Catmull-Rom Spline Research Articles

Yarn-level modeling and simulation of fancy weft-knitted fabric

Weft-knitted fabric is formed by interlocking loops, which results in an unstable and easily deformable structure. In particular, fancy weft-knitted fabric exhibits diverse structural variations and uneven distribution, leading to more prominent characteristics of instability and deformation. Achieving the desired pattern effect and dimensions often requires drawing multiple designs. In this work, to obtain the geometric model of fancy fabric, mesh-loop models with movement vectors are established based on the basic structure of four stitch types: plain stitch, tuck, float, and loop transfer. The cubic Catmull–Rom spline curves are used to fit the geometric centerline of the yarn. The movement vectors are used to represent the changes in the position of the key points of the standard loops in the fancy fabric, which are derived from the analysis of the pattern grid. A physical model is established based on the force analysis of the yarn, and the positions of yarn control points are determined by solving the Euler–Lagrange dynamic equations. Through iterative calculations, the deformation effects of the fabric are obtained, enabling the simulation of fancy weft-knitted fabric. The proposed algorithms were implemented using Visual C++. The reliability and accuracy of the simulation method are demonstrated by comparing the contours of the simulation results with the actual samples.

The quartic Catmull–Rom spline with local adjustability and its shape optimization

Parametric interpolatory curves play a vital part in geometric modeling. Cubic Catmull–Rom spline is a well-known tool for constructing parametric interpolatory curves, but it cannot be modified once its control points are fixed. We propose a novel quartic Catmull–Rom spline with free parameters to tackle this issue. The quartic Catmull–Rom spline owns shape adjustability based on inheriting the features of the cubic Catmull–Rom spline. Some modeling examples show that the shape of the quartic Catmull–Rom spline can realize both global adjustment and local adjustment by changing the free parameters. In addition, we give three schemes for optimizing the shape of the quartic Catmull–Rom spline, which can generate the spline with minimal internal energy, the shape-preserving spline, and the monotonicity-preserving spline. Numerical examples indicate that the proposed schemes are effective and the quartic Catmull–Rom spline is more practical than the cubic Catmull–Rom spline in data interpolation.

Conversion Between Cubic Bezier Curves and Catmull\u2013Rom Splines

Splines are one of the main methods of mathematically representing complicated shapes, which have become the primary technique in the fields of Computer Graphics (CG) and Computer-Aided Geometric Design (CAGD) for modeling complex surfaces. Among all, Bézier and Catmull–Rom splines are the most common in the sub-fields of engineering. In this paper, we focus on conversion between cubic Bézier and Catmull–Rom curve segments, rather than going through their properties. By deriving the conversion equations, we aim at converting the original set of the control points of either of the Catmull–Rom or Bézier cubic curves to a new set of control points, which corresponds to approximately the same shape as the original curve, when considered as the set of the control points of the other curve. Due to providing simple linear transformations of control points, the method is very simple, efficient, and easy to implement, which is further validated in this paper using some numerical and visual examples.

Направленные сплайны и их использование для сглаживания выбросов и изломов интерполянта

A method for constructing a directional cubic spline for a set of points on a plane is formulated and proposed. The spline is compared with the Schoenberg B-spline, Akima and Catmull–Rom splines. It is shown that for unequally spaced points, in comparison with the B-spline, it gives significantly lower overshoots and is practically free of strong kinks, which are characteristic of Akima splines. The spline does not give loops and oscillations, which are a characteristic drawback of parametric splines, in particular, Hermitian ones, which include the Catmull–Rom spline. A fast method for optimizing the spline guiding coefficient is proposed, the purpose of which is to minimize the discontinuities of the second derivative of the function at its intermediate points. An example of optimization of a directional third-order spline is given. A fourth-order directional spline, which is free of kinks, is also proposed. The method of optimization of the directional spline of the fourth order is formulated, the algorithm of its optimization is stated. The optimization criteria are the spline length and the smallest distance between its global maximum and minimum. It is shown that, in comparison with the Schoenberg spline, the fourth-order directional spline has smaller outliers. A method for automatic blunting of sharp peaks of curves is proposed, which can be applied to all types of splines.

