We introduce additively-weighted straight skeletons as a new generalization of straight skeletons. An additively-weighted straight skeleton is the result of a wavefront-propagation process where, unlike in previous variants of straight skeletons, wavefront edges do not necessarily start to move at the begin of the propagation process but at later points in time. We analyze the properties of add...

I.4: “If two triangles have the two sides equal to two sides respectively, and have the angles contained by the equal straight lines equal, they will also have the base equal to the base, the triangle will be equal to the remaining angles respectively, namely those which the equal sides subtend.” I.9: “To bisect a given rectilinear angle.” I.10: “To bisect a given finite straight line.” I.11: “...

A monotonous polyomino is formed by all lattice unit squares met the graph of some fixed continuous function $$f:[a,b] \to \mathbb{R}$$ with $$f(k) \notin \mathbb{Z}$$ whenever $$k \in . Our main result says that least cardinality a covering $$(m \times n)$$ -rectangle polyominoes $$\big\lceil \frac{2}{3}(m+n-\sqrt{m^2+n^2-mn})\big\rceil.$$ The paper motivated problem on arrangements straight l...

We characterize the self-parallel (mitered) offsets of a general nonconvex polytope Q in 3-space and give a canonical algorithm that constructs a straight skeleton for Q.

The straight skeleton of a polygon is the geometric graph obtained by tracing the vertices during a mitered offsetting process. It is known that the straight skeleton of a simple polygon is a tree, and one can naturally derive directions on the edges of the tree from the propagation of the shrinking process. In this paper, we ask the reverse question: Given a tree with directed edges, can it be...

In order to calculate confidence intervals and hypothesis tests, it is assumed that the errors are independent and normally distributed with mean zero and variance 2 σ . Given a sample of N observations on X and Y, the method of least squares estimates β0 and β1 as well as various other quantities that describe the precision of the estimates and the goodness-of-fit of the straight line to the d...

We study the problem of straight-line path following for fully actuated marine craft. We propose a controller that adjusts the speed of the marine craft according to the geometric distance and the rate of convergence to the path. The control law is derived using the method of least squares, which is used to find an approximate solution for overdetermined systems. The conditions under which the ...

A new algorithm for least squares matching of overlapping 3D surfaces, digitized/sampled point by point using a laser scanner device, the photogrammetric method or other techniques, is proposed. In photogrammetry, the problem statement of surface patch matching and its solution method was first addressed by Gruen (1985a) as a straight application of Least Squares Matching. There have been some ...