Monte Carlo Geometry Modeling for Particle Transport Using Conformal Geometric Algebra

  • E. Ulises Moya-SánchezEmail author
  • A. Moisés Maciel-Hernández
  • Adrian S. Niebla
  • José Ramos-Méndez
  • Oscar Carbajal-Espinosa
Part of the following topical collections:
  1. Proceedings ICCA 11, Ghent, 2017


The Monte Carlo (MC) simulations are considered the gold-standard method for calculating the transport and interaction of radiation with the matter. A fundamental component of any MC simulation is the geometrical modeling. Current implementations of the geometrical modeling are based only on the Euclidean representations. However, Euclidean representations may not be the best option for speed up the geometric debugging-modeling computations of radiation transport, due to the number of operations involved in the estimation of position and direction of particles within each geometry shape. In this work, it is proposed for the first time, the use of Conformal Geometric Algebra (CGA), for geometric modeling in MC simulation for radiation transport. In this context, we present some elemental CGA equations for the microscopic modeling of positions and rotations of a radiation particle and the macroscopic modeling of geometrical shapes. It is shown that it is possible to take advantage of the expression power of CGA to create and debug geometry modeling with a triboelectric X-ray application. Additionally, some advantages of the CGA for the microscopic geometric computations are explored.


Monte Carlo geometry Ray tracing Conformal Geometry Algebra 



This research has been supported by the CONACYT SNI Grant.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Universidad Autónoma de Guadalajara and Barcelona Supercomputing CenterZapopanMexico
  2. 2.Nexus IIBarcelonaSpain
  3. 3.Universidad Autónoma de GuadalajaraZapopanMexico
  4. 4.University of California San FranciscoSan FranciscoUSA
  5. 5.ITESM Campus GuadalajaraZapopanMexico

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