Abstraction of Man-Made Shapes Ravish Mehra 1,2, Qingnan Zhou 1, Jeremy Long 4, Alla Sheffer 1, Amy Gooch 4, Niloy J. Mitra 2,3 1 Univ. of British Columbia 2 IIT Delhi 3 KAUST 4 Univ. of Victoria Abstraction of Man-Made Shapes

Human Perception

Abstraction of Man-Made Shapes Observation © Succession Picasso

Abstraction of Man-Made Shapes Observation o Man-Made objects dominated by flat/smooth faces. o Sharp creases define the shape. Cole et al. 2008

Abstraction of Man-Made Shapes Abstract Representation o Abstraction algorithm - curves as building blocks o Extract sparse network of curves + normals o Abstract shape - union of smooth patches

Abstraction of Man-Made Shapes o Curve based NPR Suggestive contours [DeCarlo et al. 2003] Apparent ridges [Judd et al. 2007] o Curve based surface modeling Wires [Singh et al. 1998] Fiber Mesh [Nealen et al. 2007] iWires [Gal et al. 2009] o Vector representation Diffusion Curves [Orzan et al. 2008] Related Works

Abstraction of Man-Made Shapes Abstraction Pipeline 1. Original model 2. Envelope3. Curve Network 4. Reconstruction result ReconstructionVectorization Envelope generation

Abstraction of Man-Made Shapes Challenge o Input contains multiple self-intersecting components. o Can even be a polygon soup.

Abstraction of Man-Made Shapes Envelope Generation o Envelope: A tight closed manifold approximation of the original surface.

Abstraction of Man-Made Shapes Envelope Generation: Initialization o Initial envelope: A manifold surface loosely follow inputs geometry.

Abstraction of Man-Made Shapes Envelope Generation: Iterative Fitting Preserves local details Pulls each vertex towards its original position Pulls each vertex towards its mapped position

Abstraction of Man-Made Shapes Envelope Generation

Abstraction of Man-Made Shapes Vectorization o Purpose: extract a vector representation o Encodes shape-defining features; concise & enables reconstruction Envelope Vector Representation

Abstraction of Man-Made Shapes Vectorization as Mesh Segmentation o Man-made shapes - union of smooth patches. o Vectorization as mesh segmentation problem. Segmentation – collection of charts Each chart should be smooth o Vector representation = boundary of segmentation + associated normals

Abstraction of Man-Made Shapes Initial Segmentation o Variational Shape Approximation [Cohen- Steiner et al. 2004]. Speed and simplicity Satisfies smoothness criteria o Topological Simplification Merging small charts Straightening boundaries [ Julius et al ]

Abstraction of Man-Made Shapes Iterative Improvement o Optimization for each chart Smooth surface smoothly varying normals Approximate the original shape Smooth boundary helps subsequent regularization phase

Abstraction of Man-Made Shapes Iterative Improvement o Normal solve trade-off between smoothness and original normals o Per-triangle solve vertex positions satisfying desired normals stay close to original positions o Global assembly reconcile different per-triangle vertex positions

Abstraction of Man-Made Shapes Iterative Improvement

Abstraction of Man-Made Shapes Regularization and Simplification o Regularity local : linear, circular, planar global : parallel, orthogonal, symmetric o Hierarchical simplification higher levels of abstraction simplify network regularize again

Abstraction of Man-Made Shapes Curve Extraction Vector representation of 3D Shapes

Abstraction of Man-Made Shapes Reconstruction o Reconstruct the abstract model Embed each boundary loop into a plane [Kruskal and Wish 1978] Triangulate the planar loops [Shewchuk 1996] Deform the planar patches using curves position and normal as constraints [Popa et al. 2006]

Abstraction of Man-Made Shapes Results

Abstraction of Man-Made Shapes Eiffel tower 15.6K triangles 2417 components 85 curves140 curves

Abstraction of Man-Made Shapes Empire state 16K triangles 17 components 38 curves152 curves

Abstraction of Man-Made Shapes Arc de Triomphe 13K triangles 8 components 139 curves193 curves

Abstraction of Man-Made Shapes Dome of the Rock 3.8K triangles 2 components 26 curves145 curves

Abstraction of Man-Made Shapes Limitations and Future Work o Thin long features that affect topology o Not well-known objects

Abstraction of Man-Made Shapes Summary o Algorithm for generating abstractions of 3D man- made models. o Simple yet robust mechanism for approximating polygon soup by a manifold surface. o Novel vector-based representation of 3D geometry.

Abstraction of Man-Made Shapes Video

Abstraction of Man-Made Shapes Acknowledgements Sponsored by Adobe Inc. MITACS NCE Microsoft Outstanding Young Faculty Fellowship NSERC Discover Program Thanks Benjamin Cecchetto Derek Bradley Karan Singh Tiberiu Popa Vladislav Kraevoy Xi Chen Anonymous reviewers

Abstraction of Man-Made Shapes

Iterative Improvement o Normal solve Normal should change smoothly within each chart Normal should remain close to its original direction

Abstraction of Man-Made Shapes Iterative Improvement o Per-triangle solve o Global Assembly (Similar to [Sumner and Popović 2004]) Each vertex should remain close its original position The triangle should satisfy the smoothed normal Boundary triangles only: Boundary edge should be close to the locally smoothed boundary edge.

Abstraction of Man-Made Shapes Extract network geometry o Global assembly (Similar to [Sumner and Popović 2004]) Each triangle should rotate as little as possible Each vertex remains close to its original position

Curve network Purpose of curve network Concise representation ( no redundancy ) Enable reconstruction Two types of curves Regular curve : Positions and normals along each side of curve Connectivity-only curve : removes ambiguity

Abstraction of Man-Made Shapes