## The Ball-Pivoting Algorithm for Surface Reconstruction (1999)

Venue: | IEEE Transactions on Visualization and Computer Graphics |

Citations: | 223 - 14 self |

### BibTeX

@ARTICLE{Bernardini99theball-pivoting,

author = {Fausto Bernardini and Joshua Mittleman and Holly Rushmeier and Claudio Silva and Gabriel Taubin},

title = {The Ball-Pivoting Algorithm for Surface Reconstruction},

journal = {IEEE Transactions on Visualization and Computer Graphics},

year = {1999},

volume = {5},

pages = {349--359}

}

### Years of Citing Articles

### OpenURL

### Abstract

The Ball-Pivoting Algorithm (BPA) computes a triangle mesh interpolating a given point cloud. Typically the points are surface samples acquired with multiple range scans of an object. The principle of the BPA is very simple: Three points form a triangle if a ball of a user-specified radius touches them without containing any other point. Starting with a seed triangle, the ball pivots around an edge (i.e. it revolves around the edge while keeping in contact with the edge's endpoints) until it touches another point, forming another triangle. The process continues until all reachable edges have been tried, and then starts from another seed triangle, until all points have been considered. We applied the BPA to datasets of millions of points representing actual scans of complex 3D objects. The relatively small amount of memory required by the BPA, its time efficiency, and the quality of the results obtained compare favorably with existing techniques.

### Citations

2321 | Marching cubes: A high resolution 3d surface construction algorithm - Lorensen, Cline - 1987 |

855 | A volumetric method for building complex models from range images - Curless, Levoy - 1996 |

580 | A Signal Processing Approach to Fair Surface Design - Taubin - 1995 |

493 |
Zippered polygon meshes from range images
- Turk, Levoy
- 1994
(Show Context)
Citation Context ...ages of points from the overlapping scans. Estimated points in each region are then retriangulated, and the resulting meshes are stitched into a single mesh. Turk and Levoy developed a similar method =-=[9]-=-, which first stitches (or zippers) the disjoint meshes and then computes estimated surface points. We observe that in both classes of methods, the method of estimating surface points need not be so c... |

491 | Weighted alpha shapes
- Edelsbrunner
- 1992
(Show Context)
Citation Context ...ve halfplane of oriented line Ð �. form new triangles. The set of triangles formed while the ball “walks” on the surface constitutes the interpolating mesh. The BPA is closely related to alpha-=-=shapes [18], [2]. In -=-fact every triangle � computed by the �-ball walk obviously has an empty smallest open ball �� whose radius is less than � (see [2], page 50). Thus, the BPA computes a subset of the 2-faces ... |

379 | KAMVYSSELIS M.: A new Voronoi-based surface reconstruction algorithm - AMENTA, BERN |

366 | Surface reconstruction by Voronoi filtering
- AMENTA, BERN
- 1998
(Show Context)
Citation Context ...heoretical guarantees for the quality of the resulting surface, e.g. that the topology is correct, and that the surface converges to the true surface as the sampling density increases (see e.g. [16], =-=[17]-=-). However, computing the required 3D Delaunay triangulation can be prohibitively expensive in terms of time and memory required, and can lead to numerical instability when dealing with datasets of mi... |

238 | S.: Using particles to sample and control implicit surfaces - WITKIN, HECKBERT - 1994 |

178 | Geometric structures for threedimensional shape representation - Boissonnat |

167 | Automatic reconstruction of surfaces and scalar fields from 3d scans - Bajaj, Bernardini, et al. - 1995 |

102 | A general surface approach to the integration of a set of range views - Soucy, Laurendeau - 1995 |

91 | Interactive out-of-core isosurface extraction
- Chiang, Silva, et al.
- 1998
(Show Context)
Citation Context ... to the Buddha dataset. We note that such decompositions can be performed efficiently for arbitrarily large range scans (which do not necessarily need to fit in memory) by the techniques described in =-=[20].-=- The Pietà data has undergone extensive preprocessing during and after scanning and registration that is out of the scope of this paper. The data is large enough that it cannot be processed in-core, ... |

55 | Registration and Integration of Multiple Object Views for 3D Model Construction - Dorai, W, et al. - 1998 |

50 | Sampling and reconstructing manifolds using alpha-shapes
- Bernardini, Bajaj
- 1997
(Show Context)
Citation Context ...vide theoretical guarantees for the quality of the resulting surface, e.g. that the topology is correct, and that the surface converges to the true surface as the sampling density increases (see e.g. =-=[16]-=-, [17]). However, computing the required 3D Delaunay triangulation can be prohibitively expensive in terms of time and memory required, and can lead to numerical instability when dealing with datasets... |

