Loki

Loki: software for computing cut loci The paper describe the software tool Loki for computing cut loci. It can display the cut locus from a point on a genus-1 two-dimensional Riemannian manifold. This manifold can be defined via a parametrization of an embedding in ℝ 3 , or via an explicit metric. The code is freely available and it should be able to be extendable to compute conjugate loci. Loki has been created with ease of use in mind and the algorithm takes into account the global nature of the problem


References in zbMATH (referenced in 14 articles , 1 standard article )

Showing results 1 to 14 of 14.
Sorted by year (citations)

  1. Kondo, Kei; Tanaka, Minoru: Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. III (2012)
  2. Itoh, Jin-Ichi; Kiyohara, Kazuyoshi: The cut loci on ellipsoids and certain Liouville manifolds (2010)
  3. Kondo, Kei; Tanaka, Minoru: Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. II (2010)
  4. Bonnard, Bernard; Caillau, Jean-Baptiste; Sinclair, Robert; Tanaka, Minoru: Conjugate and cut loci of a two-sphere of revolution with application to optimal control (2009)
  5. Sinclair, Robert; Tanaka, Minoru: The cut locus of a two-sphere of revolution and Toponogov’s comparison theorem (2007)
  6. Sinclair, Robert; Tanaka, Minoru: Jacobi’s last geometric statement extends to a wider class of Liouville surfaces (2006)
  7. Sinclair, Robert; Tanaka, Minoru: A bound on the number of endpoints of the cut locus (2006)
  8. Gravesen, Jens; Markvorsen, Steen; Sinclair, Robert; Tanaka, Minoru: The cut locus of a torus of revolution (2005)
  9. Itoh, Jin-ichi; Sinclair, Robert: Thaw: a tool for approximating cut loci on a triangulation of a surface (2004)
  10. Sinclair, R.: On the last geometric statement of Jacobi (2003)
  11. Tanaka, Minoru: Characterization of a differentiable point of the distance function to the cut locus. (2003)
  12. Sinclair, Robert; Tanaka, Minoru: Loki: software for computing cut loci. (2002)
  13. Sinclair, Robert; Tanaka, Minoru: The set of poles of a two-sheeted hyperboloid. (2002)
  14. Tanaka, Minoru: A differentiable point of the distance function to the cut locus (2002)