Figure 1: Four different textures pasted on the bunny model. The last picture illustrates changing local orientation and scale on the body. AbstractWe present a method for creating texture over an arbitrary surface mesh using an example 2D texture. The approach is to identify interesting regions (texture patches) in the 2D example, and to repeatedly paste them onto the surface until it is completely covered. We call such a collection of overlapping patches a lapped texture. It is rendered using compositing operations, either into a traditional global texture map during a preprocess, or directly with the surface at runtime. The runtime compositing approach avoids resampling artifacts and drastically reduces texture memory requirements.Through a simple interface, the user specifies a tangential vector field over the surface, providing local control over the texture scale, and for anisotropic textures, the orientation. To paste a texture patch onto the surface, a surface patch is grown and parametrized over texture space. Specifically, we optimize the parametrization of each surface patch such that the tangential vector field aligns everywhere with the standard frame of the texture patch. We show that this optimization is solved efficiently as a sparse linear system.

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We consider the problem of creating a map between two arbitrary triangle meshes. Whereas previous approaches compose parametrizations over a simpler intermediate domain, we directly create and optimize a continuous map between the meshes. Map distortion is measured with a new symmetric metric, and is minimized during interleaved coarse-to-fine refinement of both meshes. By explicitly favoring low inter-surface distortion, we obtain maps that naturally align corresponding shape elements. Typically, the user need only specify a handful of feature correspondences for initial registration, and even these constraints can be removed during optimization. Our method robustly satisfies hard constraints if desired. Inter-surface mapping is shown using geometric and attribute morphs. Our general framework can also be applied to parametrize surfaces onto simplicial domains, such as coarse meshes (for semi-regular remeshing), and octahedron and toroidal domains (for geometry image remeshing). In these settings, we obtain better parametrizations than with previous specialized techniques, thanks to our fine-grain optimization.

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We describe a robust method for watermarking triangle meshes. Watermarking provides a mechanism for copyright protection of digital media by embedding information identifying the owner in the data. The bulk of the research on digital watermarks has focused on media such as images, video, audio, and text. Robust watermarks must be able to survive a variety of "attacks", including resizing, cropping, and filtering. For resilience to such attacks, recent watermarking schemes employ a "spread-spectrum" approach -they transform the document to the frequency domain and perturb the coefficients of the perceptually most significant basis functions. We extend this spread-spectrum approach to work for the robust watermarking of arbitrary triangle meshes.Generalizing spread spectrum techniques to surfaces presents two major challenges. First, arbitrary surfaces lack a natural parametrization for frequency-based decomposition. Our solution is to construct a set of scalar basis function over the mesh vertices using multiresolution analysis. The watermark perturbs vertices along the direction of the surface normal, weighted by the basis functions. The second challenge is that simplification and other attacks may modify the connectivity of the mesh. We use an optimization technique to resample an attacked mesh using the original mesh connectivity. Results show that our watermarks are resistant to common mesh operations such as translation, rotation, scaling, cropping, smoothing, simplification, and resampling, as well as malicious attacks such as the insertion of noise, modification of low-order bits, or even insertion of other watermarks.