45 | Robust meshes from multiple range maps - Pulli, Duchamp, et al. - 1997 |

43 | Marching triangles: Range image fusion for complex object modeling - Hilton, Stoddart, et al. - 1996 |

43 | Isosurface extraction using particle systems
- Crossno, Angel
- 1997
(Show Context)
Citation Context ...work. It would be interesting to evaluate whether BPA can be used to triangulate surfaces sampled with particle systems. This possibility was left as an open problem in [22], and further developed in =-=[23]-=- in the context of isosurface generation. By using weighted points, we might be able to generate triangulations of adaptive samplings. The sampling density could be changed depending on local surface ... |

41 | Interpolation and approximation of surfaces from three-dimensional scattered data points
- Mencl, Müller
- 1998
(Show Context)
Citation Context ...GROUND Recent years have seen a proliferation of scanning equipment and algorithms for synthesizing models from scanned data. We refer the reader to two recent reviews of research in the field [4], 1s=-=[5]-=-. In this section we focus on the role interpolating meshing schemes can play in scanning objects, and why they have not been used in practical scanning systems. A. Interpolating Meshes in Scanning Sy... |

36 | Automatic reconstruction of 3D CAD models from digital scans - Bernardini, Bajaj, et al. - 1999 |

35 | Computing consistent normals and colors from photometric data 3-D Digital Imaging and Modeling - Rushmeier, Bernardini - 1999 |

16 | A graph-based approach to surface reconstruction. Computer Graphics Forum - Mencl - 1995 |

7 |
The Florentine Pietà: Can Visualization Solve the 450-Year-Old Mystery
- Abouaf
- 1999
(Show Context)
Citation Context ...oved robust enough to handle the noise present in real scanned 3D data. It was tested on several large scanned datasets, and in particular was used to create models of Michelangelo’s Florentine Piet=-=à [3] f-=-rom hundreds of scans acquired with a structured light sensor (Visual Interface’s Virtuoso ShapeCamera). The rest of the paper is structured as follows: In section II we define the problem and discu... |

3 | ªZippered Polygon Meshes from Range Images,º - Turk, Levoy - 1994 |

2 | cke, ªThree-Dimensional Alpha Shapes,º - Edelsbrunner, MuÈ - 1994 |

2 | ªInteractive Out-of-Core Isosurface Extraction,º - Chiang, Silva, et al. - 1998 |

1 | ªRobust Meshes from Multiple Range [2 - Pulli, Duchamp, et al. - 1997 |

1 | ªThe Florentine PietaÁ: Can Visualization Solve the 450-year-old Mystery?,º - Abouaf - 1999 |

1 | Updated online version available at www.qucis.queensu.ca/cccg97 - Geometry - 1997 |

1 | ªSurface Reconstruction by Voronoi Filtering,º - Amenta, Bern - 1998 |

1 | ªWeighted Alpha Shapes,º - Edelsbrunner - 1992 |

1 | ªIsosurface Extraction Using Particle Systems,º - Crossno, Angel - 1997 |

1 | received his masters degree from Rutgers University. He has been working in graphics at IBM T.J. Watson Research Center since 1990, specializing in simplification, levelof-detail control, and other algorithms applied to rendering very complex models - Mittleman |

1 | Rushmeier received the BS, MS, and PhD degrees in mechanical engineering from Cornell University in - Holly - 1977 |

1 | received the PhD degree in computer science from the State University of New York at Stony Brook in 1996. He is a senior member of technical staff in the Information Visualization Research Department at AT&T Research. Before joining AT&T, he was a researc - Silva |

1 |
A volumetric method for building complex
- Curless, Levoy
(Show Context)
Citation Context ...ets; both assume negligible registration error and compute estimates to correct for line-of-sight error. The first of these classes is volumetric methods, such as that introduced by Curless and Levoy =-=[6]-=-. In these methods, individual aligned meshes are used to compute a signed-distance function on a volume grid encompassing the object. Estimated surface points are computed as the points on the grid w... |

1 |
models from range images
- Lorensen, Cline
- 1987
(Show Context)
Citation Context ...ed surface points are computed as the points on the grid where the distance funtion is zero. The structure of the volume then facilitates the construction of a mesh using the marching cubes algorithm =-=[7]-=-. The second class of methods are mesh stitching methods, such as the technique of Soucy and Laurendeau [8]. Disjoint height-field meshes are stitched into a single surface. Disjoint regions are defin... |