Making papercraft from triangle mesh

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Making papercraft from triangle mesh

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Outline

• Problem statement
• Background
• Related work
• My research direction

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Problem

• Papercraft
• Unfold a model (triangle meshes) onto pieces of
  paper
• Reconstruct the model from paper, by cutting and
  gluing
• The only unfoldable surface is developable
  surface
• General models need segmentation or cutting to be
  reasonably unfolded

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Background parameterization

• Preserve
• Angle
• Area
• Distortion can be measured using the two singular
  value Gand ?of Jacobian matrix
• Gand ? represent the largest and smallest length
  when mapping the unit length from texture domain
  to surface
• Distortion always exist except for developable
  surfaces

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Characteristic of paper

• Paper is developable surface
• Gaussian curvature equals zero
• Can be unfolded without any distortion

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Related work - papercraft

• Making Papercraft Toys from Meshes using
  Strip-based Approximate Unfolding. Siggraph 2004
• D-Charts Quasi-Developable Mesh Segmentation.
  Eurographics 2005
• Paper Craft Models from Meshes. Pacific
  graphics 2006

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Making Papercraft Toys from Meshes using
Strip-based Approximate Unfolding
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Making Papercraft Toys from Meshes using
Strip-based Approximate Unfolding

• Segment the model into several charts then cut
  the charts into triangle strips
• Not convenient for cutting and gluing

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D-Charts Quasi-Developable Mesh Segmentation
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Paper Craft Models from Meshes
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D-Charts Quasi-Developable Mesh Segmentation
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• Framework
• Region growing
• Use conic surface approximation of developable
  surface as error metric
• Optimize the conic surface at each iteration
• Conic surface is a subset of developable surface
• There exist an axis s.t. the angle between the
  axis and normal of every point on the surface is
  constant

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Problems of current method

• Only consider conic surface, not general
  developable surface
• Use single conic surface to approximate each
  chart, lose the potential of forming larger
  charts
• Not consider cutting explicitly, lose the
  potential of forming larger charts

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Related work cutting

• Spanning Tree Seams for Reducing
  Parameterization Distortion of Triangulated
  Surfaces. IEEE Proceedings of Shape Modeling
  International 2002

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Spanning Tree Seams for Reducing Parameterization
Distortion of Triangulated Surfaces
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Research direction

• Find more general error metric for developable
  surface
• Consider multiple developable surface
  approximation of original surface
• Consider cutting
• Smooth and short cut
• Feature preserving
• Developable NURB surface