Sequence Of Straight Line Segments Research Articles

Quasi-Developable B-Spline Surface Design with Control Rulings

An intuitive design method is proposed for generating developable ruled B-spline surfaces from a sequence of straight line segments indicating the surface shape. The first and last line segments are enforced to be the head and tail ruling lines of the resulting surface while the interior lines are required to approximate rulings on the resulting surface as much as possible. This manner of developable surface design is conceptually similar to the popular way of the freeform curve and surface design in the CAD community, observing that a developable ruled surface is a single parameter family of straight lines. This new design mode of the developable surface also provides more flexibility than the widely employed way of developable surface design from two boundary curves of the surface. The problem is treated by numerical optimization methods with which a particular level of distance error is allowed. We thus provide an effective tool for creating surfaces with a high degree of developability when the input control rulings do not lie in exact developable surfaces. We consider this ability as the superiority over analytical methods in that it can deal with arbitrary design inputs and find practically useful results.

Incorporating Constraints Improves Least-Squares Multiwell Deconvolution

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 195271, “Constrained Least-Squares Multiwell Deconvolution,” by J. Cumming, Durham University; V. Jaffrezic, SPE, Total; and T. Whittle, Imperial College, et al., prepared for the 2019 SPE Western Regional Meeting, San Jose, California, 23-26 April. The paper has not been peer reviewed. In the complete paper, the authors reduce nonuniqueness and ensure physically feasible results in multiwell deconvolution by incorporating constraints and knowledge to methodology already established in the literature. The paper demonstrates that a combination of constraints on the shapes of the deconvolved derivatives and knowledge of the reservoir results in an improved level of quality and consistency in multiwell deconvolution solutions. The new constrained least-squares multiwell deconvolution approach is illustrated by synthetic examples with known solutions involving up to nine wells. Introduction To apply multiwell deconvolution to real data, confidence must exist in the validity of the solution it provides and the consequent interpretation that is inferred. Therefore, for practical multiwell deconvolution of field data, reducing the nonuniqueness in a solution, ensuring the results are physically feasible, and providing the desired consistency and quality of solutions are essential. With these goals in mind, the authors extend existing methodology to incorporate additional constraints and introduce additional knowledge. These constraints allow encoding of information about the behavior of the deconvolved derivatives to penalize and discourage nonphysical solutions and improve solution quality. Additionally, the approach encodes a priori knowledge, for instance that all pressure responses ultimately will show a closed reservoir by imposing a constraint that future derivative behaviors should tend toward a common unit slope. Through a combination of these techniques, an improved level of quality and consistency of deconvolution solutions can be achieved. Constrained Least-Squares Multiwell Deconvolution A key issue in any deconvolution, single-well or multiwell, is the lack of a unique solution, which results in sets or ranges of possible response functions that yield pressure matches of indistinguishable quality. When this space of possible solutions is large, then the associated response function could correspond to reservoir models with multiple differing (and potentially contradictory) interpretations. Clearly, reducing the range of possible solutions as much as possible, and assessing and quantifying the uncertainty surrounding those solutions, is critical to provide confidence in the accuracy of conclusions. One primary reason why the space of potential deconvolution solutions is so large is the choice of parameterization as a sequence of straight-line segments. In single-well deconvolution, such concerns motivated the introduction of the smoothness component to the error function in order to penalize potential deconvolution solutions with unfeasibly rough or oscillatory response functions. A second source of nonuniqueness in deconvolution is the error and uncertainty associated with the measured test data. The smoothness constraint also is particularly useful in addressing this problem.

