Chord Length Parameterization Research Articles

Prediction of emissions and performance from transient driving cycles using stationary conditions: Study of advanced biofuels under the ETC test

This paper applies and improves a methodology for estimating engine responses from transient cycles using steady conditions according to a Design of Experiments (DoE). The fuels tested are diesel-farnesane, biodiesel from sugarcane, and diesel fuel S50. A common-rail engine and the European Transient Cycle (ETC) are considered. Two DoEs of 13 runs each were analysed: the 13 modes of the European Stationary Cycle (ESCDoE) and a 5-level Fractional Factorial Design (FFDoE). The mathematical transformation of the engine working region and the experimental data approximation were improved using chord length parameterization and tensor product surfaces, respectively. Both DoEs provide an instantaneous approximation of engine performance responses of high accuracy. However, in general, better results are obtained using the FFDoE (R2 > 0.92, but R2 > 0.84 for exergy rate) compared to the ESCDoE (R2 > 0.87, and R2 > 0.53 for exergy rate). The FFDoE is the most appropriate design for the instantaneous prediction of THC and NOx regulated emissions (R2 > 0.91) as well as for its specific (accumulated) emissions (relative error e < 11%). However, worse results are obtained for CO emissions prediction (R2 > 0.7 and e < 19.1%).

Surface Fitting for non-Grid Data from in-Situ Measuring Systems of Aero-engine Blade

High machining accuracy of aero-engine blade largely determines the carrying capacity, endurance, acceleration and the dynamic performance of the aero-engine, so a reliable machining error inspection and evaluation technique is imperative. In order to give a reliable error evaluation, the non- uniform rational B-spline (NURBS) technique is adopted to reconstruct the surface within a specified accuracy. Usually, data points measured from aero-engine blade are non-grid data in situ measuring systems. To overcome the difficulty of NURBS surface fitting from non-grid data, a new method based on data conversion is proposed, in which chord length parameterization and uniform parameter sampling are combined together to realize the data convertation, and subsequently hierarchical fitting strategy is applied to finish the NURBS surface reconstruction. The way proposed for data conversion is easy to realize, and by which gemetrical features of original measured data are also reserved well, which make the whole method outstanding in low time cost. Experimental results show that the method is fast, effective. The source code has been implemented in VC++, while the resulting pictures are constructed in Matlab with the obtained control points, knot vectors, and the orders.

Arabic Fonts Representation in Cubic Bézier Curve using Different Soft Computing Algorithm

This study presents the comparison between two meta-heuristic algorithms for curve reconstruction of Arabic fonts. The two algorithms namely Sine Cosine Algorithm (SCA) and Whale Optimization Algorithm (WOA) are used for comparison purposes. These algorithms have been applied to optimize the solution of curve fitting problem by using cubic Bezier curve. There are several pre-processing steps involve before curve fitting process has been done. Firstly, extract the boundary. Then, detect the corner of outline fonts and the third step is chord length parameterization. The aim of this study is to find the best curve that fit the data. Sum Square Errors (SSE) has been used to calculate the error given by original image and parametric curve. The finding of this study shows that, WOA gives better curve approximation based on the errors result than SCA. This algorithm significantly improves the shape of the corner of the outline Arabic fonts.

Thermal Image Approximation Using B-Spline Surfaces

This article presents a method of filtering thermal images by means of approximation using cubic B-spline patch surfaces. Approximation uses chord length parameterization with non-uniform distribution of knots, depending on the change rate of pixel values in rows and columns of the image. Advantages of approximation with such parameterization are compared with popular uniform parameterization. Presented method is very versatile and can be used for example in 3D surface topography of objects tested with stereoscopic microscopes, in resolution change of arbitrary images or modeling processes depending on two parameters. Filtering results are presented using plugin for the Soft4Image program, which was designed to unify different digital signal processing algorithms.

Pre-bent shape design of full free-form curved beams using isogeometric method and semi-analytical sensitivity analysis

In this paper, isogeometric analysis (IGA) is employed to solve the problem of a curved beam with free-form geometry, arbitrary loading, and variable flexural/axial rigidity. The main objective of the study is to develop a unified approach for full free-from curved beam problems that can be integrated with a newly developed semi-analytical sensitivity analysis to solve pre-bent shape design problems. The required set of B-spline control points are calculated using an interpolation technique based on chord-length parameterization. The one-to-one correspondence is considered for parameters of the geometry, loading, and rigidity which is proven to have extreme importance. An IGA curved beam element is suggested based on the Euler-Bernoulli beam theory for the general curvilinear coordinate. The validity and effectiveness of the proposed formulation is confirmed by application to a variety of examples. Moreover, three shape optimization examples are taken into consideration. In the first two examples, the pre-bent shapes of spiral and Tschinhausen curved beams with free-form geometry under distributed loading are obtained. In the third example, the pre-bending problem of wind turbine blades is addressed as an industrial example.

