Showing papers on "Delaunay triangulation published in 1970"
TL;DR: Delaunay's reduced Hamiltonian of the main problem in lunar theory is checked against a new analytical theory based on Lie transforms in this article, and it is found to be correct up to order 9 with the exception of one error in addition at order 7.
Abstract: Delaunay's reduced Hamiltonian of the main problem in lunar theory is checked against a new analytical theory based on Lie transforms. It is found to be correct up to order 9 with the exception of one error in addition at order 7.
35 citations
01 Jan 1970
TL;DR: In this article, a geometrical technique based on shape construction was employed to reconstruct the simulated domain of 3D bubbles in gas-solid fluidized beds from Two-Fluid Model simulations.
Abstract: A geometrical technique based on shape construction was employed to reconstruct the simulated domain of 3D bubbles in gas-solid fluidized beds from Two-Fluid Model simulations. The Delaunay triangulation of the cloud of points that represent volume fraction iso-surfaces was filtered using α-shapes, allowing a topologically accurate description of the bubbles.
TL;DR: In this article, the authors present the n-locus of a triangle, upon which lie several points of geometric interest and derive formulae for the coordinates of various special forms of Least Squares Fits to a triangle.
Abstract: This Compendium attempts to collate and coalesce those aspects of triangulation theory related to position-fix techniques employing lines-of-bearing. The author presents the discovery of the n-locus of a triangle, upon which lie several points of geometric interest. Formulae for the coordinates of various special forms of Least Squares Fits to a triangle are derived. The well known method of “resection by intersection” is examined, complemented by variations of the technique. The m-Loeus of a triangle is discovered, yielding the Classical Least Squares for triangulation theory. The m-locus dissolves the mystery surrounding the technique employing equi-angular adjustment to the triangulation measurements to reduce the error-triangle to a point. The treatise concludes with formulae for the direct calculation of the Classical Least Squares, bypassing the need of the vertices of the triangle of error and consequently the lengths of the sides of the triangle.