Task Space Trajectory Planning for Robot Manipulators to Follow 3-D Curved Contours

The demand for robots has increased in the industrial field, where robots are utilized in tasks that require them to move through complex paths. In the motion planning of a manipulator, path planning is carried out to determine a series of the positions of robot end effectors without collision. Therefore, it is necessary to carry out trajectory planning to determine position, velocity, and acceleration over time and to control an actual industrial manipulator. Although several methods have already been introduced for point-to-point trajectory planning, a trajectory plan which moves through multiple knots is required to allow robots to adapt to more complicated tasks. In this study, a trajectory planning based on the Catmull–Rom spline is proposed to allow a robot to move via several points in a task space. A method is presented to assign intermediate velocities and time to satisfy the velocity conditions of initial and final knots. To optimize the motion of the robot, a time-scaling method is presented to minimize the margin between the physical maximum values of velocity and acceleration in real robots and the planned trajectory, respectively. A simulation is then performed to verify that the proposed method can plan the trajectory for moving multiple knots without stopping, and also to check the effects of control parameters. The results obtained show that the proposed methods are applicable to trajectory planning and require less computation compared with the cubic spline method. Furthermore, the robot follows the planned trajectory, and its motion does not exceed the maximum values of velocity and acceleration. An experiment is also executed to prove that the proposed method can be applied to real robotic tasks to dispense glue onto the sole in the shoe manufacturing process. The results from this experiment show that the robot can follow the 3-D curved contour in uniform speed using the proposed method.

Shape optimisation of the sharp-heeled Kaplan draft tube: Performance evaluation using Computational Fluid Dynamics

Abstract A methodology to assess the performance of an elbow-type draft tube is outlined. This was achieved using Computational Fluid Dynamics (CFD) to evaluate the pressure recovery and mechanical energy losses along a draft tube design, while using open-source and commercial software to parameterise and regenerate the geometry and CFD grid. An initial validation study of the elbow-type draft tube is carried out, focusing on the grid-regeneration methodology, steady-state assumption, and turbulence modelling approach for evaluating the design’s efficiency. The Grid Convergence Index (GCI) technique was used to assess the uncertainty of the pressure recovery to the grid resolution. It was found that estimating the pressure recovery through area-weighted averaging significantly reduced the uncertainty due to the grid. Simultaneously, it was found that this uncertainty fluctuated with the local cross-sectional area along the geometry. Subsequently, a study of the inflow cone and outer-heel designs on the flowfield and pressure recovery was carried out. Catmull-Rom splines were used to parameterise these components, so as to recreate a number of proposed designs from the literature. GCI analysis is also applied to these designs, demonstrating the robustness of the grid-regeneration methodology.

An optimized yarn-level geometric model for Finite Element Analysis of weft-knitted fabrics

Knitted fabrics are widely used in clothing because of their distinctive ability to be shaped and formed, which is fundamentally different from the behavior of woven cloth. Since stitches produce complex interactions between yarns, the macroscopic behavior of knitted fabrics depends more on their loop structure and stitch patterns than on the physical properties of the yarn. In order to explore the unique mechanical properties of knitted textiles we have developed a yarn-level model for weft-knitted fabrics that can be used in Finite Element Analysis (FEA) simulations. Producing geometric models of yarns in a knitted material is framed as an optimization problem. In this computing context, a single “cost” function is defined that captures the various required features of the final geometric model. The function is specified in such a way that finding the variable values that results in a minimum function evaluation produces the desired geometric result. The centerlines of the fabric's yarns are defined as Catmull-Rom splines, and the cost function is minimized by adjusting the locations of the spline's control points. The optimization is based on physical parameters such as yarn interpenetration, length of the yarn and bending energy. The optimized models are written to a file which can be directly read by an FEA software. The results show that our approach can create yarn-level models of weft-knitted fabrics consisting of an arbitrary pattern of knit and purl stitches, with a range of sizes, that are suitable for FEA simulations.