Research of the reconstruction method for the image feature of non-rigid 3D point cloud

In the reconstruction of non-rigid three dimensional (3D) point cloud image features, the image data is large, which leads to the difficulty for analysis, and the achieving process is complex. In this paper, the reconstruction method for non-rigid 3D point cloud image features based on NURBS curve is proposed to collect non-rigid 3D point cloud image data, and achieve triangulation. The operation of point cloud data neighborhood search is limited in the local area, and the data of non-rigid 3D point cloud images are divided with the idea of space division. The least square plane is obtained by using preprocessed non-rigid 3D point cloud data, and the non-rigid 3D point cloud data is mapped and converted into a two dimensional (2D) point cloud model. The cumulative chord length parameterization method is adopted to introduce weighting factor for NURBS curve description using the rational polynomial function, based on the definition and properties of NURBS curve, point, line, surface reconstruction model is utilized to reconstruct the non-rigid 3D point cloud image feature. The simulation results show that the proposed method can reconstruct the 3D point cloud images feature with less time and the reconstruction effect is better than the Crust method.

Graphic-processing-unit-accelerated real-time exposure fusion method using pixel-level optimal exposure criterion

High dynamic range (HDR) imaging is an important and challenging research topic in computational photography. A simple but effective image fusion method is proposed to accomplish the multi-exposure image composition in both static and dynamic scenes. The foundation of the proposed method is an experiential criterion that optimizes the exposure that occurs at a dramatic alteration point in the low dynamic range image sequence (LDRI). To extract these well-exposed pixel vectors, each pixel curve formed by the pixel vectors at same position along all frames in the LDRIs is first preprocessed by the chord length parameterization. Then a single high-quality pseudo-HDR image can be extracted directly and efficiently from the LDRIs using a pixel-level fusion index matrix derived from the first- and second-order difference quotients of the preprocessed pixel curves. The main advantage of the proposed method is its use of a single independent pixel in computing. It is highly parallel, allowing a graphic processing unit-based, real-time implementation. The experiments on various scenes discussed here indicate that the proposed exposure fusion method can combine a large image sequence with 10 megapixels into a visually compelling pseudo-HDR image at a rate of 30 frames/s on a consumer hardware.

Curves and surfaces with rational chord length parameterization

The investigation of rational varieties with chord length parameterization (shortly RCL varieties) was started by Farin (2006) who observed that rational quadratic circles in standard Bézier form are parametrized by chord length. Motivated by this observation, general RCL curves were studied. Later, the RCL property was extended to rational triangular Bézier surfaces of an arbitrary degree for which the distinguishing property is that the ratios of the three distances of a point to the three vertices of an arbitrary triangle inscribed to the reference circle and the ratios of the distances of the parameter point to the three vertices of the corresponding domain triangle are identical. In this paper, after discussing rational tensor-product surfaces with the RCL property, we present a general unifying approach and study the conditions under which a k-dimensional rational variety in d-dimensional Euclidean space possesses the RCL property. We analyze the entire family of RCL varieties, provide their general parameterization and thoroughly investigate their properties. Finally, the previous observations for curves and surfaces are presented as special cases of the introduced unifying approach.

Curves with chord length parameterization

Motivated by the recent work (Farin, G., 2006. Rational quadratic circles are parameterized by chord length, Computer Aided Geometric Design 23, 722–724), we identify a family of curves that can be parameterized by chord length. The α- and ( α , β ) -schemes are presented for characterizing planar and spatial curves respectively. Rational chord-length parameterizations are thoroughly investigated. In particular, the low-degree rational curves such as cubics and quartics are studied and applied to geometric Hermite interpolation. The results advise that this new class of curves, subsuming straight lines and circular arcs, have several obvious advantages over general polynomial and rational curves.

Fast Distortion Measurement Using Chord-Length Parameterization Within the Vertex-Based Rate-Distortion Optimal Shape Coding Framework

Existing vertex-based operational rate-distortion (ORD) optimal shape coding algorithms can use a number of different distortion measurement techniques, including the shortest absolute distance (SAD), the distortion band (DB), the tolerance band (TB), and the accurate distortion measurement technique for shape coding (ADMSC). From a computational time perspective, an N-point contour requires O(N2 ) time for DB and TB for both polygon and B-spline-based encoding, while SAD and ADMSC incur O(N) time for polygonal encoding but O(N2 ) for B-spline based encoding, thereby rendering the ORD optimal algorithms computationally inefficient. This letter presents a novel distortion measurement strategy based on chord-length parameterization (DMCLP) of a boundary that incurs order O(N) complexity for both polygon and B-spline-based encoding while preserving a comparable rate-distortion performance to the original ORD optimal shape coding algorithms