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@inproceedings{Oztireli10Spectral,

author = {\"{O}ztireli, A. Cengiz and Alexa, Marc and Gross, Markus},

title = {Spectral sampling of manifolds},

booktitle = {ACM SIGGRAPH Asia 2010 papers},

series = {SIGGRAPH ASIA '10},

year = {2010},

isbn = {978-1-4503-0439-9},

location = {Seoul, South Korea},

pages = {168:1--168:8},

articleno = {168},

numpages = {8},

url = {http://doi.acm.org/10.1145/1866158.1866190},

doi = {http://doi.acm.org/10.1145/1866158.1866190},

acmid = {1866190},

publisher = {ACM},

address = {New York, NY, USA},

keywords = {Laplace-Beltrami, Poisson disk sampling, heat kernel, sampling},

}

author = {\"{O}ztireli, A. Cengiz and Alexa, Marc and Gross, Markus},

title = {Spectral sampling of manifolds},

booktitle = {ACM SIGGRAPH Asia 2010 papers},

series = {SIGGRAPH ASIA '10},

year = {2010},

isbn = {978-1-4503-0439-9},

location = {Seoul, South Korea},

pages = {168:1--168:8},

articleno = {168},

numpages = {8},

url = {http://doi.acm.org/10.1145/1866158.1866190},

doi = {http://doi.acm.org/10.1145/1866158.1866190},

acmid = {1866190},

publisher = {ACM},

address = {New York, NY, USA},

keywords = {Laplace-Beltrami, Poisson disk sampling, heat kernel, sampling},

}

Sampling manifolds defined by points sets is an essential step in the geometry processing pipeline. We propose a new method for sampling point based manifolds. Our method is memory and time efficient, results in high quality samplings and reconstructions, and simple to implement. We assume that we are given a point set and a kernel definition that is used to reconstruct the smooth manifold. The result of our algorithms is an isotropic and adaptive sampling implied by the input point set and the kernel. The distributions of the points have blue noise characteristics. Since we treat manifolds in general, our methods are applicable to Euclidean or high dimensional cases as well. Due to our out-of-core simplification algorithm, we can handle very large datasets. The running time of this algorithm is linear in the number of input points. After simplifying the point cloud data, our resampling algorithm can be used to further optimize the positions of the remaining points.

We can get isotropic samplings of a surface using an isotropic kernel definition such as a radially decaying Gaussian.

By adapting the kernel to the features on the surface, adaptive sampling can also be achieved.

If we use our methods to sample a planar domain, we can analyze the distributions and see that they have blue noise properties.

Reconstructions obtained by using the sampled point set is very accurate.

Our samplings can be used to remesh surfaces with high quality triangles.

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