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110
Dual Contouring of Hermite Data
, 2002
"... This paper describes a new method for contouring a signed grid whose edges are tagged by Hermite data (exact intersection points and normals). This method avoids the need to explicitly identify and process "features" as required in previous Hermite contouring methods. We extend this contou ..."
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Cited by 261 (17 self)
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This paper describes a new method for contouring a signed grid whose edges are tagged by Hermite data (exact intersection points and normals). This method avoids the need to explicitly identify and process "features" as required in previous Hermite contouring methods. We extend this contouring method to the case of multisigned functions and demonstrate how to model textured contours using multisigned functions. Using a new, numerically stable representation for quadratic error functions, we develop an octreebased method for simplifying these contours and their textured regions. We next extend our contouring method to these simplified octrees. This new method imposes no constraints on the octree (such as being a restricted octree) and requires no "crack patching". We conclude with a simple test for preserving the topology of both the contour and its textured regions during simplification.
Feature Sensitive Surface Extraction from Volume Data
"... The representation of geometric objects based on volumetric data structures has advantages in many geometry processing applications that require, e.g., fast surface interrogation or boolean operations such as intersection and union. However, surface based algorithms like shape optimization (fairing) ..."
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Cited by 154 (11 self)
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The representation of geometric objects based on volumetric data structures has advantages in many geometry processing applications that require, e.g., fast surface interrogation or boolean operations such as intersection and union. However, surface based algorithms like shape optimization (fairing) or freeform modeling often need a topological manifold representation where neighborhood information within the surface is explicitly available. Consequently, it is necessary to find effective conversion algorithms to generate explicit surface descriptions for the geometry which is implicitly defined by a volumetric data set. Since volume data is usually sampled on a regular grid with a given step width, we often observe severe alias artifacts at sharp features on the extracted surfaces. In this paper we present a new technique for surface extraction that performs feature sensitive sampling and thus reduces these alias effects while keeping the simple algorithmic structure of the standard Marching Cubes algorithm. We demonstrate the effectiveness of the new technique with a number of application examples ranging from CSG modeling and simulation to surface reconstruction and remeshing of polygonal models. 1
A topology preserving level set method for geometric deformable models
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2003
"... Active contour and surface models, also known as deformable models, are powerful image segmentation techniques. Geometric deformable models implemented using level set methods have advantages over parametric models due to their intrinsic behavior, parameterization independence, and ease of implement ..."
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Cited by 120 (7 self)
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Active contour and surface models, also known as deformable models, are powerful image segmentation techniques. Geometric deformable models implemented using level set methods have advantages over parametric models due to their intrinsic behavior, parameterization independence, and ease of implementation. However, a long claimed advantage of geometric deformable models—the ability to automatically handle topology changes—turns out to be a liability in applications where the object to be segmented has a known topology that must be preserved. In this paper, we present a new class of geometric deformable models designed using a novel topologypreserving level set method, which achieves topology preservation by applying the simple point concept from digital topology. These new models maintain the other advantages of standard geometric deformable models including subpixel accuracy and production of nonintersecting curves or surfaces. Moreover, since the topologypreserving constraint is enforced efficiently through local computations, the resulting algorithm incurs only nominal computational overhead over standard geometric deformable models. Several experiments on simulated and real data are provided to demonstrate the performance of this new deformable model algorithm.
Topological Noise Removal
"... 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 to ..."
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Cited by 113 (5 self)
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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 nonseparating cuts along which we cut and seal the mesh, reducing the genus and thus the topological complexity of the mesh.
SemiRegular Mesh Extraction from Volumes
, 2000
"... We present a novel method to extract isosurfaces from distance volumes. It generates high quality semiregular multiresolution meshes of arbitrary topology. Our technique proceeds in two stages. First, a very coarse mesh with guaranteed topology is extracted. Subsequently an iterative multiscale f ..."
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Cited by 105 (13 self)
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We present a novel method to extract isosurfaces from distance volumes. It generates high quality semiregular multiresolution meshes of arbitrary topology. Our technique proceeds in two stages. First, a very coarse mesh with guaranteed topology is extracted. Subsequently an iterative multiscale forcebased solver refines the initial mesh into a semiregular mesh with geometrically adaptive sampling rate and good aspect ratio triangles. The coarse mesh extraction is performed using a new approach we call surface wavefront propagation. A set of discrete isodistance ribbons are rapidly built and connected while respecting the topology of the isosurface implied by the data. Subsequent multiscale refinement is driven by a simple forcebased solver designed to combine good isosurface fit and high quality sampling through reparameterization. In contrast to the Marching Cubes technique our output meshes adapt gracefully to the isosurface geometry, have a natural multiresolution structure and good aspect ratio triangles, as demonstrated with a number of examples.
Skin: A Constructive Approach to Modeling Freeform Shapes
 Proceedings of SIGGRAPH 99
, 1999
"... We present a new particlebased surface representation with which a user can interactively sculpt freeform surfaces. The particles maintain mesh connectivity and operate under rules that lead them to form triangulations with properties that make them suitable for use in subdivision. A user interact ..."
