Many geometry processing applications, such as morphing, shape blending, transfer of texture or material properties, and fitting template meshes to scan data, require a bijective mapping between two or more models. This mapping, or crossparameterization, typically needs to preserve the shape and features of the parameterized models, mapping legs to legs, ears to ears, and so on. Most of the applications also require the models to be represented by compatible meshes, i.e. meshes with identical connectivity, based on the cross-parameterization. In this paper we introduce novel methods for shape preserving cross-parameterization and compatible remeshing. Our crossparameterization method computes a low-distortion bijective mapping between models that satisfies user prescribed constraints. Using this mapping, the remeshing algorithm preserves the user-defined feature vertex correspondence and the shape correlation between the models. The remeshing algorithm generates output meshes with significantly fewer elements compared to previous techniques, while accurately approximating the input geometry. As demonstrated by the examples, the compatible meshes we construct are ideally suitable for morphing and other geometry processing applications.

Figure 1: Applications: (left) texture transfer and morphing; (right) three-sided blending. AbstractMany geometry processing applications, such as morphing, shape blending, transfer of texture or material properties, and fitting template meshes to scan data, require a bijective mapping between two or more models. This mapping, or crossparameterization, typically needs to preserve the shape and features of the parameterized models, mapping legs to legs, ears to ears, and so on. Most of the applications also require the models to be represented by compatible meshes, i.e. meshes with identical connectivity, based on the cross-parameterization. In this paper we introduce novel methods for shape preserving cross-parameterization and compatible remeshing. Our crossparameterization method computes a low-distortion bijective mapping between models that satisfies user prescribed constraints. Using this mapping, the remeshing algorithm preserves the user-defined feature vertex correspondence and the shape correlation between the models. The remeshing algorithm generates output meshes with significantly fewer elements compared to previous techniques, while accurately approximating the input geometry. As demonstrated by the examples, the compatible meshes we construct are ideally suitable for morphing and other geometry processing applications.

Quasi-developable mesh segmentation is required for many applications in graphics and CAD, including texture atlas generation and the design of patterns for model fabrication from sheets of material. In this work we introduce D-Charts, a simple and robust algorithm for mesh segmentation into (nearly) developable charts. As part of our method we introduce a new metric of developability for mesh surfaces. Thanks to this metric, using our segmentation for texture atlas generation, we can bound the distortion of the atlas directly during the segmentation stage. We demonstrate that by using this bound, we generate more isometric atlases for the same number of charts compared to existing state-of-the-art techniques. Using our segmentation algorithm we also develop a technique for automatic pattern design. To demonstrate the practicality of this technique, we use the patterns produced by our algorithm to make fabric and paper copies of popular computer graphics models.

Many model editing operations, such as morphing, blending, and shape deformation, require the ability to interactively transform the surface of a model in response to some control mechanism. For most computer graphics applications, it is important to preserve the local shape properties of input models during editing operations. Our work introduces the first, to our knowledge, mesh editing technique that explicitly preserves local shape properties. The method is based on a local shape representation, which we refer to as pyramid coordinates. The pyramid coordinates capture the local shape of the mesh around each vertex and help maintain this shape under various editing operations. They are based on a set of angles and lengths relating a vertex to its immediate neighbors. This representation is invariant under rigid transformations. Using pyramid coordinates, we introduce a new technique for mesh deformation and morphing based on a small number of user-specified control vertices. Our algorithm generate natural looking deformations and morphing sequences in seconds with minimal user interaction.

Figure 1: Resizing a clock model (267 connected components): Standard non-uniform scale distorts the shape of parts of the model, e.g. the dial (b). Our approach resizes the clock in a more natural manner protecting its shape (c). (d) and (e) show part of the protective grid before and after resizing. AbstractResizing of 3D models can be very useful when creating new models or placing models inside different scenes. However, uniform scaling is limited in its applicability while straightforward nonuniform scaling can destroy features and lead to serious visual artifacts. Our goal is to define a method that protects model features and structures during resizing. We observe that typically, during scaling some parts of the models are more vulnerable than others, undergoing undesirable deformation. We automatically detect vulnerable regions and carry this information to a protective grid defined around the object, defining a vulnerability map. The 3D model is then resized by a space-deformation technique which scales the grid non-homogeneously while respecting this map. Using space-deformation allows processing of common models of man-made objects that consist of multiple components and contain non-manifold structures. We show that our technique resizes models while suppressing undesirable distortion, creating models that preserve the structure and features of the original ones.