Small Number Of Control Points Research Articles

Improving the approximation quality of tensor product B-spline surfaces by local parameterization

Abstract Freeform surfaces like tensor product B-spline surfaces have been proven to be a suitable tool to model laser scanner point clouds, especially those representing artificial objects. However, when it comes to the modelling of point clouds representing natural surfaces with a lot of local structures, tensor product B-spline surfaces reach their limits. Refinement strategies are usually used as an alternative, but their functional description is no longer nearly as compact as that of classical tensor product B-spline surfaces, making subsequent analysis steps considerably more cumbersome. In this publication, the approximation quality of classical tensor product B-spline surfaces is improved by means of local parameterization. By using base surfaces with a local character, relevant information about local structures of the surface to be estimated are stored in the surface parameters during the parameterization step. As a consequence, the resulting tensor product B-spline surface is able to represent these structures even with only a small number of control points. The developed locally parameterized B-spline surfaces are used to model four data sets with different characteristics. The results reveal a clear improvement compared to the classical tensor product B-spline surfaces in terms of correctness, goodness-of-fit and stability.

Optimal design of strain sensor placement for distributed static load determination

Abstract In many applications it is desirable to inverse-calculate the distributed loading on a structure using a limited number of sensors. Yet, the calculated loads can be extremely sensitive to the placement of these sensors. In the case of predicting point loading applied at a known location, best results are typically achieved when one sensor is collocated with the force. However, the extension of this rule to distributed loading remains uncertain, and even simple sensor system design scenarios often require the designer to directly optimize the sensor placements using a numerical model. In an effort to provide designers with guidance, we identify optimal sensor configurations for predicting static distributed loads on beams with classical boundary conditions. An influence coefficient method, wherein the strain is related linearly to the static load, is used to estimate the applied forces. The loading distribution on the structure is assumed to be either a piece-wise linearly-distributed load or a uniformly-distributed load, allowing for distributed loads to be estimated using the magnitudes of a small number of control points. Given the simplicity of the beam structure, the equations of the influence coefficient method are derived analytically, which allows for the sensor placement to be specified using continuous optimization methods. The condition number of the influence coefficient matrix is used as a surrogate for error during optimization. ‘Rules of thumb’ for sensor placement are presented based on the optimization results. Results show that the optimal and rule-of-thumb sensor configurations are more resistant to input noise than naïve configurations, with the rule-of-thumb configurations yielding similar force predictions relative to the optimal configurations. We expect the rules of thumb to be useful guidelines for engineers designing tests on beam-like structures such as aircraft wings or marine propellers where the inverse calculation of distributed loads is of interest.

An iso-contour method for automated fiber placement optimization of composite structures

A new method for numerical optimization of fiber-steered composites is presented, which allows to control efficiently and effectively the curvature of the fibers of single- or multi-layer composite structures. It is based on the introduction of an artificial surface defined and controlled by a relatively small number of control points, which is optimized to identify optimal fiber orientations varying smoothly over the panels. Curvature constraints like the maximum fiber curvature constraint, MFCC, or the average fiber curvature constraint, AFCC, are respected explicitly by the method to ensure manufacturability of the composite component. Three validation cases are regarded where results of the unconstrained case are compared to those of established methods to illustrate the validity of the new approach. They are complemented by results considering curvature constraints showing that optimal structures depend strongly on the chosen curvature thresholds. Finally, a rib optimization of a wingbox structure is realized as a more complex case.

An efficient iterative method for reconstructing the refractive index in complex domains from far field data

We present a computational method for reconstructing the refractive index of an unknown complex-shaped two-dimensional medium with embedded metal inclusions from its transverse magnetic electromagnetic scattering properties. We present a novel hybrid surface-volume integral equation that generalises the Lippmann–Schwinger equation to media containing embedded scatterers. Using this hybrid equation, we show that the Frechet derivative of the forward-mapping satisfies a particular inhomogeneous wave scattering problem. We solve the inhomogeneous wave scattering problem using a novel coupled FEM-BEM formulation. Our numerical scheme is based on a thin plate spline ansatz for the refractive index, which can be constructed using a relatively small number of control points, and can be efficiently constructed and evaluated even for the complex-shaped multiply-connected domains of interest. Numerical experiments demonstrate the effectiveness of our method by reconstructing several challenging media.

