Ball-Pivoting Lifting (Point Cloud to Simplicial Complex)

[nemo1120]

The ball pivoting algorithm reconstructs surfaces from oriented point cloud data sets. The algorithm works by, at initialization, selecting three points at random to form a triangle (note, all three points must fall within a ball of radius r (specified by the user), while no other points fall within the same ball). Once this triangle has been formed, a ball of radius r is rolled along the edges of the triangle. If a point falls within the this ball during its rolling (and when no other points are within the ball), a new triangle is added where the new point is a vertex in the triangle. This process is continued until all reachable edges have been tried. A new seed triangle is picked and the process is restarted until all points in the point cloud have been reached. For a more in-depth look at the algorithm, see the following reference. The images below demonstrate an example lifting on a spherical point cloud (note, this reconstruction is walked through in the tutorial ball_pivoting jupyter notebook).

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[1] F. Bernardini, J. Mittleman, H. Rushmeier, C. Silva and G. Taubin, "The ball-pivoting algorithm for surface reconstruction," in IEEE Transactions on Visualization and Computer Graphics, vol. 5, no. 4, pp. 349-359, Oct.-Dec. 1999, doi: 10.1109/2945.817351.

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This pull request adds the Ball-Pivoting algorithm for point cloud to simplicial complex lifting.

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Codecov Report

Attention: Patch coverage is 84.21053% with 9 lines in your changes missing coverage. Please review.

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Files	Patch %	Lines
...ngs/pointcloud2simplicial/ball_pivoting_lifting.py	72.72%	9 Missing :warning:

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