Geometry

1909 Submissions

[2] viXra:1909.0174 [pdf] submitted on 2019-09-08 14:35:08

Curve Decimation in SE(2) and SE(3)

Authors: Jan Hakenberg
Comments: 9 Pages.

We generalize the Ramer-Douglas-Peucker algorithm to operate on a sequence of elements from a Lie group. As the original, the new algorithm bounds the approximation error, and has an expected runtime complexity of O(n log n). We apply the curve decimation to data recorded from a car-like robot in SE(2), as well as from a drone in SE(3). The results show that many samples of the original sequence can be dropped while maintaining a high-quality approximation to the original trajectory.
Category: Geometry

[1] viXra:1909.0028 [pdf] submitted on 2019-09-01 08:30:19

Triple Cosines Theorem

Authors: Yuly Shipilevsky
Comments: 1 Page.

We prove that in Cartesian Coordinate System, the cosine of the angle between lines, belonging to two coordinate planes and both lines go through the origin with the corresponding angles to the same common axis is equal to multiplication of cosines of these angles.
Category: Geometry