Surface geometry is often modeled with irregular triangle meshes. The process of remeshing refers to approximating such geometry using a mesh with (semi)-regular connectivity, which has advantages for many graphics applications. However, current techniques for remeshing arbitrary surfaces create only semi-regular meshes. The original mesh is typically decomposed into a set of disk-like charts, onto which the geometry is parametrized and sampled. In this paper, we propose to remesh an arbitrary surface onto a completely regular structure we call a geometry image. It captures geometry as a simple 2D array of quantized points. Surface signals like normals and colors are stored in similar 2D arrays using the same implicit surface parametrization — texture coordinates are absent. To create a geometry image, we cut an arbitrary mesh along a network of edge paths, and parametrize the resulting single chart onto a square. Geometry images can be encoded using traditional image compression algorithms, such as wavelet-based coders.

We develop a novel method for fitting high-resolution template meshes to detailed human body range scans with sparse 3D markers. We formulate an optimization problem in which the degrees of freedom are an affine transformation at each template vertex. The objective function is a weighted combination of three measures: proximity of transformed vertices to the range data, similarity between neighboring transformations, and proximity of sparse markers at corresponding locations on the template and target surface. We solve for the transformations with a non-linear optimizer, run at two resolutions to speed convergence. We demonstrate reconstruction and consistent parameterization of 250 human body models. With this parameterized set, we explore a variety of applications for human body modeling, including: morphing, texture transfer, statistical analysis of shape, model fitting from sparse markers, feature analysis to modify multiple correlated parameters (such as the weight and height of an individual), and transfer of surface detail and animation controls from a template to fitted models.

This paper presents an example-based method for calculating skeleton-driven body deformations. Our example data consists of range scans of a human body in a variety of poses. Using markers captured during range scanning, we construct a kinematic skeleton and identify the pose of each scan. We then construct a mutually consistent parameterization of all the scans using a posable subdivision surface template. The detail deformations are represented as displacements from this surface, and holes are filled smoothly within the displacement maps. Finally, we combine the range scans using k-nearest neighbor interpolation in pose space. We demonstrate results for a human upper body with controllable pose, kinematics, and underlying surface shape.

Normal meshes are new fundamental surface descriptions inspired by differential geometry. A normal mesh is a multiresolution mesh where each level can be written as a normal offset from a coarser version. Hence the mesh can be stored with a single float per vertex. We present an algorithm to approximate any surface arbitrarily closely with a normal semi-regular mesh. Normal meshes can be useful in numerous applications such as compression, filtering, rendering, texturing, and modeling.

We introduce multi-chart geometry images, a new representation for arbitrary surfaces. It is created by resampling a surface onto a regular 2D grid. Whereas the original scheme of Gu et al. maps the entire surface onto a single square, we use an atlas construction to map the surface piecewise onto charts of arbitrary shape. We demonstrate that this added flexibility reduces parametrization distortion and thus provides greater geometric fidelity, particularly for shapes with long extremities, high genus, or disconnected components. Traditional atlas constructions suffer from discontinuous reconstruction across chart boundaries, which in our context create unacceptable surface cracks. Our solution is a novel zippering algorithm that creates a watertight surface. In addition, we present a new atlas chartification scheme based on clustering optimization.

Meshes obtained from laser scanner data often contain topological noise due to inaccuracies in the scanning and merging process. This topological noise complicates subsequent operations such as remeshing, parameterization and smoothing. We introduce an approach that removes unnecessary nontrivial topology from meshes. Using a local wave front traversal, we discover the local topologies of the mesh and identify features such as small tunnels. We then identify non-separating cuts along which we cut and seal the mesh, reducing the genus and thus the topological complexity of the mesh.

Good parameterizations are of central importance in many digital geometry processing tasks. Typically the behavior of such processing algorithms is related to the smoothness of the parameterization and how much distortion it contains, i.e., how rapidly the derivatives of the parameterization change. Since a parameterization maps a bounded region of the plane to the surface, a parameterization for a surface which is not homeomorphic to a disc must be made up of multiple pieces. We present a novel parameterization algorithm for arbitrary topology surface meshes which computes a globally smooth parameterization with low distortion. We optimize the patch layout subject to criteria such as shape quality and parametric distortion, which are used to steer a mesh simplification approach for base complex construction. Global smoothness is achieved through simultaneous relaxation over all patches, with suitable transition functions between patches incorporated into the relaxation procedure. We demonstrate the quality of our parameterizations through numerical evaluation of distortion measures; the rate distortion behavior of semi-regular remeshes produced with these parameterizations; and a comparison with globally smooth subdivision methods. The numerical algorithms required to compute the parameterizations are robust and run on the order of minutes even for large meshes.

dynamics by driving the scene with parameterized interactions representative of runtime usage. (b) Model reduction on observed dynamic deformations yields a low-rank approximation to the system’s parameterized impulse response functions. (c) Deformed state geometries are then sampled and used to precompute and coparameterize a radiance transfer model for deformable objects. (d) The final simulation responds plausibly to interactions similar to those precomputed, includes complex collision and global illumination effects, and runs in real time. We present an approach for precomputing data-driven models of interactive physically based deformable scenes. The method permits real-time hardware synthesis of nonlinear deformation dynamics, including self-contact and global illumination effects, and supports real-time user interaction. We use data-driven tabulation of the system’s deterministic state space dynamics, and model reduction to build efficient low-rank parameterizations of the deformed shapes. To support runtime interaction, we also tabulate impulse response functions for a palette of external excitations. Although our approach simulates particular systems under very particular interaction conditions, it has several advantages. First, parameterizing all possible scene deformations enables us to precompute novel reduced coparameterizations of global scene illumination for lowfrequency lighting conditions. Second, because the deformation dynamics are precomputed and parameterized as a whole, collisions are resolved within the scene during precomputation so that runtime self-collision handling is implicit. Optionally, the data-driven models can be synthesized on programmable graphics hardware, leaving only the low-dimensional state space dynamics and appearance data models to be computed by the main CPU.

Cutting and pasting to combine different elements into a common structure are widely used operations that have been successfully adapted to many media types. Surface design could also benefit from the availability of a general, robust, and efficient cut-andpaste tool, especially during the initial stages of design when a large space of alternatives needs to be explored. Techniques to support cut-and-paste operations for surfaces have been proposed in the past, but have been of limited usefulness due to constraints on the type of shapes supported and the lack of real-time interaction. In this paper, we describe a set of algorithms based on multiresolution subdivision surfaces that perform at interactive rates and enable intuitive cut-and-paste operations.

We present the “Geometry Video,” a new data structure to encode animated meshes. Being able to encode animated meshes in a generic source-independent format allows people to share experiences. Changing the viewpoint allows more interaction than the fixed view supported by 2D video. Geometry videos are based on the “Geometry Image” mesh representation introduced by Gu et al. 4. Our novel data structure provides a way to treat an animated mesh as a video sequence (i.e., 3D image) and is well suited for network streaming. This representation also offers the possibility of applying and adapting existing mature video processing and compression techniques (such as MPEG encoding) to animated meshes. This paper describes an algorithm to generate geometry videos from animated meshes. The main insight of this paper, is that Geometry Videos re-sample and re-organize the geometry information, in such a way, that it becomes very compressible. They provide a unified and intuitive method for level-of-detail control, both in terms of mesh resolution (by scaling the two spatial dimensions) and of frame rate (by scaling the temporal dimension). Geometry Videos have a very uniform and regular structure. Their resource and computational requirements can be calculated exactly, hence making them also suitable for applications requiring level of service guarantees.