Nicolas Ray

Least squares conformal maps for automatic texture atlas generation

A Texture Atlas is an efficient color representation for 3D Paint Systems. The model to be textured is decomposed into charts homeomorphic to discs, each chart is parameterized, and the unfolded charts are packed in texture space. Existing texture atlas methods for triangulated surfaces suffer from several limitations, requiring them to generate a large number of small charts with simple borders. The discontinuities between the charts cause artifacts, and make it difficult to paint large areas with regular patterns.In this paper, our main contribution is a new quasi-conformal parameterization method, based on a least-squares approximation of the Cauchy-Riemann equations. The so-defined objective function minimizes angle deformations, and we prove the following properties: the minimum is unique, independent of a similarity in texture space, independent of the resolution of the mesh and cannot generate triangle flips. The function is numerically well behaved and can therefore be very efficiently minimized. Our approach is robust, and can parameterize large charts with complex borders.We also introduce segmentation methods to decompose the model into charts with natural shapes, and a new packing algorithm to gather them in texture space. We demonstrate our approach applied to paint both scanned and modeled data sets.

Generation of Radiosity Texture Atlas for Realistic Real-Time Rendering

Radiosity methods are a both physically correct and efficient way to compute the global illumination giving the visual atmosphere to a 3D scene. In this paper, we present a new approach to optimizing the visualization of meshed models illuminated using these methods. Our approach is based on a texture atlas, which makes it possible to store the global illumination in a set of textures, that can be mapped in real-time onto the model by the graphics hardware. Our contribution is a new robust atlas generation method well adapted to the visualization of illuminated complex meshed models, and based on a tight cooperation between the segmentation and the parameterization algorithms. In our segmentation method, the combinatorial information of the mesh is systematically preferred over the geometry whenever possible, which makes the algorithm both simpler and more robust. Large industrial models with complex topologies and poor mesh qualities can be efficiently processed. The paper concludes with some results, showing our method applied to architectural and car design industry models, and demonstrating that it both speeds up the visualization and is easy to integrate into existing advanced rendering software.

Practical 3D frame field generation

Given a tetrahedral mesh, the algorithm described in this article produces a smooth 3D frame field, i.e. a set of three orthogonal directions associated with each vertex of the input mesh. The field varies smoothly inside the volume, and matches the normals of the volume boundary. Such a 3D frame field is a key component for some hexahedral meshing algorithms, where it is used to steer the placement of the generated elements. We improve the state-of-the art in terms of quality, efficiency and reproducibility. Our main contribution is a non-trivial extension in 3D of the existing least-squares approach used for optimizing a 2D frame field. Our algorithm is inspired by the method proposed by Huang et al. [2011], improved with an initialization that directly enforces boundary conditions. Our initialization alone is a fast and easy way to generate frames fields that are suitable for remeshing applications. For better robustness and quality, the field can be further optimized using nonlinear optimization as in Li et al [2012]. We make the remark that sampling the field on vertices instead of tetrahedra significantly improves both performance and quality.