Interior Distance Using Barycentric Coordinates

dc.contributor.authorRustamov, R. M.en_US
dc.contributor.authorLipman, Y.en_US
dc.contributor.authorFunkhouser, T.en_US
dc.date.accessioned2015-02-23T15:43:25Z
dc.date.available2015-02-23T15:43:25Z
dc.date.issued2009en_US
dc.description.abstractThis paper introduces a framework for defining a shape-aware distance measure between any two points in the interior of a surface mesh. Our framework is based on embedding the surface mesh into a high-dimensional space in a way that best preserves boundary distances between vertices of the mesh, performing a mapping of the mesh volume into this high-dimensional space using barycentric coordinates, and defining the interior distance between any two points simply as their Euclidean distance in the embedding space. We investigate the theoretical properties of the interior distance in relation to properties of the chosen boundary distances and barycentric coordinates, and we investigate empirical properties of the interior distance using diffusion distance as the prescribed boundary distance and mean value coordinates. We prove theoretically that the interior distance is a metric, smooth, interpolating the boundary distances, and reproducing Euclidean distances, and we show empirically that it is insensitive to boundary noise and deformation and quick to compute. In case the barycentric coordinates are non-negative we also show a maximum principle exists. Finally, we use it to define a new geometric property, barycentroid of shape, and show that it captures the notion of semantic center of the shape.en_US
dc.description.number5en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume28en_US
dc.identifier.doi10.1111/j.1467-8659.2009.01505.xen_US
dc.identifier.issn1467-8659en_US
dc.identifier.pages1279-1288en_US
dc.identifier.urihttps://doi.org/10.1111/j.1467-8659.2009.01505.xen_US
dc.publisherThe Eurographics Association and Blackwell Publishing Ltden_US
dc.titleInterior Distance Using Barycentric Coordinatesen_US
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