CPT - Closest Point Transform: This package provides an algorithm for computing the closest point transform in 1-D, 2-D, and 3-D. This is used to implement the Ghost fluid method in the Virtual Test Facility. This code implements an algorithm for computing the closest point transform to a triangle mesh surface on a regular 3-D grid. The closest point transform finds the Euclidean distance to the triangle mesh. In addition, it can compute the closest point on the surface, the closest triangle face in the mesh and the gradient of the distance. The distance, etc., are computed to within a specified distance of the surface. The closest point, closest face, distance and gradient of the distance to the mesh surface are calculated by solving the Eikonal equation $ |abla u|^2 = 1 $ with the method of characteristics. The method of characteristics is implemented efficiently with the aid of computational geometry and polyhedron scan conversion. The computed distance is accurate to within machine precision. The computational complexity of the algorithm is linear in both the number of grid points for which the distance is computed and the size of the mesh. Thus for many problems, it has the optimal computational complexity. Visit http://www.its.caltech.edu/ sean/ for publications on solving static Hamilton-Jacobi equations and in particular for computing the CPT.

References in zbMATH (referenced in 16 articles )

Showing results 1 to 16 of 16.
Sorted by year (citations)

  1. Roosing, Alo; Strickson, Oliver; Nikiforakis, Nikos: Fast distance fields for fluid dynamics mesh generation on graphics hardware (2019)
  2. Gokhale, Nandan; Nikiforakis, Nikos; Klein, Rupert: A dimensionally split Cartesian cut cell method for the compressible Navier-Stokes equations (2018)
  3. Gokhale, Nandan; Nikiforakis, Nikos; Klein, Rupert: A dimensionally split Cartesian cut cell method for hyperbolic conservation laws (2018)
  4. de Jesus, Wellington C.; Roma, Alexandre M.; Pivello, Márcio R.; Villar, Millena M.; da Silveira-Neto, Aristeu: A 3D front-tracking approach for simulation of a two-phase fluid with insoluble surfactant (2015)
  5. Upreti, K.; Song, T.; Tambat, A.; Subbarayan, G.: Algebraic distance estimations for enriched isogeometric analysis (2014)
  6. Rüberg, Thomas; Cirak, Fehmi: An immersed finite element method with integral equation correction (2011)
  7. Buoni, Matthew; Petzold, Linda: An algorithm for simulation of electrochemical systems with surface-bulk coupling strategies (2010)
  8. Rangarajan, Ramsharan; Lew, Adrián; Buscaglia, Gustavo C.: A discontinuous-Galerkin-based immersed boundary method with non-homogeneous boundary conditions and its application to elasticity (2009)
  9. Velić, Mirko; May, Dave; Moresi, Louis: A fast robust algorithm for computing discrete Voronoi diagrams (2009)
  10. Buoni, Matthew; Petzold, Linda: An efficient, scalable numerical algorithm for the simulation of electrochemical systems on irregular domains (2007)
  11. Kim, Laehyun; Park, Se Hyung: Haptic interaction and volume modeling techniques for realistic dental simulation (2006) ioport
  12. Marchandise, Emilie; Remacle, Jean-François; Chevaugeon, Nicolas: A quadrature-free discontinuous Galerkin method for the level set equation (2006)
  13. Arienti, Marco; Hung, Patrick; Morano, Eric; Shepherd, Joseph E.: A level set approach to Eulerian--Lagrangian coupling. (2003)
  14. Tsai, Yen-hsi Richard: Rapid and accurate computation of the distance function using grids (2002)
  15. Bertalmío, Marcelo; Cheng, Li-Tien; Osher, Stanley; Sapiro, Guillermo: Variational problems and partial differential equations on implicit surfaces (2001)
  16. Mémoli, Facundo; Sapiro, Guillermo: Fast computation of weighted distance functions and geodesics on implicit hyper-surfaces (2001)