### Abstract

We advocate the use of point sets to represent shapes. We provide a definition of a smooth manifold surface from a set of points close to the original surface. The definition is based on local maps from differential geometry, which are approximated by the method of moving least squares (MLS). We present tools to increase or decrease the density of the points, thus, allowing an adjustment of the spacing among the points to control the fidelity of the representation. To display the point set surface, we introduce a novel point rendering technique. The idea is to evaluate the local maps according to the image resolution. This results in high quality shading effects and smooth silhouettes at interactive frame rates.

Original language | English (US) |
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Title of host publication | Proceedings of the IEEE Visualization Conference |

Editors | T. Ertl, K. Joy, A. Varshney |

Pages | 21-28 |

Number of pages | 8 |

State | Published - 2001 |

Event | Visualization 2001 - San Diego, CA, United States Duration: Oct 21 2001 → Oct 26 2001 |

### Other

Other | Visualization 2001 |
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Country | United States |

City | San Diego, CA |

Period | 10/21/01 → 10/26/01 |

### Fingerprint

### Keywords

- 3D acquisition
- Moving least squares
- Point sample rendering
- Surface representation and reconstruction

### ASJC Scopus subject areas

- Computer Science(all)
- Engineering(all)

### Cite this

*Proceedings of the IEEE Visualization Conference*(pp. 21-28)

**Point set surfaces.** / Alexa, M.; Behr, J.; Cohen-Or, D.; Fleishman, S.; Levin, D.; Silva, C. T.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the IEEE Visualization Conference.*pp. 21-28, Visualization 2001, San Diego, CA, United States, 10/21/01.

}

TY - GEN

T1 - Point set surfaces

AU - Alexa, M.

AU - Behr, J.

AU - Cohen-Or, D.

AU - Fleishman, S.

AU - Levin, D.

AU - Silva, C. T.

PY - 2001

Y1 - 2001

N2 - We advocate the use of point sets to represent shapes. We provide a definition of a smooth manifold surface from a set of points close to the original surface. The definition is based on local maps from differential geometry, which are approximated by the method of moving least squares (MLS). We present tools to increase or decrease the density of the points, thus, allowing an adjustment of the spacing among the points to control the fidelity of the representation. To display the point set surface, we introduce a novel point rendering technique. The idea is to evaluate the local maps according to the image resolution. This results in high quality shading effects and smooth silhouettes at interactive frame rates.

AB - We advocate the use of point sets to represent shapes. We provide a definition of a smooth manifold surface from a set of points close to the original surface. The definition is based on local maps from differential geometry, which are approximated by the method of moving least squares (MLS). We present tools to increase or decrease the density of the points, thus, allowing an adjustment of the spacing among the points to control the fidelity of the representation. To display the point set surface, we introduce a novel point rendering technique. The idea is to evaluate the local maps according to the image resolution. This results in high quality shading effects and smooth silhouettes at interactive frame rates.

KW - 3D acquisition

KW - Moving least squares

KW - Point sample rendering

KW - Surface representation and reconstruction

UR - http://www.scopus.com/inward/record.url?scp=0035175291&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035175291&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0035175291

SP - 21

EP - 28

BT - Proceedings of the IEEE Visualization Conference

A2 - Ertl, T.

A2 - Joy, K.

A2 - Varshney, A.

ER -