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Cited by 68 (6 self)
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We present a new particlebased surface representation with which a user can interactively sculpt freeform surfaces. The particles maintain mesh connectivity and operate under rules that lead them to form triangulations with properties that make them suitable for use in subdivision. A user interactively guides the particles, which we call skin, to grow over a given collection of polyhedral elements (or skeletons), yielding a smooth surface (through subdivision) that approximates the underlying skeletal shapes. Skin resembles blobby modeling in the constructive approach to modeling it supports, but allows a richer vocabulary of skeleton shapes, supports sharp creases where desired, and provides a convenient mechanism for adding multiresolution surface detail. CR Categories and Subject Descriptors: I.3.5 [Computer Graphics ]: Computational Geometry and Object Modeling I.3.6 [Computer Graphics]: Methodology and Techniques Additional Key Words: Freeform modeling, meshes, subdivision, m...
Variational Implicit Surfaces
, 1999
"... We introduce a new method of creating smooth implicit surfaces of arbitrary manifold topology. These surfaces are described by specifying locations in 3D through which the surface should pass, and also identifying locations that are interior or exterior to the surface. A 3D implicit function is crea ..."
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Cited by 62 (2 self)
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We introduce a new method of creating smooth implicit surfaces of arbitrary manifold topology. These surfaces are described by specifying locations in 3D through which the surface should pass, and also identifying locations that are interior or exterior to the surface. A 3D implicit function is created from these constraints using a variational scattered data interpolation approach. We call the isosurface of this function a variational implicit surface. Like other implicit surface descriptions, these surfaces can be used for CSG and interference detection, may be interactively manipulated, are readily approximated by polygonal tilings, and are easy to ray trace. A key strength is that variational implicit surfaces allow the direct specification of both the location of points on the surface and surface normals. These are two important manipulation techniques that are difficult to achieve using other implicit surface representations such as sums of spherical or ellipsoidal Gaussian functions ("blobbies"). We show that these properties make variational implicit surfaces particularly attractive for interactive sculpting using the particle sampling technique introduced by Witkin and Heckbert in [30]. Our formulation also yields a simple method for converting a polygonal model to a smooth implicit model.
Provably Good Surface Sampling and Approximation
, 2003
"... We present an algorithm for meshing surfaces that is a simple adaptation of a greedy "farthest point" technique proposed by Chew. Given a surface S, it progressively adds points on S and updates the 3dimensional Delaunay triangulation of the points. The method is very simple and works in ..."
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Cited by 44 (1 self)
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We present an algorithm for meshing surfaces that is a simple adaptation of a greedy "farthest point" technique proposed by Chew. Given a surface S, it progressively adds points on S and updates the 3dimensional Delaunay triangulation of the points. The method is very simple and works in 3dspace without requiring to parameterize the surface. Taking advantage of recent results on the restricted Delaunay triangulation, we prove that the algorithm can generate good samples on S as well as triangulated surfaces that approximate S. More precisely, we show that the restricted Delaunay triangulation Del # S of the points has the same topology type as S, that the Hausdorff distance between Del # S and S can be made arbitrarily small, and that we can bound the aspect ratio of the facets of Del # S . The algorithm has been implemented and we report on experimental results that provide evidence that it is very effective in practice. We present results on implicit surfaces, on CSG models and on polyhedra. Although most of our theoretical results are given for smooth closed surfaces, the method is quite robust in handling smooth surfaces with boundaries, and even nonsmooth surfaces.
Adaptive implicit surface polygonization using marching triangles
 COMPUTER GRAPHICS FORUM
, 2001
"... This paper presents several improvements to the marching triangles algorithm for general implicit surfaces. The original method generates equilateral triangles of constant size almost everywhere on the surface. We present several modifications to adapt the size of the triangles to the curvature of t ..."
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Cited by 41 (6 self)
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This paper presents several improvements to the marching triangles algorithm for general implicit surfaces. The original method generates equilateral triangles of constant size almost everywhere on the surface. We present several modifications to adapt the size of the triangles to the curvature of the surface. As cracks may arise in the resulting polygonization, we propose a specific crackclosing method invoked at the end of the mesh growing step. Eventually, we show that the marching triangles can be used as an incremental meshing technique in an interactive modeling environment. In contrast to existing incremental techniques based on spatial sudvision, no extra datastructure is needed to incrementally edit skeletal implicit surfaces, which saves both memory and computation time.
Sampling and meshing a surface with guaranteed topology and geometry
 Proc. 20th
, 2004
"... This paper presents an algorithm for sampling and triangulating a smooth surface Σ ⊂ R 3 where the triangulation is homeomorphic to Σ. The only assumption we make is that the input surface representation is amenable to certain types of computations, namely computations of the intersection points of ..."
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Cited by 38 (6 self)
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This paper presents an algorithm for sampling and triangulating a smooth surface Σ ⊂ R 3 where the triangulation is homeomorphic to Σ. The only assumption we make is that the input surface representation is amenable to certain types of computations, namely computations of the intersection points of a line with the surface, computations of the critical points of some height functions defined on the surface and its restriction to a plane, and computations of some silhouette points. The algorithm ensures bounded aspect ratio, size optimality, and smoothness of the output triangulation. Unlike previous algorithms, this algorithm does not need to compute the local feature size for generating the sample points which was a major bottleneck. Experiments show the usefulness of the algorithm in remeshing and meshing CAD surfaces that are piecewise smooth. 1