In this paper we describe a new tool for interactive free-form fair surface design. By generalizing classical discrete Fourier analysis to two-dimensional discrete surface signals -- functions defined on polyhedral surfaces of arbitrary topology --, we reduce the problem of surface smoothing, or fairing, to low-pass filtering. We describe a very simple surface signal low-pass filter algorithm that applies to surfaces of arbitrary topology. As opposed to other existing optimization-based fairing methods, which are computationally more expensive, this is a linear time and space complexity algorithm. With this algorithm, fairing very large surfaces, such as those obtained from volumetric medical data, becomes affordable. By combining this algorithm with surface subdivision methods we obtain a very effective fair surface design technique. We then extend the analysis, and modify the algorithm accordingly, to accommodate different types of constraints. Some constraints can be imposed without any modification of the algorithm, while others require the solution of a small associated linear system of equations. In particular, vertex location constraints, vertex normal constraints, and surface normal discontinuities across curves embedded in the surface, can be imposed with this technique.

We present a sketching interface for quickly and easily designing freeform models such as stuffed animals and other rotund objects. The user draws several 2D freeform strokes interactively on the screen and the system automatically constructs plausible 3D polygonal surfaces. Our system supports several modeling operations, including the operation to construct a 3D polygonal surface from a 2D silhouette drawn by the user: it inflates the region surrounded by the silhouette making wide areas fat, and narrow areas thin. Teddy, our prototype system, is implemented as a Java ™ program, and the mesh construction is done in real-time on a standard PC. Our informal user study showed that a first-time user typically masters the operations within 10 minutes, and can construct interesting 3D models within minutes.

A method based on graph theory is investigated for creating global parametrizations for surface triangulations for the purpose of smooth surface fitting. The parametrizations, which are planar triangulations, are the solutions of linear systems based on convex combinations.

We generalize basic signal processing tools such as downsampling, upsampling, and filters to irregular connectivity triangle meshes. This is accomplished through the design of a non-uniform relaxation procedure whose weights depend on the geometry and we show its superiority over existing schemes whose weights depend only on connectivity. This is combined with known mesh simplification methods to build subdivision and pyramid algorithms. We demonstrate the power of these algorithms through a number of application examples including smoothing, enhancement, editing, and texture mapping.

Recent progress in acquiring shape from range data permits the acquisition of seamless million-polygon meshes from physical models. In this paper, we present an algorithm and system for converting dense irregular polygon meshes of arbitrary topology into tensor product B-spline surface patches with accompanying displacement maps. This choice of representation yields a coarse but efficient model suitable for animation and a fine but more expensive model suitable for rendering. The first step in our process consists of interactively painting patch boundaries over a rendering of the mesh. In many applications, interactive placement of patch boundaries is considered part of the creative process and is not amenable to automation. The next step is gridded resampling of eachboundedsection of the mesh. Our resampling algorithm lays a grid of springs acrossthe polygonmesh, then iterates between relaxing this grid and subdividing it. This grid provides a parameterization for the mesh section, w...

Surface editing operations commonly require geometric details of the surface to be preserved as much as possible. We argue that geometric detail is an intrinsic property of a surface and that, consequently, surface editing is best performed by operating over an intrinsic surface representation. We provide such a representation of a surface, based on the Laplacian of the mesh, by encoding each vertex relative to its neighborhood. The Laplacian of the mesh is enhanced to be invariant to locally linearized rigid transformations and scaling. Based on this Laplacian representation, we develop useful editing operations: interactive free-form deformation in a region of interest based on the transformation of a handle, transfer and mixing of geometric details between two surfaces, and transplanting of a partial surface mesh onto another surface. The main computation involved in all operations is the solution of a sparse linear system, which can be done at interactive rates. We demonstrate the effectiveness of our approach in several examples, showing that the editing operations change the shape while respecting the structural geometric detail.

Figure 1: Objects created with our system. (a) boolean operations with scanned geometry, (b) an Octopus modeled by deforming and extruding a sphere, (c) a design study for a Siggraph coffee mug created by boolean operations, free-form deformation and displacement mapping. We present a versatile and complete free-form shape modeling framework for point-sampled geometry. By combining unstructured point clouds with the implicit surface definition of the moving least squares approximation, we obtain a hybrid geometry representation that allows us to exploit the advantages of implicit and parametric surface models. Based on this representation we introduce a shape modeling system that enables the designer to perform large constrained deformations as well as boolean operations on arbitrarily shaped objects. Due to minimum consistency requirements, point-sampled surfaces can easily be re-structured on the fly to support extreme geometric deformations during interactive editing. In addition, we show that strict topology control is possible and sharp features can be generated and preserved on point-sampled objects. We demonstrate the effectiveness of our system on a large set of input models, including noisy range scans, irregular point clouds, and sparsely as well as densely sampled models.

Advances in computer speed, memory capacity, and hardware graphics acceleration have made the interactive manipulation and visualization of complex, detailed (and therefore large) three-dimensional models feasible. These models are either painstakingly designed through an elaborate CAD process or reverse engineered from sculpted prototypes using modern scanning technologies and integration methods. The availability of detailed data describing the shape of an object offers the computer vision practitioner new ways to recognize and localize free-form objects. This survey reviews recent literature on both the 3D model building process and techniques used to match and identify free-form objects from imagery. c ○ 2001 Academic Press 1.

In this paper, we propose a general tridimensional reconstruction algorithm of range and volumetric images, based on deformable simplex meshes. Simplex meshes are topologically dual of triangulations and have the advantage of permitting smooth deformations in a simple and e cient manner. Our reconstruction algorithm can handle surfaces without any restriction on their shape or topology. The di erent tasks performed during the reconstruction include the segmentation of given objects in the scene, the extrapolation of missing data, and the control of smoothness, density, and geometric quality of the reconstructed meshes. The reconstruction takes place in two stages. First, the initialization stage creates a simplex mesh in the vicinity of the data model either manually or using an automatic procedure. Then, after a few iterations, the mesh topology can be modi ed by creating holes or by increasing its genus. Finally, aniterativere nement algorithm decreases the distance of the mesh from the data while preserving high geometric and topological quality. Several reconstruction examples are provided with quantitative and qualitative results.

This paper addresses the problem of integrating multiple registered 2.5D range images into a single 3D surface model which has topology and geometry consistent with the measurements. Reconstruction of a model of the correct surface topology is the primary goal. Extraction of the correct surface topology is recognised as a fundamental step in building 3D models. Model optimization can then be performed to fit the data to the desired accuracy with an efficient representation. A novel integration algorithm is presented that is based on local reconstruction of surface topology using operations in 3D space. A new continuous implicit surface function is proposed which merges the connectivity information inherent in the individual sampled range images. This enables the construction of a single triangulated model using a standard method. The algorithm is guaranteed to reconstruct the correct topology of surface features larger than the range image sampling resolution. Reconstruction of triangu...