Galaxies with “rows”: A new catalog

Galaxies with 'rows' in Vorontsov-Velyaminov's terminology stand out among the variety of spiral galactic patterns. A characteristic feature of such objects is the sequence of straight-line segments that forms the spiral arm. In 2001 A. Chernin and co-authors published a catalog of such galaxies which includes 204 objects from the Palomar Atlas. In this paper, we supplement the catalog with 276 objects based on an analysis of all the galaxies from the New General Catalogue and Index Catalogue. The total number of NGC and IC galaxies with rows is 406, including the objects of Chernin et al. (2001). The use of more recent galaxy images allowed us to detect more 'rows' on average, compared with the catalog of Chernin et al. When comparing the principal galaxy properties we found no significant differences between galaxies with rows and all S-type NGC/IC galaxies.We discuss twomechanisms for the formation of polygonal structures based on numerical gas-dynamic and collisionless N-body calculations, which demonstrate that a spiral pattern with rows is a transient stage in the evolution of galaxies and a system with a powerful spiral structure can pass through this stage. The hypothesis of A. Chernin et al. (2001) that the occurrence frequency of interacting galaxies is twice higher among galaxies with rows is not confirmed for the combined set of 480 galaxies. The presence of a central stellar bar appears to be a favorable factor for the formation of a system of 'rows'.

Polygonal Approximation of Digital Curves Using Evolutionary Programming

This paper proposes an Evolutionary Programming (EP) approach to solve the polygonal approximation of digital curves. The solution provided by the method consists of a sequence of straight line segments to be applied as Advance and Rotate motion primitives of a 2D Cartesian robot. The proposed approach finds automatically the number of segments and the startingand ending points of each of them. We have tested our approach on a test set of digital curves that exhibits two main qualitative features: openess and straightness, in different degrees. We show that our method obtains good results for approximating the curves in the test set. We present both quantitative and qualitative results of these test.

Modelling Positional Uncertainty of Line Features by Accounting for Stochastic Deviations from Straight Line Segments

AbstractThe assessment of positional uncertainty in line and area features is often based on uncertainty in the coordinates of their elementary vertices which are assumed to be connected by straight lines. Such an approach disregards uncertainty caused by sampling and approximation of a curvilinear feature by a sequence of straight line segments. In this article, a method is proposed that also allows for the latter type of uncertainty by modelling random rectangular deviations from the conventional straight line segments. Using the model on a dense network of sub‐vertices, the contribution of uncertainty due to approximation is emphasised; the sampling effect can be assessed by applying it on a small set of randomly inserted sub‐vertices. A case study demonstrates a feasible way of parameterisation based on assumptions of joint normal distributions for positional errors of the vertices and the rectangular deviations and a uniform distribution of missed sub‐vertices along line segments. Depending on the magnitudes of the different sources of uncertainty, not accounting for potential deviations from straight line segments may drastically underestimate the positional uncertainty of line features.

Line-Based Modified Iterated Hough Transform for Autonomous Single-Photo Resection

Automatic single photo resection (SPR) remains to be one of the challenging problems in digital photogrammetry. Earlier attempts to automate the space resection task were mainly point-based, where image-point primitives are first extracted and matched with their object counterparts. The matched primitives are then used to estimate the exterior orientation parameters (EOP). However, visibility and uniqueness of distinct control points in the input imagery limit robust automation of the pose estimation procedure. Recent advances in digital photogrammetry mandate adopting higher-level primitives such as control linear features replacing traditional control points. Linear features can be automatically extracted in image space. On the other hand. object-space control linear features can he extracted from an existing GIS layer containing 3D vector data such as a road network and/or terrestrial mobile mapping systems (MMS). In this paper, we present a line-based approach for simultaneously determining the position and attitude of the involved imagery as well as establishing the correspondence between image- and object-space features. This approach is motivated by the fact that captured imagery over a man-made environment is rich in straight-line segments. Moreover, free-form linear features can be reliably represented with sufficient accuracy by a sequence of straight-line segments (i.e., polylines). The suggested methodology starts by establishing a general mathematical model for relating conjugate straight-line segments to the EOP of the image under consideration. Then, a Modified Iterated Hough Transform (MIHT) strategy is adopted to derive the correspondence between image and object primitives as well as the position and the attitude of the involved imagery. This approach does not necessitate having one-to-one correspondence between image- and object-space primitives. which makes it robust against changes and/or discrepancies between the primitives. The parameter estimation and matching processes follow an optimum sequential procedure, which depends on the sensitivity of the mathematical model, relating corresponding primitives with different orientation at various image regions, to incremental changes in the EOP. Experimental results using real data proved the feasibility and robustness of the proposed approach even in the presence of a large percentage of outliers and/or discrepancies between the image- and object-space features.

