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Computing and rendering point set surfaces
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). The computation of points on the surface is local, which results in an out-of-core technique that can handle any point set. We show that the approximation error is bounded and present tools to increase or decrease the density of the points, thus allowing an adjustment of the spacing among the points to control the error. 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.
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Cited by
Towards 3D Point cloud based object maps for household environments
Rusu, R. B., Marton, Z. C., Blodow, N., Dolha, M., & Beetz, M. (2008) · Robotics and Autonomous Systems · doi:10.1016/j.robot.2008.08.005 · Cited by 1,084
LiDAR Point Clouds to 3-D Urban Models$:$ A Review
Wang, R., Peethambaran, J., & Chen, D. (2018) · IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing · doi:10.1109/jstars.2017.2781132 · Cited by 319
Wen, C., Sun, X., Li, J., Wang, C., Guo, Y., & Habib, A. (2019) · ISPRS Journal of Photogrammetry and Remote Sensing · doi:10.1016/j.isprsjprs.2018.10.007 · Cited by 158
P2P-NET: bidirectional point displacement net for shape transform
Yin, K., Huang, H., Cohen-Or, D., & Zhang, H. (2018) · ACM Transactions on Graphics · doi:10.1145/3197517.3201288 · Cited by 102
Self-citationRobust principal axes determination for point-based shapes using least median of squares
Liu, Y.-S., & Ramani, K. (2009) · Computer-Aided Design · doi:10.1016/j.cad.2008.10.012 · Cited by 46
Metadata
- Authors
- Alexa, M., Behr, J., Cohen-Or, D., Fleishman, S., Levin, D., & Silva, C. T.
- Venue
- IEEE Transactions on Visualization and Computer Graphics
- Published
- 2003-01
- Volume
- 9
- Issue
- 1
- Pages
- 3-15
- ISSN
- 1077-2626 (ISSN-L)
- OpenAlex
- W2137531922
- Cited by
- 1,089
- References
- 0
- FWCI
- 63.14
- Type
- journal article
- Language
- en
- Open access
- closed
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- Alexa, M., Behr, J., Cohen-Or, D., Fleishman, S., Levin, D., & Silva, C. T. (2003). Computing and rendering point set surfaces. IEEE Transactions on Visualization and Computer Graphics. https://doi.org/10.1109/tvcg.2003.1175093
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
