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2D Part Orienting

Abstract

orient_example

The project deals with the problem of orienting a given polygon P without the use of sensors. We focus on a method called oblivious push-plans, which means we push P using a straight arm from several different directions, and construct this series of directions such that P will always end up in the same, predetermined orientation, regardless of the orientation in which it is given to us. The project includes the implementation of several algorithms that construct valid and optimal push-plans for a given polygon P, as well as a simulation program, which can be used to demonstrate how the push-plan we obtain operates on different orientations of P.

radius function push function
A polygonal part and its radius function. The minima of the radius
function correspond to normals to polygon edges that intersect the
center-of-mass. The maxima correspond to tangents to polygon
vertices whose normals intersect the center-of-mass.
A polygonal part and its push function. The horizontal steps of the
push function are angular intervals between two successive maxima
of the radius function.

overlay   interval
Using the overlay of the Gaussian map
and the central map of P to construct
the radius function of P. In this case,
n(ei)
is immediately between d(vi)
and d(vi+1) in the overlay, and thus
n(ei) is a minimum point for the radius
function, and it constitutes a step of
the push function.
  Deciding whether an interval I1 of orientations
can be "collapsed" into an interval I2  with a
single push is done by comparing the known-
angle
of I1 with the fit-angle of I2. A single
push suffices if and only if the former is
smaller than the latter. The figure shows the
known-angle
(blue) and fit-angle (orange) of
the interval [d1, d2].

References

Links

  • Geva Kipper
    2D Part Orienting [pdf]
    Presentation [pdf, Hebrew]
    Code [link]

Contacts

Geva Kipper

null
Efi Fogel http://www.cs.tau.ac.il/~efif efifogel@gmail.com
Dan Halperin http://acg.cs.tau.ac.il/danhalperin danha@post.tau.ac.il
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