Related papers: Testing the Existence of a Supporting Plane
We introduce and study a three-folded linear operator depending on three parameters that has associated a triangular number tilling of the plane. As a result the set of all triples of integers is decomposed in classes of equivalence…
In [1], we have presented the theoretical background for finding the Elementary Invariants for a 3D system of first order rational differential equations (1ODEs). We have also provided an algorithm to find such Invariants. Here we introduce…
We present an algorithm for testing halfspaces over arbitrary, unknown rotation-invariant distributions. Using $\tilde O(\sqrt{n}\epsilon^{-7})$ random examples of an unknown function $f$, the algorithm determines with high probability…
Three-dimensional catalogues of objects at cosmological distances can potentially yield candidate topologically lensed pairs of sets of objects, which would be a sign of the global topology of the Universe. In the spherical case, a…
Quadcopters are increasingly used for applications ranging from hobby to industrial products and services. This paper serves as a tutorial on the design, simulation, implementation, and experimental outdoor testing of digital quadcopter…
Fix a point in a finite-dimensional complex vector space and consider the sequence of iterates of this point under the composition of a unitary map with the orthogonal projection on the hyperplane orthogonal to the starting point. We prove…
The scattering of electromagnetic waves by three--dimensional periodic structures is important for many problems of crucial scientific and engineering interest. Due to the complexity and three-dimensional nature of these waves, the fast,…
In this paper we study some Erdos type problems in discrete geometry. Our main result is that we show that there is a planar point set of n points such that no four are collinear but no matter how we choose a subset of size $n^{5/6+o(1)} $…
Path planning is an essential component of mobile robotics. Classical path planning algorithms, such as wavefront and rapidly-exploring random tree (RRT) are used heavily in autonomous robots. With the recent advances in machine learning,…
Vector-based algorithms are novel algorithms in optimal any-angle path planning that are motivated by bug algorithms, bypassing free space by directly conducting line-of-sight checks between two queried points, and searching along obstacle…
Extracting planes from a 3D scene is useful for downstream tasks in robotics and augmented reality. In this paper we tackle the problem of estimating the planar surfaces in a scene from posed images. Our first finding is that a surprisingly…
Wing-assisted inclined running (WAIR) observed in some young birds, is an attractive maneuver that can be extended to legged aerial systems. This study proposes a control method using a modified Variable Length Inverted Pendulum (VLIP) by…
Template matching is a basic method in image analysis to extract useful information from images. In this paper, we suggest a new method for pattern matching. Our method transform the template image from two dimensional image into one…
In modeling quantum systems or wave phenomena, one is often interested in identifying eigenstates that approximately carry a specified property; scattering states approximately align with incoming and outgoing traveling waves, for instance,…
We develop a theory of vector spaces spanned by orbit-finite sets. Using this theory, we give a decision procedure for equivalence of weighted register automata, which are the common generalization of weighted automata and register automata…
Many man-made objects are characterised by a shape that is symmetric along one or more planar directions. Estimating the location and orientation of such symmetry planes can aid many tasks such as estimating the overall orientation of an…
We consider the following classification problem: Given a population of individuals characterized by a set of attributes represented as a vector in ${\mathbb R}^N$, the goal is to find a hyperplane in ${\mathbb R}^N$ that separates two sets…
Two planar graphs G1 and G2 sharing some vertices and edges are `simultaneously planar' if they have planar drawings such that a shared vertex [edge] is represented by the same point [curve] in both drawings. It is an open problem whether…
This paper presents the experimental comparison of fourteen stereo matching algorithms in variant illumination conditions. Different adaptations of global and local stereo matching techniques are chosen for evaluation The variant strength…
We consider the binary hypothesis testing problem with two observers. There are two possible states of nature (or hypotheses). Observations collected by the two observers are statistically related to the true state of nature. The knowledge…