Images are an important source of information for spacecraft navigation and three-dimensional reconstruction observed space objects. Both these applications take the form a triangulation problem when camera has known attitude measurements extracted from image line sight (LOS) directions. This work provides comprehensive review history theoretical foundations triangulation. A variety classical a...

We show that there is no triangulation of the infinite real Grassmannian G(k,R∞) nicely situated with respect to the coordinate axes. In terms of matroid theory, this says there is no triangulation of G(k,R∞) subdividing the matroid stratification. This is proved by an argument in projective geometry, considering a specific sequence of configurations of points in the plane. The Grassmannian G(k...

A new O(nlog(n)) algorithm is presented for performing Delaunay triangulation of sets of 2D points. The novel component of the algorithm is a radially propagating sweep-hull (sequentially created from the radially sorted set of 2D points, giving a non-overlapping triangulation), paired with a final triangle flipping step to give the Delaunay triangluation. In empirical tests the algorithm runs ...

We show that every set of n points in general position has a minimum pseudo-triangulation whose maximum vertex degree is five. In addition, we demonstrate that every point set in general position has a minimum pseudo-triangulation whose maximum face degree is four (i.e. each interior face of this pseudo-triangulation has at most four vertices). Both degree bounds are tight. Minimum pseudo-trian...

The Delaunay triangulation and the weighted Delaunay triangulation are not uniquely defined when the input set is degenerate. We present a new symbolic perturbation that allows to always define these triangulations in a unique way, as soon as the points are not all coplanar. No flat tetrahedron exists in the defined triangulation. The perturbation scheme is easy to code; It is implemented in cg...