DATA-DRIVEN DESIGN OF HMM TOPOLOGY FOR ONLINE HANDWRITING RECOGNITION

Although HMM is widely used for online handwriting recognition, there is no simple and well-established method of designing the HMM topology. We propose a data-driven systematic method to design HMM topology. Data samples in a single pattern class are structurally simplified into a sequence of straight-line segments, and then these simplified representations of the samples are clustered. An HMM is constructed for each of these clusters, by assigning a state to each straight-line segments. Then the resulting multiple models of the class are combined to form an architecture of a multiple parallel-path HMM, which behaves as a single HMM. To avoid excessive growing of the number of the states, parameter tying is applied such that structural similarity among patterns is reflected. Experiments on online Hangul recognition showed about 19% of error reductions, compared to the intuitive design method.

An approximate string matching algorithm for on-line Chinese character recognition

We model a Chinese character by a linear sequence of straight line segments. The 2-dimensional structure of the character is captured by the use of pseudo strokes and stroke length attributes. An effective string match algorithm has been developed which can tolerate common types of distortions, e.g. connected strokes, missing/extra strokes, and variations in writing sequence. A prototype system with 5401 commonly used Chinese characters has been built, and good recognition performance has been achieved.

On the effective tool path planning algorithms for sculptured surface manufacture

This paper describes the cutter path planning and cutter interference (gouging) analysis algorithms developed to generate optimal tool path for manufacturing sculptured surfaces on three axes CNC machine tools. Cutter path planning algorithm approximates the parametric curves on three dimensional surfaces by a sequence of straight line segments and generates optimal tool paths by minimizing the number of interpolation points while keeping the path deviations within the specified tolerances. Cutter interference analysis algorithm checks for the self intersection of an offset surface and determines the self-intersection curve. The tool path is then planned over the cutter contact (CC) surface after removing the CC data that lies inside the self-intersection curve. Finally, the effectiveness of these algorithms is demonstrated by implementing them in CAD/CAM system.

Angular homeostasis VIII. Pursuit of a slowly moving target in a plane: Relevance to lateralization in cardiovascular ontogeny

We explore the pursuit in a plane of a target moving at constant slow speed in a straight line. Two models of the pursuit are given. In the continuous case, the pursuer is moving at constant speed and is subject to proportionate angular homeostasis with correction constant b. In the discrete version movement occurs at a constant speed in a sequence of straight line segments of constant length (called the step size, s) the end of the segments being called the vertices. The pattern considered is not the absolute position of the pursuer, but its distance and orientation relative to the target. Both the transients and the asymptotic orbit are addressed. A key quantity is r, the speed of the target expressed as a fraction of that of the pursuer. If the speed of the pursuer is defined as unity, r is also the ratio of the speeds. There exists a critical speed fraction, R(b,s), a function of b and s, that defines what the term slow designates. R(b,s), which has to be found numerically, has the following property. For r less than R(b,s), the asymptotic path is a simple closed curve. In the discrete case the vertices converge to a simple closed curve. The larger r, the more the path (or in the discrete analogue its set of vertices) departs from a circle, and the more eccentric the target is with respect to it. Interest centers on two issues. First we address the transient patterns of the path, notably whether or not the sense of any particular path (clockwise or counterclockwise) is the same throughout, or changes at some stage.(ABSTRACT TRUNCATED AT 250 WORDS)

