# CPT

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.

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## References in zbMATH (referenced in 16 articles )

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