Abstract Implicit representations of shapes are broadly used in computer graphics since they offer many valuable properties in design, modeling, and animation. However, their implicit and volumetric nature makes applying 2D textures fundamentally challenging. We propose a method to compute point‐wise and parallelizable semi‐global parameterizations of implicit surfaces for texturing, rendering, and modeling purposes. Our method not only defines local patches of parameterization, but also enables the merging of multiple adjacent patches into large and spatially coherent ones that conform to the geometry. Implemented in shaders into a sphere‐tracing pipeline, our method allows users to edit the uv‐fields with real‐time visualization. We demonstrate how to add rendering details (texture, normal, displacement, etc.) using our parameterization, as well extending modeling tools with implicit shell maps. Furthermore, the textured objects remain implicit and can still be used in a modeling pipeline.

Voxel based modeling is a very attractive way to represent complex multi-material objects. Beside artistic choices of pixel/voxel arts, representing objects as voxels allows efficient and dynamic interactions with the scene. For geometry processing purposes, many applications in material sciences, medical imaging or numerical simulation rely on a regular partitioning of the space with labeled voxels. In this article, we consider a variational approach to reconstruct interfaces in multi-labeled digital images. This approach efficiently produces piecewise smooth quadrangulated surfaces with some theoretical stability guarantee. Non-manifold parts at intersecting interfaces are handled naturally by our model. We illustrate the strength of our tool for digital surface regularization, as well as voxel art regularization by transferring colorimetric information to regularized quads and computing isotropic geodesic on digital surfaces.

Abstract The Mumford‐Shah functional approximates a function by a piecewise smooth function. Its versatility makes it ideal for tasks such as image segmentation or restoration, and it is now a widespread tool of image processing. Recent work has started to investigate its use for mesh segmentation and feature lines detection, but we take the stance that the power of this functional could reach far beyond these tasks and integrate the everyday mesh processing toolbox. In this paper, we discretize an Ambrosio‐Tortorelli approximation via a Discrete Exterior Calculus formulation. We show that, combined with a new shape optimization routine, several mesh processing problems can be readily tackled within the same framework. In particular, we illustrate applications in mesh denoising, normal map embossing, mesh inpainting and mesh segmentation.

Abstract We propose a novel method to regularize a normal vector field defined on a digital surface (boundary of a set of voxels). When the digital surface is a digitization of a piecewise smooth manifold, our method localizes sharp features (edges) while regularizing the input normal vector field at the same time. It relies on the optimisation of a variant of the Ambrosio‐Tortorelli functional, originally defined for denoising and contour extraction in image processing [ AT90 ]. We reformulate this functional to digital surface processing thanks to discrete calculus operators. Experiments show that the output normal field is very robust to digitization artifacts or noise, and also fairly independent of the sampling resolution. The method allows the user to choose independently the amount of smoothing and the length of the set of discontinuities. Sharp and vanishing features are correctly delineated even on extremely damaged data. Finally, our method can be used to enhance considerably the output of state‐of‐the‐art normal field estimators like Voronoi Covariance Measure [ MOG11 ] or Randomized Hough Transform [ BM12 ].