Curvature-dependent parameterization of curves and surfaces

An efficient way of drawing parametric curves and surfaces is to approximate the curve or surface by a sequence of straight-line segments or a mesh of polygons, respectively. In such an approximation, many small line segments or polygons are needed in regions of high curvature, and fewer and larger ones are needed in regions of low curvature. In the paper, special parameterizations of curves and surfaces, called angle parametrizations, are defined such that good approximations to curves and surfaces can be found by uniformly subdividing the parameter space, and applying the special parameterization. A pleasing feature of these parameterizations is that they are easily computed numerically. The numerical methods only require explicit expressions for the 1st- and 2nd-order derivatives of the original parameterization. This implies that the methods presented are applicable to the polynomial and rational curves and surfaces customarily used in computer-aided design, but are not limited to these. Some specific examples are presented. The numerical algorithm for surfaces is inherently suited to implementation on a network of processors operating in parallel, and such an implementation is briefly discussed.

A path generation method for sculptured surface manufacture

This paper describes a new path generation algorithm. When given a mathematical surface description and accuray tolerance, the algorithm approximates the surface representation by a sequence of straight line segments for graphical displays and linear cutter paths for surface manufacturing on computer-integrated numerical control (CNC) machines with five or more axes. This path generation method is generally applicable to sculptured surface manufacturing where multi-axis milling machines are necessary to produce smooth three-dimensional surfaces.

Vertical spatial coherence of an acoustical signal along a rearm‐ray path

COVERT is a computer model which predicts the effects of stochastic volume scattering on the vertical spatial coherence of an acoustic signal along a single path (as determined by a mean sound‐speed field). The propagation path is termed a macro‐ray path and is described by a sequence of straight line segments. The program algorithm calculates the effects of scattering over each segment in turn as if it were in a homogeneous medium. The scattering term [J. J. McCoy and M. J. Beran, J. Acoust. Soc. Am. 66, 1468–1481 (1979)] takes into account the angle of the path segment relative to the anisotropic scattering mechanism, and the scattering strength may vary with the depth of the segment. Major advantages of COVERT are that it is easy to use and relatively fast. Its current principal limitations are that it treats a single macro‐ray path and does not incorporate coupling between the volume scattering and subsequent effects of refraction and diffraction. Thus, COVERT's main utility is for single‐path, high‐f...

A method of evaluating the effect of temperature on an organism when the response is non-linear

The accumulated temperature idea is extended to embrace any temperature response which can be represented as a sequence of straight-line segments. The technique is found to require a more, precise and consistent method of calculating accumulated temperatures than is generally used. Such a method, in which the daily temperature wave is represented by a sinusoid, is presented. The sporulation of the eyespot fungus of wheat is used as an example to demonstrate the new methods. Finally it is pointed out that further applications will depend on closer definition by biologists of the relation between rate of development and temperature for different organisms.

On the Approximation Problem in Network Synthesis

A procedure is presented for the synthesis of a network to yield a prescribed magnitude versus frequency characteristic. The given characteristic is replaced by a sequence of straight line segments of arbitrary slope. Each line segment is associated with a zero-pole pair properly placed on the real p axis, where p is the complex frequency variable. In this manner a real, rational network function is obtained whose magnitude variation approximates the given one. Methods for predicting the realizability of the approximating function are discussed in the application to the design of two terminal and two-terminal pair networks. To illustrate the methods outlined in the paper, a complete procedure is given for the design of attenuation equalizers using constant-resistance ladder sections.

Steam logs of the Pacific, Collins steamer, plying between New York and Liverpool

We present a method for routing of a preformed hose in a static surrounding of obstacles. Routing of a preformed hose is the process of finding a preformed design of the hose that connects a start and a goal point in a collision-free way. A preformed hose design is in this paper represented by a center curve on the form of a sequence of straight line segments joined by circular arcs. The method generates a set of center curves that are collision-free and satisfy minimum allowed straight length and radius of curvature constraints. Each center curve takes a topologically different path with respect to the surrounding geometry and is locally of minimum length. The main scientific contribution is the coupling of a generalized bi-directional grid search with local curve optimization and curve filtering. The method was applied to a set of benchmark cases from the automotive industry and relevant routing solutions were generated in the magnitude of seconds.