Zelinka, SteveGarland, MichaelRoberto Scopigno and Denis Zorin2014-01-292014-01-2920043-905673-13-41727-8384http://dx.doi.org/10.2312/SGP/SGP04/209-218We present several powerful new techniques for similarity-based modelling of surfaces using geodesic fans, a new framework for local surface comparison. Similarity-based surface modelling provides intelligent surface manipulation by simultaneously applying a modification to all similar areas of the surface. We demonstrate similaritybased painting, deformation, and filtering of surfaces, and show how to vary our similarity measure to encompass geometry, textures, or other arbitrary signals. Geodesic fans are neighbourhoods uniformly sampled in the geodesic polar coordinates of a point on a surface. We show how geodesic fans offer fast approximate alignment and comparison of surface neighbourhoods using simple spoke reordering. As geodesic fans offer a a structurally equivalent definition of neighbourhoods everywhere on a surface, they are amenable to standard acceleration techniques and are well-suited to extending image domain methods for modelling by example to surfaces.Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Curve, surface, solid, and object representations I.4.7 [Image Processing and Computer Vision]: Size and shape