B-spline surface approximation method for achieving optimum dwell time in deterministic polishing

In the computer-controlled optical surfacing (CCOS) process, the accurate calculation of the dwell time map is essential for achieving the desired amount of material removal distribution. However, it remains challenging for current methods to generate a smooth dwell time map that reduces the dynamic requirements of machine tools while maintaining the high finishing capability on freeform optics. This paper proposes a B-spline surface approximation method for obtaining the optimum dwell time in deterministic polishing. The B-spline surface representation allows the dwell time map to be expressed by a small number of control points instead of a large number of discrete dwell points. The dwell time deconvolution then becomes a linear least-squares problem with only a few control points as variables, which significantly reduces the scale of the problem. To achieve a more accurate and smoother dwell time map, a knot position optimization algorithm is proposed to adapt the knots to the geometric features of the target removal surface. Simulation results demonstrate that the proposed B-spline-based dwell time algorithm significantly outperforms common dwell time algorithms in terms of the computational accuracy, efficiency, as well as smoothness of the dwell time map. To validate the effectiveness and practicability of the proposed method, experimental polishing of a bi-sinusoidal optical surface has been carried out. The results show that the developed algorithm has greatly reduced the tracking error of the machine tool caused by dwell time fluctuations, and consequently, the corresponding residual error of material removal in deterministic polishing.

A Robust Method for Block Adjustment of UAV SAR Images

To reduce the number of ground control points required for block adjustment of unmanned aerial vehicle (UAV) synthetic aperture radar (SAR) images, a robust block adjustment method is pro-posed. The proposed method aims to solve the problem of unstable adjustment solutions caused by the jittering of UAV SAR platforms. This method is based on the range Doppler model. By analyzing the correlation between the antenna phase center, velocity, and Doppler centroid of the seven orientation parameters, this method performs a block adjustment of UAV SAR images with three orientation parameters: the antenna phase center initial imaging moment, Doppler centroid, and proximity delay. UAV SAR images obtained from an area of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\times $ </tex-math></inline-formula> 3 km in Dengfeng were used to conduct adjustment experiments. The results obtained using different orientation parameter set-tings verify the robustness and effectiveness of the proposed method. The adjustment results under various control-point layout plans indicate that a uniform layout plan can achieve an adjustment accuracy better than 1 m with a small number of control points.

A jerk-limited heuristic feedrate scheduling method based on particle swarm optimization for a 5-DOF hybrid robot

Compared with machine tools, five degrees-of-freedom (DOFs) hybrid robots have been widely concerned in the manufacturing of large complex surface parts due to their characteristics of high flexibility and large workspace. It is of great significance to schedule the time-optimal feedrate that satisfies the high-order constraints (e.g., jerk or jounce) in the toolpath and joint systems to achieve the high-precision and high-efficiency machining of the robot. To overcome the complexity of five-axis feedrate scheduling and improve the optimality of machining time, this paper proposes a jerk-limited heuristic feedrate scheduling (HFS) method with near-optimal time. Firstly, the analytical equations between all constraints and the parametric feedrate are derived, and the mathematical model for control points optimization of the parametric feedrate profile expressed by a B-spline curve is established. Then, combined with the global search particle swarm optimization (GSPSO) algorithm, a proposed moving window planning method optimizes a small number of control points so that the feedrate curve has enough rising space. Subsequently, to obtain the near time-optimal feedrate, the local search PSO (LSPSO) algorithm within the moving window is developed to locally adjust the non-uniformly inserted control points. Compared with the existing methods, the HFS method is beneficial to further optimize the machining time with a faster computation speed, and ensure the stability of the robot machining. Finally, simulations and experiments on the developed TriMule-800 hybrid robot verify the effectiveness of this method.

