Spatial gradients from irregular, multiple-point spacecraft configurations

On Matching Point Configurations

We present an algorithm that verifies if two unlabeled configurations of N points in Rd are or are not an orthogonal transformation of one another, and if applicable, explicitly compute that transformation. We also give a formula for the orthogonal transformation in the case of noisy measurements. AMS subject classification: 65F15, 65F35, 65G99.

1 Finite Point Configurations

The study of combinatorial properties of finite point configurations is a vast area of research in geometry, whose origins go back at least to the ancient Greeks. Since it includes virtually all problems starting with “consider a set of n points in space,” space limitations impose the necessity of making choices. As a result, we will restrict our attention to Euclidean spaces and will discuss p...

Synchronized multiple spacecraft rotations

On spatial power gradients

The variation of the instantaneous power versus distance for a narrowband channel is an important parameter in modern digital systems, relevant for variations during a burst and for power control algorithms. This paper gives the statistical distribution for the power gradient, both in decibels and in natural units for a Rayleigh fading channel. The former has been known for some time to be Stud...

Subquadratic Encodings for Point Configurations

For most algorithms dealing with sets of points in the plane, the only relevant information carried by the input is the combinatorial configuration of the points: the orientation of each triple of points in the set (clockwise, counterclockwise, or collinear). This information is called the order type of the point set. In the dual, realizable order types and abstract order types are combinatoria...