In this paper we present an object-space morphing technique that blends the interiors of given shapes rather than their boundaries. The resulting sequence of in-between shapes is least-distorting in the sense that the shapes are transformed as rigidly as possible, both globally and locally. Assuming that the vertex correspondence of the source and target shapes is given, we develop a closed-form equation to allocate vertices along their path from source to target locations as a function of time.

The source and target shapes are decomposed into isomorphic simplicial complexes. For each of the simplices we define an affine transformation which is factored into a rotation and a stretching transformation. These local transformations are interpolated over time and composed into a global coherent non-distorting transformation, which minimizes the overall local deformation.

* Joint work with Marc Alexa & Daniel
Cohen-Or.

We present a novel technique for texture mapping on arbitrary surfaces with minimal distortions, by preserving the local and global structure of the texture. The recent introduction of the fast marching method on triangulated surfaces made it possible to compute geodesic distances in O(n lg n) where n is the number of triangles that represent the surface. We use this method to design a surface flattening approach based on multi-dimensional scaling (MDS). MDS is a family of methods that map a set of points into a finite dimensional flat (Euclidean) domain, where the only given data is the corresponding distances between every pair of points. The MDS mapping yields minimal changes of the distances between the corresponding points. We then solve an `inverse' problem and map a flat texture patch onto the curved surface while preserving the structure of the texture.

* Joint work with Ron Kimmel & Nahum
Kiryati.

We describe a 3D scene streaming approach for remote walkthroughs. In a remote walkthrough, a user on a client machine interactively navigates through a scene that resides on a remote server. Our approach allows a user to walk through a remote 3D scene, without having to download the entire scene from the server. Our algorithm achieves this by selectively transmitting only small parts of the scene, and lower quality representations of objects, based on the user's viewing parameters and the available connection bandwidth. An online optimization algorithm selects which object representations to send, based on the integral of a benefit measure along the predicted path of movement. Rendering quality depends on the available bandwidth, but practical navigation of the scene is possible even when bandwidth is low.

* Joint work with Dani Lischinski.