Fitting Terrestrial Laser Scanner Point Clouds with T-Splines: Local Refinement Strategy for Rigid Body Motion

T-splines have recently been introduced to represent objects of arbitrary shapes using a smaller number of control points than the conventional non-uniform rational B-splines (NURBS) or B-spline representatizons in computer-aided design, computer graphics and reverse engineering. They are flexible in representing complex surface shapes and economic in terms of parameters as they enable local refinement. This property is a great advantage when dense, scattered and noisy point clouds are approximated using least squares fitting, such as those from a terrestrial laser scanner (TLS). Unfortunately, when it comes to assessing the goodness of fit of the surface approximation with a real dataset, only a noisy point cloud can be approximated: (i) a low root mean squared error (RMSE) can be linked with an overfitting, i.e., a fitting of the noise, and should be correspondingly avoided, and (ii) a high RMSE is synonymous with a lack of details. To address the challenge of judging the approximation, the reference surface should be entirely known: this can be solved by printing a mathematically defined T-splines reference surface in three dimensions (3D) and modeling the artefacts induced by the 3D printing. Once scanned under different configurations, it is possible to assess the goodness of fit of the approximation for a noisy and potentially gappy point cloud and compare it with the traditional but less flexible NURBS. The advantages of T-splines local refinement open the door for further applications within a geodetic context such as rigorous statistical testing of deformation. Two different scans from a slightly deformed object were approximated; we found that more than 40% of the computational time could be saved without affecting the goodness of fit of the surface approximation by using the same mesh for the two epochs.

Automated calculation of the profile of a disk cutter for the manufacture of helical grooves

The calculation of the profile of disk cutters, excluding undercutting for any complex profile of the helical groove, is proposed. The feature of the method is in the fact that the profile is specified by a small number of control points, which, using interpolation, is increased by tens or hundreds of times. The rational profile of the cutter is investigated depending on its three setting parameters. A numerical experiment was carried out for the profile of the cutter with the optimization of the setting parameters. Keywords: disk cutter, profile, helical groove, computer-aided design, calculation zov20@mail.ru

Comparison of spatial and temporal interaction techniques for 3D audio trajectory authoring

With the popularity of immersive media, developing usable tools for content development is important for the production process. In the context of 3D audio production, user interfaces for authoring and editing 3D audio trajectories enable content developers, composers, practitioners, and recording and mixing engineers to define how audio sources travel in time. However , common interaction techniques in 3D audio production tools can make the workflow of this task tedious and difficult to accomplish. This study investigates this problem by classifying the atomic tasks (spatially and temporally) of a general composite task of authoring 3D audio trajectories and then evaluating different interaction techniques across these tasks. Common graphical user interfaces were compared with input devices having varying degrees-of-freedom for spatial atomic tasks in order to investigate the effect of direct manipulation and integrality of interaction techniques. Continuous and discrete interaction techniques were compared for temporal tasks in order to investigate the effect of direct manipulation. Results suggest that interaction techniques with high degrees of integrality and direct manipulation reduce task completion time compared to standard GUI techniques. The design of temporal tasks can create a visual bias, and discrete-time controls can be a suitable method for traversing a small number of control points. These results and further observations provide directions on the study of interaction technique design for 3D audio tools, which in turn should improve workflows of 3D audio content creation.

Method for assessing the adequacy of a crankshaft strain state model

Using the Finite Element Method (FEM) in the SolidWorks software environment, the strain crankshaft state is modelled. The assessment of the adequacy of the model by experimental crankshaft in a running engine is complex and is possible for a small number of control points. The method shown proposes to replace the variable crankshaft strains in motion by examining a static strain state of the crankshaft. The results obtained show a high degree of adequacy of the model. The differences can be minimised by specifying the physical properties of the material used in the simulation, taking into account the elasticity of the supports.

Non-rigid registration of serial section images by blending transforms for 3D reconstruction

In this research, we propose a novel registration method for three-dimensional (3D) reconstruction from serial section images. 3D reconstructed data from serial section images provides structural information with high resolution. However, there are three problems in 3D reconstruction: non-rigid deformation, tissue discontinuity, and accumulation of scale change. To solve the non-rigid deformation, we propose a novel non-rigid registration method using blending rigid transforms. To avoid the tissue discontinuity, we propose a target image selection method using the criterion based on the blending of transforms. To solve the scale change of tissue, we propose a scale adjustment method using the tissue area before and after registration. The experimental results demonstrate that our method can represent non-rigid deformation with a small number of control points, and is robust to a variation in staining. The results also demonstrate that our target selection method avoids tissue discontinuity and our scale adjustment reduces scale change.

