Spherical parametrization and remeshing

original spherical parametrization octahedral parametrization geometry image (lit) remeshed geometry Figure 1: Demonstration of spherical parametrization and subsequent resampling into a geometry image. The traditional approach for parametrizing a surface involves cutting it into charts and mapping these piecewise onto a planar domain. We introduce a robust technique for directly parametrizing a genus-zero surface onto a spherical domain. A key ingredient for making such a parametrization practical is the minimization of a stretch-based measure, to reduce scaledistortion and thereby prevent undersampling. Our second contribution is a scheme for sampling the spherical domain using uniformly subdivided polyhedral domains, namely the tetrahedron, octahedron, and cube. We show that these particular semiregular samplings can be conveniently represented as completely regular 2D grids, i.e. geometry images. Moreover, these images have simple boundary extension rules that aid many processing operations. Applications include geometry remeshing, level-ofdetail, morphing, compression, and smooth surface subdivision

Real-time fur over arbitrary surfaces

We introduce a method for real-time rendering of fur on surfaces of arbitrary topology. As a pre-process, we simulate virtual hair with a particle system, and sample it into a volume texture. Next, we parameterize the texture over a surface of arbitrary topology using “lapped textures ” — an approach for applying a sample texture to a surface by repeatedly pasting patches of the texture until the surface is covered. The use of lapped textures permits specifying a global direction field for the fur over the surface. At runtime, the patches of volume textures are rendered as a series of concentric shells of semi-transparent medium. To improve the visual quality of the fur near silhouettes, we place “fins ” normal to the surface and render these using conventional 2D texture maps sampled from the volume texture in the direction of hair growth. The method generates convincing imagery of fur at interactive rates for models of moderate complexity. Furthermore, the scheme allows real-time modification of viewing and lighting conditions, as well as local control over hair color, length, and direction. Additional Keywords: hair rendering, lapped textures, volume textures. 1

Abstract. Consistent Spherical Parameterization

Many applications benefit from surface parameterization, including texture mapping, morphing, remeshing, compression, object recognition, and detail transfer, because processing is easier on the domain than on the original irregular mesh. We present a method for simultaneously parameterizing several genus-0 meshes possibly with boundaries onto a common spherical domain, while ensuring that corresponding user-highlighted features on each of the meshes map to the same domain locations. We obtain visually smooth parameterizations without any cuts, and the constraints enable us to directly associate semantically important features such as animal limbs or facial detail. Our method is robust and works well with either sparse or dense sets of constraints. Fig 1. Consistent Spherical Parameterization of a collection of heads

Abstract Robust Mesh Watermarking

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