and merging meshes for polygonal modeling

  • jonathan d. denning+, fabio pellacini+∗

+dartmouth college, ∗sapienza university of rome

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  • riginal

derivative

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  • riginal

derivative

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  • riginal

derivative

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  • riginal

derivative

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del, add

  • riginal

derivative

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exact matching

  • riginal

derivative

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surface correspondence

  • riginal

derivative

[kim et al. 2011]

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graph matching

  • riginal

derivative

[cour et al. 2006]

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adjacency matching

  • riginal

derivative

[eppstein et al. 2009]

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meshgit

  • riginal

derivative

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string edit distance / mesh edit distance

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mesh edit distance

min cost of partially matching meshes

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C(O) = Cu(O) + Cg(O) + Ca(O) Cu : unmatched faces and verts Cg : geometric changes Ca : adjacency changes

O : partial matching of two meshes

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C(O) = Cu(O) + Cg(O) + Ca(O) e e′

  • riginal

derivative

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C(O) = Cu(O) + Cg(O) + Ca(O) Cu(O) = Nu + N ′

u

N : number of unmatched faces and verts

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C(O) = Cu(O) + Cg(O) + Ca(O)

  • riginal

derivative

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C(O) = Cu(O) + Cg(O) + Ca(O) e e′

  • riginal

derivative

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C(O) = Cu(O) + Cg(O) + Ca(O) Cg(O) =

  • e∈E
  • d(xe, xe′)

d(xe, xe′) + 1 + (1 − ne · ne′)

  • E : matched faces and verts

x : position n : normal d(xe, xe′) = |xe − xe′|

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C(O) = Cu(O) + Cg(O) + Ca(O)

  • riginal

derivative

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C(O) = Cu(O) + Cg(O) + Ca(O) e1 e2 e′

1

e′

2

  • riginal

derivative

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C(O) = Cu(O) + Cg(O) + Ca(O) e1 e2 e′

1

e′

2

  • riginal

derivative

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C(O) = Cu(O) + Cg(O) + Ca(O) Ca(O) =           

  • (e1,e2)∈{U,U′}

1 v(e1) + v(e2) + +

  • (e1,e2)∈{A,A′}

w(e1, e2, e′

1, e′ 2)

v(e1) + v(e2)

U, U ′ : unmatched adj pair A, A′ : matched adj pair v(·) : valence w(e1, e2, e′

1, e′ 2) = |d(xe1, xe2) − d(xe′

1, xe′ 2)|

d(xe1, xe2) + d(xe′

1, xe′ 2)

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C(O) = Cu(O) + Cg(O) + Ca(O)

  • riginal

derivative

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min C(O) / max common subgraph isomorphism NP-Hard

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iterative greedy algorithm

feasibly approximate med

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  • 1. init
  • 2. greedy
  • 3. backtrack
  • 4. repeat 2,3
  • riginal

derivative

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  • 1. init
  • 2. greedy
  • 3. backtrack
  • 4. repeat 2,3
  • riginal

derivative

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  • 1. init
  • 2. greedy
  • 3. backtrack
  • 4. repeat 2,3
  • riginal

derivative

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  • 1. init
  • 2. greedy
  • 3. backtrack
  • 4. repeat 2,3
  • riginal

derivative

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  • 1. init
  • 2. greedy
  • 3. backtrack
  • 4. repeat 2,3
  • riginal

derivative

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  • 1. init
  • 2. greedy
  • 3. backtrack
  • 4. repeat 2,3
  • riginal

derivative

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  • 1. init
  • 2. greedy
  • 3. backtrack
  • 4. repeat 2,3
  • riginal

derivative

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  • 1. init
  • 2. greedy
  • 3. backtrack
  • 4. repeat 2,3
  • riginal

derivative

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  • 1. init
  • 2. greedy
  • 3. backtrack
  • 4. repeat 2,3
  • riginal

derivative

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mesh edit operations

turn one mesh into another

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delete : unmatched geometry in original add : unmatched geometry in derivative transform : matched vertices with geometric cost

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2-way diff

visualize edits from original to derivative

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deleted faces colored red added faces colored green transformed vertices colored blue unmoved vertices colored gray

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  • riginal

derivative

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  • riginal

derivative

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  • riginal

derivative

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3-way diff

visualize edits from original to two independent derivatives

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brightness of add/del face indicates derivative

  • verlapping deleted faces colored yellow
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derivative a

  • riginal

derivative b

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derivative a

  • riginal

derivative b

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derivative a

  • riginal

derivative b

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diff sequence

visualize edits along sequence

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added then deleted faces colored orange

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mesh edit merge

combining independent edits

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merge is automatic if edits do not overlap on original adjacency is maintained; subdivision surfaces

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3-way + merge merge subd

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3-way + merge merge subd

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derivative a

  • riginal

derivative b

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derivative a

  • riginal

derivative b

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edit partitioning

reduce granularity of conflicts

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choose a neither choose b derivative a

  • riginal

derivative b

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future work

single object / hierarchical, component attributes low-level ops / high-level operations diff, merge / spatial undo, feature permutation, etc.

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summary

mesh edit distance : match polygonal meshes iterative greedy algorithm : feasibly approx med mesh edit operations : visualize, apply changes edit partitioning : reduce granularity of conflicts

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acknowledgements

blender böhler goralczyk grassard kuhn lumpycow nyman silva thomas vazquez williamson intel nsf sloan foundation

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thank you!

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  • riginal

derivative

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timing

chairs 3951 4.7s creature 17433 14.5s dragon 96616 307.9s durano 3722 1.5s hand 209 0.1s keys 1854 6.7s shaolin 2158 2.4s sintel 1810 2.7s spaceship 2173 0.9s shuttle 193970 585.3s woman 13984 33.7s