Details
| Translated title of the contribution | Kurven- und Flächen-Approximation von 3D-Punktwolken |
|---|---|
| Original language | English |
| Pages (from-to) | 315-327 |
| Number of pages | 13 |
| Journal | AVN Allgemeine Vermessungs-Nachrichten |
| Volume | 123 |
| Issue number | 11-12 |
| Publication status | Published - 2016 |
Abstract
In many geodetic applications and tasks it is necessary to describe a 3D-point cloud by continuous mathematical functions in order to utilise them for further processing steps, especially for deformation analysis. Depending on the complexity of the object, captured by the 3D-point cloud, and the desired quality of the approximation, different functions can be used. This paper describes the most important mathematical (free-form) surfaces from polynomial functions to Bezier and B-Spline functions to Non-uniform rational B-Splines (NURBS) in this context. Beside the mathematical basics of the functions, the approximation process for curves and surfaces and the crucial modification parameters, especially the model selection, are described.
Keywords
- B-spline, Bezier, Curve, NURBS, Polynomials, Surf
ASJC Scopus subject areas
- Engineering(all)
- Civil and Structural Engineering
- Social Sciences(all)
- Geography, Planning and Development
- Earth and Planetary Sciences(all)
- Earth and Planetary Sciences (miscellaneous)
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In: AVN Allgemeine Vermessungs-Nachrichten, Vol. 123, No. 11-12, 2016, p. 315-327.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Curve and surface approximation of 3D point clouds
AU - Bureick, Johannes
AU - Neuner, Hans
AU - Harmening, Corinna
AU - Neumann, Ingo
PY - 2016
Y1 - 2016
N2 - In many geodetic applications and tasks it is necessary to describe a 3D-point cloud by continuous mathematical functions in order to utilise them for further processing steps, especially for deformation analysis. Depending on the complexity of the object, captured by the 3D-point cloud, and the desired quality of the approximation, different functions can be used. This paper describes the most important mathematical (free-form) surfaces from polynomial functions to Bezier and B-Spline functions to Non-uniform rational B-Splines (NURBS) in this context. Beside the mathematical basics of the functions, the approximation process for curves and surfaces and the crucial modification parameters, especially the model selection, are described.
AB - In many geodetic applications and tasks it is necessary to describe a 3D-point cloud by continuous mathematical functions in order to utilise them for further processing steps, especially for deformation analysis. Depending on the complexity of the object, captured by the 3D-point cloud, and the desired quality of the approximation, different functions can be used. This paper describes the most important mathematical (free-form) surfaces from polynomial functions to Bezier and B-Spline functions to Non-uniform rational B-Splines (NURBS) in this context. Beside the mathematical basics of the functions, the approximation process for curves and surfaces and the crucial modification parameters, especially the model selection, are described.
KW - B-spline
KW - Bezier
KW - Curve
KW - NURBS
KW - Polynomials
KW - Surf
UR - http://www.scopus.com/inward/record.url?scp=85002823103&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:85002823103
VL - 123
SP - 315
EP - 327
JO - AVN Allgemeine Vermessungs-Nachrichten
JF - AVN Allgemeine Vermessungs-Nachrichten
SN - 0002-5968
IS - 11-12
ER -