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Design Unstructured set of rich objects plus Rich expression rule Sparse representation.

KNOWMESH - MESHLESS GEOMETRY WITH KNOWLEDGE REPRESENTATION Prof W Randolph Franklin, Prof Barbara Cutler Rensselaer Polytechnic Institute, Troy NY. Design Unstructured set of rich objects plus Rich expression rule Sparse representation. No explicit global topology.

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Design Unstructured set of rich objects plus Rich expression rule Sparse representation.

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  1. KNOWMESH - MESHLESS GEOMETRY WITH KNOWLEDGE REPRESENTATIONProf W Randolph Franklin, Prof Barbara CutlerRensselaer Polytechnic Institute, Troy NY Design Unstructured set of rich objects plus Rich expression rule • Sparse representation. • No explicit global topology. • All input is legal; will create a representation of something. • Expression rule built on knowledge representation. • Mechanization of descriptive geometry – what an intelligent observer would say to an intelligent listener. Technical rationale • Compact, to fit in PDAs to to transmit quickly. • Facilitates parallel processing. • Emphasizes the features that are important, rather the minimizing geometric error (unless that is important). • Enables recognition and important operations on the data. Contact info: Franklin: wrf@ecse.rpi.edu, http://wrfranklin.org/ (518) 276-6077 Cutler: cutler@cs.rpi.edu, http://www.cs.rpi.edu/~cutler (518) 276-3274

  2. Application to Architecture • Represent a real campus of buildings. • Give an abbreviated description as an architect would. • Make a rough sketch of an architectural design using small scale physical building elements (top row). • Camera photographs the geometry. Computer vision techniques detect and identify components (2nd row). • Ground plane divided into an arrangement of line segments and cells (3rd row). Relative enclosure analyzed to determine an appropriate interpretation of this design. • Full 3D model constructed by automatically closing gaps between walls and clipping away unnecessary portions of walls.

  3. Application to Cartography • Features more important than precise elevations. • Facilitate operations like mobility. • Must understand real terrain: often discontinuous, sharp local maxima, lateral symmetry breaking, features do not superimpose linearly. • Not a differentiable linear system – nonlinearity rules. • Legal terrain via scooping • Start from a given point, and proceed downhill from there along some trajectory until the edge of the dataset. • Creates discontinuities, never creates interior local minimum. • Progressive transmission follows naturally. • Bathymetry • Extreme unevenness of data. • Conventional data-fitting techniques fail. • Rendering with ODETLAP generates only the features that are justified. Bathymetry tracklines • Structure that people can recognize even though it is hard to formalize: peninsulas or fjords? Bad surface from kriging Good surface from ODETLAP

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