We present a method for constructing seamless parametrization for surfaces of any genus that can handle any feasible cone configuration with any type of cones. The mapping is guaranteed to be locally injective, which is due to careful construction of a simple domain boundary polygon. The polygon’s complexity depends on the cones in the field, and it is independent of mesh geometry. The result is a small polygon that can be optimized prior to the interior mapping, which contributes to the robustness of the pipeline. For a surface of genus >0, non-contractible loops play an important role, and their holonomies significantly affect mapping quality. We enable holonomy prescription, where local injectivity is guaranteed. Our prescription, however, is limited and cannot handle all feasible holonomies due to monotonicity constraints that keep our polygon simple. Yet this work is an important step toward fully solving the holonomy prescription problem.

Abstract We present a method for constructing seamless parametrization for genus‐0 surfaces, which can handle any feasible cone configuration, thus allowing users to arbitrarily design and tailor a mapping as desired. The method directly constructs a self‐overlapping metapolygon of the domain boundary of the mapped cut mesh, which relieves the need of using an auxiliary surface. This simplifies the pipeline and allows for a necessary optimization of the boundary polygon before mapping the interior. Moreover, it enables handling larger meshes with more cones than previous methods can handle. Our construction is purely combinatorial, and it guarantees that the mapping is locally injective – a prerequisite to today's advanced optimization methods. This is achieved via careful construction of a simple domain boundary polygon, where existence of such a polygon is proven for all cases. We offer a numerically robust algorithm to automate the construction, which involves a solution of two linear problems. We offer a full pipeline, suggesting elegant solutions to sub‐problems, and demonstrate robustness through extensive experiments.

We present a framework for global parametrization that utilizes the edge lengths (squared) of the mesh as variables. Given a mesh with arbitrary topology and prescribed cone singularities, we flatten the original metric of the surface under strict bounds on the metric distortion (various types of conformal and isometric measures are supported). Our key observation is that the space of bounded distortion metrics (given any particular bounds) is convex, and a broad range of useful and well-known distortion energies are convex as well. With the addition of nonlinear Gaussian curvature constraints, the parametrization problem is formulated as a constrained optimization problem, and a solution gives a locally injective map. Our method is easy to implement. Sequential convex programming (SCP) is utilized to solve this problem effectively. We demonstrate the flexibility of the method and its uncompromised robustness and compare it to state-of-the-art methods.

Computation of mappings is a central building block in many geometry processing and graphics applications. The pursuit to compute mappings that are injective and have a controllable amount of conformal and isometric distortion is a long endeavor which has received significant attention by the scientific community in recent years. The difficulty of the problem stems from the fact that the space of bounded distortion mappings is nonconvex. In this paper, we consider the special case of harmonic mappings which have been used extensively in many graphics applications. We show that, somewhat surprisingly, the space of locally injective planar harmonic mappings with bounded conformal and isometric distortion has a convex characterization. We describe several projection operators that, given an arbitrary input mapping, are guaranteed to output a bounded distortion locally injective harmonic mapping that is closest to the input mapping in some special sense. In contrast to alternative approaches, the optimization problems that correspond to our projection operators are shown to be always feasible for any choice of distortion bounds. We use the boundary element method (BEM) to discretize the space of planar harmonic mappings and demonstrate the effectiveness of our approach through the application of planar shape deformation.

In recent years, the As-Rigid-As-Possible (ARAP) shape deformation and shape interpolation techniques gained popularity, and the ARAP energy was successfully used in other applications as well. We improve the ARAP animation technique in two aspects. First, we introduce a new ARAP-type energy, named SR-ARAP, which has a consistent discretization for surfaces (triangle meshes). The quality of our new surface deformation scheme competes with the quality of the volumetric ARAP deformation (for tetrahedral meshes). Second, we propose a new ARAP shape interpolation method that is superior to prior art also based on the ARAP energy. This method is compatible with our new SR-ARAP energy, as well as with the ARAP volume energy.

We present a new framework for real-time shape deformation with local shape preservation and volume control. Given a 3D object, in any form, one would like to manipulate the object using convenient handles, so that the resulting shape is a natural variation of the given object. It is also important that the deformation is controlled, thereby enabling localized changes that do not influence nearby branches. For example, given a horse model, a movement of one of its hooves should not affect the other hooves. Another goal is the minimization of local shape distortion throughout the object. The first ingredient of our method is the use of interior radial basis functions (IRBF), where the functions are radial with respect to interior distances within the object. The second important ingredient is the reduction of local distortions by minimizing the distortion of a set of spheres placed within the object. Our method achieves the goals of convenient shape manipulation and local influence property, and improves the latest state-of-the-art cage-based methods by replacing the cage with the more flexible IRBF centers. The latter enables extra flexibility and fully automated construction, as well as simpler formulation. We also suggest the IRBF interpolation method that can extend any surface mapping to the whole subspace in a shape-aware manner.

Abstract We present ArtiSketch – a system which allows the conversion of a wealth of existing 2D content into 3D content by users who do not necessarily possess artistic skills. Using ArtiSketch, a novice user may describe a 3D model as a set of articulated 2D sketches of a shape from different viewpoints. ArtiSketch then automatically converts the sketches to an articulated 3D object. Using common interactive tools, the user provides an initial estimate of the 3D skeleton pose for each frame, which ArtiSketch refines to be consistent between frames. This skeleton may then be manipulated independently to generate novel poses of the 3D model.

We describe a snake-type method for shape registration in 2D and 3D, by fitting a given polygonal template to an acquired image or volume data. The snake aspires to fit itself to the data in a shape which is locally As-Similar-As-Possible (ASAP) to the template. Our ASAP regulating force is based on the Moving Least Squares (MLS) similarity deformation. Combining this force with the traditional internal and external forces associated with a snake leads to a powerful and robust registration algorithm, capable of extracting precise shape information from image data.