Le mura di Leonardo. I rilievi del 1502

Leonardo’s Walls. Surveys in 1502In the summer of 1502, Cesare Borgia appointed Leonardo da Vinci for his engineering expertise. His assignment was specific and concerning with military architecture: he was expected to “see, measure and do good estimation”. The Codex L, a small notebook conserved in the Library of the Institute of France, show the results of the survey of the city walls of Cesena and Urbino. The technique Leonardo adopted consists in traversing rectilinear stretches, measuring their length by means of an instrument able to count his steps and establishing their orientation by means of a compass. At the end of the path, the data relative to the sides of a closed polygon are obtained, resulting the geometric plan of the walls. This practice is testified by some residual eidotypes provided with quotas and orientations. In some cases, only the lists of distances in numbers are present, but the analysis of the figures makes it possible to reconstruct the surveyed plans, as Nando De Toni pioneered many years ago. This study focuses on the tools and the urban survey technique used by Leonardo. The analysis of some sheets from the Codex L, contextualized with respect to the actual topography of the sites, allows to understand the correct sequence of the operations carried out first in the site and then at the drawing board. By means of specific digital reconstructions, it is therefore possible to study the instrumental and operational limits of this practice and, by comparing it with the current state, to reconstruct the entire defensive structure.

Persistent fontanelles in Chihuahuas and inter- and intra-rater reliability of fontanelle area measurement in computed tomography images

Background: The Chihuahua dog breed is known for frequent occurrence of a bregmatic fontanelle on the dorsal skull. A common conception is that this skull defect is clinically irrelevant in Chihuahuas. No studies, however, describe the prevalence of this malformation, whether it is accompanied by fontanelles at other locations on the skull or how to assess the severity of these lesions. Our primary aim was, by using computed tomography imaging, to describe the presence, number, and location of persistent fontanelles (PF) at cranial sutures on dorsal, lateral and caudal cranial surfaces in Chihuahuas. The secondary aim was to develop a method to measure the fontanelle area in computed tomography images by using the closed polygon tool of Osirix Medical Imaging Software. Results: Of the 50 dogs evaluated, 46 (92%) had either one or several PFs. The mean ± SD number of affected cranial sutures per dog was 2.4 ± 2.3 (range 0-10), and mean ± SD number of PFs was 2.8 ± 3.0 (range 0-13). Of the 46 dogs with affected sutures, 7 (15%) had no PF at a location typical for a bregmatic fontanelle. The inter-rater reliability of the fontanelle area measurement was almost “perfect”, and intra-rater reliability reached “excellent” agreement. Conclusions: PFs are almost ubiquitous in the examined group of Chihuahuas. They are located at dorsal, lateral, and caudal surfaces of the cranium, and hence are not all recognized reliably by palpation in adult dogs. Though the pathogenesis of the PFs described here is unknown, bone-deficient lesions may occur due to congenital defects in cranial bone ossification, delayed closure of cranial sutures, or bone resorption, as is observable in children with craniosynostosis (premature cranial suture closure). Because the imaging findings described in the Chihuahuas of this study are similar to findings among children with craniosynostosis/premature cranial base synchondrosis closure, this growth disorder may be a predisposing factor for the PFs described here. Further studies are necessary to evaluate the pathogenesis and clinical relevance of these lesions. Due to high inter- and intra-rater reliability of the method of fontanelle area measurement it may be useful in future studies.

Plasma-assisted filling electron beam lithography for high throughput patterning of large area closed polygon nanostructures

The PFEBL process allows enhancement of electron beam writing efficiency for patterning of closed polygon structures using a post-exposure plasma treatment.

Setting and Discriminant Method of Electronic Fence in Location Services

Regulation activities of motion object in the computer system, and to determine whether a motion object within a specified area activity is a commonly used function of location service. The designated area on the electronic map is a closed polygon graph, namely the electronic fence. On reporting the location of the movement object coordinate relationship between the location of the polygon on calculation and analysis to determine the object is inside the fence or outside the fence. This paper introduces the electronic fence setting and discriminant algorithm implementation. The methods presented in this paper has achieved good results in practical application.

Critical configurations of planar robot arms

It is known that a closed polygon P is a critical point of the oriented area function if and only if P is a cyclic polygon, that is, P can be inscribed in a circle. Moreover, there is a short formula for the Morse index. Going further in this direction, we extend these results to the case of open polygonal chains, or robot arms. We introduce the notion of the oriented area for an open polygonal chain, prove that critical points are exactly the cyclic configurations with antipodal endpoints and derive a formula for the Morse index of a critical configuration.

A New Algorithm for Detecting Position Relationship between Point and Polygon

A new algorithm for position relationship between detecting point and polygon is proposed based on the research of radial method, and as the first step, transform polygon in convex polygon, then determine the position relationship between detecting point and original polygon by judging the position relationship between detecting point and transformed convex polygon and closed polygon. The new method can accurately determine the position relationship between point and arbitrary shape polygon which fully considers all kinds of position conditions including detecting point inside, on (including vertex) and outside the polygon.

Piecewise constant collocation for first-kind boundary integral equations

We wish to correct a minor error in the recent paper [2]. That paper was concerned with an integral equation defined on a closed polygon Γ with r corners at the points x0, x2, …, x2r = x0. We parameterized Γ using a mapping γ:[−π,π] → Γ defined as follows. For each l, introduce the mid-point x2l−1 of the side joining x2l—2 to x2l. Then introduce 2r + 1 points in parameter spacewith the property that for each j = 1, …, 2rwhere mj are integers and . Then γ(s) is defined byfor j = 1, …, 2r. The {Sj} are then the preimages of the {xj} under γ. Moreover, in view of (1), a family of uniform meshes can be constructed on [−π, π] which include {Sj} as the break-points. Then γ maps these to meshes which are uniform on each segment joining xj−1 to xj (which we denote Γj). These meshes are used to discretize the integral equation.