Calculating Center of Mass in an Unbounded 2D Environment

@article{Bai2008CalculatingCO,
  title={Calculating Center of Mass in an Unbounded 2D Environment},
  author={Linge Bai and David E. Breen},
  journal={Journal of Graphics Tools},
  year={2008},
  volume={13},
  pages={53 - 60}
}
We study the behavior of simple, 2D, self-organizing primitives that interact and move in an unbounded environment to create aggregated shapes. Each primitive is represented by a disk and a unit point mass. In order to compare the aggregated shape produced by the primitives to other shapes, the centers of mass of the two shapes must be aligned. We present an algorithm for calculating the center of mass (COM) for a set of point masses that are distributed in an unbounded 2D environment. The… 
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References

SHOWING 1-6 OF 6 REFERENCES
Self-organizing primitives for automated shape composition
TLDR
The cell interactions of MPs and the GP-based method used to define the chemical field functions needed to produce user- specified shapes from simple aggregating primitives are described.
Automated shape composition based on cell biology and distributed genetic programming
TLDR
The cell interactions of MPs are described and a distributed genetic programming method to discover the chemical fields needed to produce macroscopic shapes from simple aggregating primitives is described.
Spherical averages and applications to spherical splines and interpolation
TLDR
A method for computing weighted averages on spheres based on least squares minimization that respects spherical distance is introduced, and existence and uniqueness properties of the weighted averages are proved, and fast iterative algorithms with linear and quadratic convergence rates are given.
Genetic programming - on the programming of computers by means of natural selection
  • J. Koza
  • Computer Science
    Complex adaptive systems
  • 1993
TLDR
This book discusses the evolution of architecture, primitive functions, terminals, sufficiency, and closure, and the role of representation and the lens effect in genetic programming.
and D
  • E. Breen. “Self-Organizing Primitives for Automated Shape Composition.” In Proc. IEEE International Conference on Shape Modeling and Applications, pp. 147–154. Los Alamitos, CA: IEEE Press
  • 2008
Fillmore
  • “Spherical Averages and Applications to Spherical Splines and Interpolation.” In ACM Transactions on Graphics (TOG), 20(2), pp. 95-126,
  • 2001