We construct smooth parameterizations of irregular connectivity triangulations of arbitrary genus 2-manifolds. Our algorithm uses hierarchical simplification to efficiently induce a parameterization of the original mesh over a base domain consisting of a small number of triangles. This initial parameterization is further improved through a hierarchical smoothing procedure based on Loop subdivision applied in the parameter domain. Our method supports both fully automatic and user constrained operations. In the latter, we accommodate point and edge constraints to force the align- # wailee@cs.princeton.edu + wim@bell-labs.com # ps@cs.caltech.edu cowsar@bell-labs.com dpd@cs.princeton.edu ment of iso-parameter lines with desired features. We show how to use the parameterization for fast, hierarchical subdivision connectivity remeshing with guaranteed error bounds. The remeshing algorithm constructs an adaptively subdivided mesh directly without first resorting to uniform subdivision followed by subsequent sparsification. It thus avoids the exponential cost of the latter. Our parameterizations are also useful for texture mapping and morphing applications, among others.

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...

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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.

Surface reconstruction provides a powerful paradigm for modeling shapes from samples. For point cloud data with only geometric coordinates as input, Delaunay based surface reconstruction algorithms have been shown to be quite effective both in theory and practice. However, a major complaint against Delaunay based methods is that they are slow and cannot handle large data. We extend the COCONE algorithm to handle supersize data. This is the first reported Delaunay based surface reconstruction algorithm that can handle data containing more than a million sample points on a modest machine.

There is a growing interest for the problem of reconstructing the shape of an object from multiple range images. Several methods, based on heuristics, have been described in the literature. We propose the use of alpha-shapes, which allow us to give a formal characterization of the reconstruction problem and to prove that, when certain sampling requirements are satisfied, the reconstructed alpha-shape is homeomorphic to the original object and approximate it within a fixed error bound. In a companion paper, we describe practical methods to automatically select an optimal alpha value, to deal with less-than-ideal scans, and to fit smooth piecewise algebraic surface to the data points. 1 Introduction Cheaper, easier-to-use 3D digitizers are fostering a growing interest for the problem of shapereconstruction. Automatic methods for reconstructing an accurate geometric model of an object from a set of digital scans have applications in reverse engineering, shape analysis, virtual worlds aut...

Deformable models have raised much interest and found various applications in the fields of computer vision and medical imaging. They provide an extensible framework to reconstruct shapes. Deformable surfaces, in particular, are used to represent 3D objects. They have been used for pattern recognition [35,2], computer animation [100], geometric modelling [59], simulation [28], boundary tracking [11], image segmentation [69,67,91,5,45], etc. In this paper we propose a survey on deformable surfaces. Many surface representation have been proposed to meet different 3D reconstruction problem requirements. We classify the main representations proposed in the literature and we study the influence of the representation on the model evolution behavior, revealing some similarities between different approaches.

Aprocedure for reconstructing solid models of conventional engineering objects from a multiple-view, 3D point cloud is described. (Conventional means bounded by simple analytical surfaces, swept surfaces and blends.) Emphasis is put on producing accurate and topologically consistent boundary representation models, ready to be used in computer aided design and manufacture. The basic phases of our approach to reverse engineering are summarised, and related computational difficulties are analysed. Four key algorithmic components are presented in more detail: efficiently segmenting point data into regions; creating translational and rotational surfaces with smooth, constrained profiles; creating the topology of B-rep models; and finally adding blends. The application of these algorithms in an integrated system is illustrated by means of various examples, including a well-known reverse engineering benchmark. 1.

In this paper an algorithm is proposed that takes as input a generic set of unorganized points, sampled on a real object, and returns a closed interpolating surface. Specifically, this method generates a closed 2-manifold surface made of triangular faces, without limitations on the shape or genus of the original solid. The reconstruction method is based on generation of the Delaunay tetrahedralization of the point set, followed by a sculpturing process constrained to particular criteria. The main applications of this tool are in medical analysis and in reverse engineering areas. It is possible, for example, to reconstruct anatomical parts starting from surveys based on TACs or magnetic resonance.

We present an approach for the reconstruction and approximation of 3D CAD models from an unorganized collection of points. Applications include rapid reverse engineering of existing objects for use in a synthetic computer environment, including computer aided design and manufacturing. Our reconstruction approach is flexible enough to permit interpolation of both smooth surfaces and sharp features, while placing few restrictions on the geometry or topology of the object. Our algorithm is based on alpha-shapes to compute an initial triangle mesh approximating the object's surface. A mesh reduction technique is applied to the dense triangle mesh to build a simplified approximation, while retaining important topological and geometric characteristics of the model. The reduced mesh is interpolated with piecewise algebraic surface patches which approximate the original points. The process is fully automatic, and the reconstruction is guaranteed to be homeomorphic and error bounded with respec...