Vladislav Kraevoy

Cross-parameterization and compatible remeshing of 3D models

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 cross-parameterization, 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 cross-parameterization 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.

D-Charts: Quasi-Developable Mesh Segmentation

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.

Pyramid coordinates for morphing and deformation

Many model editing operations, such as morphing, blending, and shape deformation requires 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. We introduce the 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 technique for mesh deformation and morphing based on a small number of user-specified control vertices. Our algorithm generates natural looking deformations and morphing sequences in seconds with minimal user interaction.

Non-homogeneous resizing of complex models

Resizing 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 non-uniform 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.

Template-based mesh completion

Meshes generated by range scanners and other acquisition tools are often incomplete and typically contain multiple connected components with irregular boundaries and complex holes. This paper introduces a robust algorithm for completion of such meshes using a mapping between the incomplete mesh and a template model. The mapping is computed using a novel framework for bijective parameterization of meshes with gaps and holes. We employ this mapping to correctly glue together the components of the input mesh and to close the holes. The template is used to fill in the topological and geometric information missing in the input. The completed models are guaranteed to have the same topology as the template. Furthermore, if no appropriate template exists or if only topologically correct completion is required a standard canonical shape can be used as a template. As part of our completion method we propose a boundary-mapping technique useful for mesh editing operations such as merging, blending, and detail transfer. We demonstrate that by using this technique we can automatically perform complex editing operations that previously required a large amount of user interaction.

Modeling from contour drawings

Occlusion contours are a natural feature to draw when tracing an object in an image or when drawing an object. We investigate the development of 3D models from multi-stroke contour drawings with the help of a 3D template model that serves as a shape prior. The template is aligned and then deformed by our method to match the drawn contours. At the heart of this process is the need to provide good correspondences between points on the contours and vertices on the model, which we pose as an optimisation problem using a hidden Markov model. An alternating correspond-and-deform process then progressively deforms the 3D template to match the image contours. We demonstrate the method on a wide range of examples.

Wrinkling Captured Garments Using Space‐Time Data‐Driven Deformation

The presence of characteristic fine folds is important for modeling realistic looking virtual garments. While recent garment capture techniques are quite successful at capturing the low‐frequency garment shape and motion over time, they often fail to capture the numerous high‐frequency folds, reducing the realism of the reconstructed space‐time models. In our work we propose a method for reintroducing fine folds into the captured models using data‐driven dynamic wrinkling. We first estimate the shape and position of folds based on the original video footage used for capture and then wrinkle the surface based on those estimates using space‐time deformation. Both steps utilize the unique geometric characteristics of garments in general, and garment folds specifically, to facilitate the modeling of believable folds. We demonstrate the effectiveness of our wrinkling method on a variety of garments that have been captured using several recent techniques.

Mean-Value Geometry Encoding

Geometry editing operations commonly use mesh encodings which capture the shape properties of the models. Given modified positions for a set of anchor vertices, the encoding is used to compute the positions for the rest of the mesh vertices, preserving the model shape as much as possible. In this paper, we introduce a new shape preserving and rotation invariant mesh encoding. We use this encoding for a variety of mesh editing applications: deformation, morphing, blending and motion reconstruction from Mocap data. The editing algorithms based on our encoding and decoding mechanism generate natural looking models that preserve the shape properties of the input.

Model repair and editing tools

With the declining production cost and improvement of scanning technology, three-dimensional model acquisition systems are rapidly becoming more affordable. At the same time, personal computers with graphics hardware capable of displaying complex 3D models have become inexpensive enough to be available to a large population. As a result, there is, potentially, an opportunity to consider new virtual reality uses from areas as diverse as cultural heritage exploration and retail sales applications that will allow people to view associated large classes of realistic 3D objects on home computers and media devices. Although there are many physical techniques for acquiring 3D data, including laser scanners, CT or MRI scans, the basic pipeline of operations (Figure 1.1) lacks a sufficient set of tools to take the acquired data and produce a usable 3D model. This dissertation proposes a set of efficient and robust 3D data reconstruction and editing tools for such a pipeline. We look at the fundamental problems of range scan data completion, modeling, and parameterization. We propose a new cross-parameterization method for efficient calculation of a low-distortion bijective mapping between models. Recent research in digital geometry processing suggests multiple new applications for such a mapping, including pair-wise model editing [11] transferring texture and surface properties (BRDFs, normal maps, etc) [61], and fitting template meshes to multiple data sets [7, 55]. We also extend our cross-parameterization technique to support models with gaps and holes. This allows us to develop a new and robust method for template-based range scan data completion. One of the most significant obstacles in computer graphics is providing easy-to-use tools for creating and editing detailed 3D models. To this end, we present a new set of tools with which non-expert user can create detailed geometric models quickly and easily. In particular, we propose a new modeling system for creating new, original models by mixing and matching parts of pre-existing models. In this way, we eliminate the need for a user to perform complex geometric operations, and thereby reduce the modeling process to that of part selection. This dissertation also proposes a new technique for image-based modeling that allows a user to easily transform a sketch or picture into a 3D model using a 3D template model. The 3D template provides the geometric detail that cannot be inferred from an image alone. This allows the user to create detailed geometric models from pictures alone. We also introduce a real-time editing algorithm that allows the creation of new models through the deformation of existing ones. Our proposed editing algorithm has applications in such common geometric operations as mesh deformation, morphing, and blending. Thus, we propose contributions to the model repair and editing pipeline that simplifies the task of creating and repairing detailed 3D models.

Real toys from virtual models

Motivated by the papercraft toys developed in [Mitani and Suzuki 2004], we created an algorithm suitable for use with fabric. In contrast to paper, fabric, for the most part, can be slightly stretched, allowing a less restrictive approach when defining the sewing patterns. As part of our method, we introduce a new metric of developability for mesh surfaces and show how to use this metric to segment surfaces into (nearly) developable patches. A surface patch is developable if it may be isometrically mapped (i.e., unfolded) onto the plane. These patches play a key role in our method since we want to minimize the distortion created when unfolding them into planar patterns which are then sewn together to form the 3D model. As a compact developable segmentation does not typically exist, we allow patches to be nearly developable based on user prescribed tolerances.