Weighted Averages on Surfaces

Daniele Panozzo, Ilya Baran, Olga Diamanti, Olga Sorkine-Hornung

Weight averages on surfaces!

Interactive control for various geometry processing and modeling applications made possible with weighted averages on surfaces. Clockwise: texture transfer, splines on surfaces, semiregular remeshing and Laplacian smoothing.


We consider the problem of generalizing affine combinations in Euclidean spaces to triangle meshes: computing weighted averages of points on surfaces. We address both the forward problem, namely computing an average of given anchor points on the mesh with given weights, and the inverse problem, which is computing the weights given anchor points and a target point. Solving the forward problem on a mesh enables applications such as splines on surfaces, Laplacian smoothing and remeshing. Combining the forward and inverse problems allows us to define a correspondence mapping between two different meshes based on provided corresponding point pairs, enabling texture transfer, compatible remeshing, morphing and more. Our algorithm solves a single instance of a forward or an inverse problem in a few microseconds. We demonstrate that anchor points in the above applications can be added/removed and moved around on the meshes at interactive framerates, giving the user an immediate result as feedback.


accompanying video


We thank the anonymous reviewers for their insightful comments and Emily Whiting for narrating the accompanying video. The Boy model in Figure 11 of the paper was kindly provided by Maurizio Nitti. This work was supported in part by the ERC grant iModel (StG-2012-306877), by an SNF award 200021_137879 and a gift from Adobe Research.