Lunar Brightness Temperature Map and TB Distribution Model

The microwave radiometer (MRM) on-board the Chinese Chang’e-2 (CE-2) lunar probe measures the lunar brightness temperature (also referred to as TB) data that are large-scale scientific data. In order to construct lunar TB map, the optimized hierarchical MK splines method is proposed, which uses a hierarchy of coarse-to-fine control lattices to generate a fine control lattice. The computation of the TB construction function is limited to the small number of control points in the merged control lattice, and then the desired high-resolution TB maps are constructed. At the same time, some basis relations between the lunar TB and frequencies are also analyzed based on the constructed TB maps. It can be found that the high-frequency TB map shows lunar topographic features with close similarity. Furthermore, to express the TB distribution features quantitatively, the lunar TB distribution models, including the global TB model of the Moon, the TB model of the lunar far side, and the TB model of the lunar near side, are established based on the constructed TB maps, and the obtained TB distribution models are log-normal distributions. The establishment of the lunar TB distribution model is important to reasonably select the color layer and intensity of color for the lunar TB maps, and is helpful for studying the lunar TB distribution law. In addition, the topographic data measured by the lunar orbiter laser altimeter are selected to discuss the influence of elevation on the lunar TB, and the CE-2 TB data combined with the FeO and TiO2 abundances are used to study the microwave thermal emission features of the lunar regolith. The research results have important implications for studying the thermal radiation of the Moon.

FasTFit: A fast T-spline fitting algorithm

T-spline has been recently developed to represent objects of arbitrary shapes using a smaller number of control points than the conventional NURBS or B-spline representations in computer aided design, computer graphics, and reverse engineering. However, existing methods for fitting a T-spline over a point cloud are slow. By shifting away from the conventional iterative fit-and-refine paradigm, we present a novel split-connect-fit algorithm to more efficiently perform the T-spline fitting. Through adaptively dividing a point cloud into a set of B-spline patches, we first discover a proper topology of T-spline control points, i.e., the T-mesh. We then connect these B-spline patches into a single T-spline surface with different continuity options between neighboring patches according to the data. The T-spline control points are initialized from their correspondences in the B-spline patches, which are refined by using a conjugate gradient method. In experiments using several types of large-sized point clouds, we demonstrate that our algorithm is at least an order of magnitude faster than state-of-the-art algorithms while provides comparable or better results in terms of quality and conciseness.

Storage-efficient reconstruction framework for planar contours

A storage-efficient reconstruction framework for cartographic planar contours is developed. With a smaller number of control points, we aim to calculate the area and perimeter as well as to reconstruct a smooth curve. The input data forms an oriented contour, each control point of which consists of three values: the Cartesian coordinates (x, y) and tangent angle θ. Two types of interpolation methods are developed, one of which is based on an arc spline while the other one is on a cubic Hermite spline. The arc spline-based method reconstructs a G1 continuous curve, with which the exact area and perimeter can be calculated. The benefit of using the Hermite spline-based method is that it can achieve G2 continuity on most control points and can obtain the exact area, whereas the resulting perimeter is approximate. In a numerical experiment for analytically defined curves, more accurate computation of the area and perimeter was achieved with a smaller number of control points. In another experiment using a digital elevation model data, the reconstructed contours were smoother than those by a conventional method.

Horizon volumes with interpreted constraints

Horizons are geologically significant surfaces that can be extracted from seismic images. Color coding of horizons based on amplitude or other attributes can help reveal ancient sedimentary environments and structural features. Extracted horizons are also used for building structure models and stratigraphic interpretations. We propose two methods for constructing seismic horizons aligned with reflectors in a 3D seismic image. The first method generates horizons one at a time; the second method generates an entire volume of horizons at once by first computing a relative geologic time volume from seismic normal vectors. Rather than gradually building a horizon by extending one or more seed points to a surface along seismic reflectors, both of our methods generate whole horizons at once by solving partial differential equations derived from seismic normal vectors. The most significant new aspect of both methods is the ability to specify, perhaps interactively during interpretation, a small number of control points that may be scattered throughout a 3D seismic image. Experiments revealed that with our method, control points enable the extraction of more accurate horizons from seismic images in which noise, unconformities, and faults are apparent. These points represent constraints that we implemented as preconditioners in the conjugate gradient method used to construct horizons.

NURBS Curve Extraction from 2D Laser Sensor Data and 3D Simulated Data

This paper proposes a non-uniform rational B-spline (NURBS) curve extraction algorithm from 2D laser sensor data and 3D simulated data. In robot localization and mapping application, the raw sensor data cannot be stored due to its need of large storage space. However, only a small number of control points of NURBS curve are needed to be stored to recover the geometrical feature of raw data. To comprise the number of control points and accuracy of the extracted curve, global approximation method is adopted to minimize the error between the raw data and the extracted curve. In extraction process, all the weights are set as one firstly. After find the control points, a weight calculation method is developed to update the weight values. The NURBS curve with new weight has smaller error than with original weights. Finally, NURBS curve extraction results from real 2D laser sensor data and 3D simulated data are shown to check the feasibility of proposed algorithms.

A comprehensive system for facial animation of generic 3D head models driven by speech

A comprehensive system for facial animation of generic 3D head models driven by speech is presented in this article. In the training stage, audio-visual information is extracted from audio-visual training data, and then used to compute the parameters of a single joint audio-visual hidden Markov model (AV-HMM). In contrast to most of the methods in the literature, the proposed approach does not require segmentation/classification processing stages of the audio-visual data, avoiding the error propagation related to these procedures. The trained AV-HMM provides a compact representation of the audio-visual data, without the need of phoneme (word) segmentation, which makes it adaptable to different languages. Visual features are estimated from the speech signal based on the inversion of the AV-HMM. The estimated visual speech features are used to animate a simple face model. The animation of a more complex head model is then obtained by automatically mapping the deformation of the simple model to it, using a small number of control points for the interpolation. The proposed algorithm allows the animation of 3D head models of arbitrary complexity through a simple setup procedure. The resulting animation is evaluated in terms of intelligibility of visual speech through perceptual tests, showing a promising performance. The computational complexity of the proposed system is analyzed, showing the feasibility of its real-time implementation.

Constrained optimization of the shape of a wave energy collector by genetic algorithm

Wave energy extraction requires the conversion of the energy within the waves to drive the power take off system, often by means of a principal interface, or collector. This paper describes part of the development of a robust, systematic method of optimizing the collector shape to improve energy extraction using a genetic algorithm. The collector geometry uses a parametric description based upon bi-cubic B-spline surfaces, generated from a relatively small number of control points to reduce the dimensionality of the search space. The collector shapes that are optimized have one plane of symmetry and move in one degree of freedom (surge). Each candidate shape is assessed in a wave climate based upon data from a site in the North-East Atlantic Ocean. Three cost functions, distinguished by the severity of the penalty put on the size of the candidate collectors, and four constraint regimes, defined by two displacement and two power rating limits, are the governing influences on the twelve optimization procedures described. The selected collector shapes from each optimization run are appraised in terms of size, complexity and their performance compared to that of ‘benchmark’ box-shaped collectors.

Medial design of blades for hydroelectric turbines and ship propellers

We present a method for constructing blades of hydroelectric turbines and ship propellers based on design parameters that possess a clear hydraulic meaning. The design process corresponds to the classical construction of a blade using the medial surface of the blade and profile curves attached to it. The main new contribution of the paper consists in realizing this construction using B-spline techniques. In particular, it is shown how to obtain blade boundary surfaces (which describe the pressure and the suction side of the blade) which are joined with C1-smoothness along the leading edge. Moreover, special attention is paid to the construction of propeller blades with a well-defined tangent plane at the tip, which is a singular point of the blade boundary surfaces. In order to guarantee these smoothness properties, we generate and analyze singularly parameterized medial surfaces. We contribute novel shape modeling techniques that are based on singular parameterizations and demonstrate their potential for applications in industry. Finally, it is shown how to represent the blades as B-spline surfaces with a relatively small number of control points.