Semi-Automated Generation of Road Transition Lines Using Mobile Laser Scanning Data

This paper recognizes the research gaps and difficulties in generating transition lines (the paths that pass through a road intersection) in road intersections from mobile laser scanning (MLS) point clouds. The proposed method contains three modules: road surface detection, lane marking extraction, and transition line generation. First, the points covering the road surface are extracted using the voxel-based upward growing and the improved region growing. Then, lane markings are extracted and identified according to the multi-thresholding and the geometric filtering. Finally, transition lines are generated through a combination of the lane node structure generation algorithm and the cubic Catmull–Rom spline algorithm. The experimental results demonstrate that transition lines can be successfully generated for both T- and cross-intersections with promising accuracy. In the validation of lane marking extraction using the manually interpreted lane marking points, the method can achieve average precision, recall, and F1-score of 90.80%, 92.07%, and 91.43%, respectively. The success rate of transition line generation is 96.5%. Furthermore, the buffer-overlay-statistics (BOS) method validates that the proposed method can generate lane centerlines and transition lines within 20-cm-level localization accuracy from the MLS point clouds.

Evaluation of Methods of Interpolation (Existing and Proposed) using Monte Carlo Simulation Technique and Delete-D Jackknife Method

It is possible to encounter missing value in a research. Missing value may be as a result of none response in primary data collection or unavailability of data in the case of secondary data. It may occur within a set of observations or at the tail end of the observations. The paper addresses missing value within a set of observations (interpolation). Existing methods considered are linear, log-linear, Catmull-Rom spline and cardinal spline and a method of estimating missing value is presented. For evaluation of the methods, random data are simulated using Monte Carlo simulation approach and analytical approach is used to determine the most effective method. Among the findings, linear, log-linear and the proposed method give high precision estimate compare to the CS and CSR methods. With the use of tension parameter, CS is better than CSR method.

Automated Extraction of Driving Lines from Mobile Laser Scanning Point Clouds

Abstract. This paper presents a novel approach to automated generation of driving lines from mobile laser scanning (MLS) point cloud data. The proposed method consists of three steps: road surface segmentation, road marking extraction and classification, and driving line generation. The voxel-based upward-growing algorithm was firstly used to extract ground points from the raw MLS point clouds followed by segmentation of road surface using a region-growing algorithm. Then, the statistical outlier removal filter was applied to separate and refine the road marking points followed by extracting and classifying the lane markings based on the geometric features of different road markings using empirical hierarchical decision trees. Finally, land node structures were constructed followed by generation of driving lines using a curve-fitting algorithm. The proposed method was tested on both circular road sections and irregular intersections. The smoothing spline curve fitting model was tested on the circular road sections, while the Catmull-Rom spline with five control points was used to generate the driving lines at road intersections. The overall performance of the proposed algorithms is promising with 96.0% recall, 100.0% precision, and 98.0% F1-score for the lane marking extraction specifically. Most significantly, the validation results demonstrate that the driving lines can be effectively generated within 20 cm-level localization accuracy at an average of 3.5% miscoding using MLS point clouds, which meets the requirement of localization accuracy of fully autonomous driving functions. The results demonstrate the proposed methods can successfully generate road driving lines in the test datasets to support the development of high-definition maps.

Identification of distributed dynamic excitation based on Taylor polynomial iteration and cubic Catmull–Rom spline interpolation

ABSTRACTThis paper devotes to identifying the distributed dynamic excitation in time domain via a comprehensive algorithm combining Taylor polynomial iteration and cubic Catmull–Rom spline interpolation. Under the premise of obtaining structural characteristic and node response, Taylor polynomial iteration algorithm is introduced to reconstruct the distributed force amplitudes in node positions of a simple supported beam. Then the load amplitudes at nodes are used as control points, thereby cubic Catmull–Rom spline is adopted to interpolate the complete spatial course of distributed dynamic load along the whole beam. Numerical examples illustrate that the integration method is able to acquire relatively accurate identification result of distributed force. Furthermore, noise immunity of this method is investigated and it displays a strong anti-noise performance.

Fast Cylinder Shape Matching Using Random Sample Consensus in Large Scale Point Cloud

In this paper, an algorithm is proposed that can perform cylinder type matching faster than the existing method in point clouds that represent space. The existing matching method uses Hough transform and completes the matching through preprocessing such as noise filtering, normal estimation, and segmentation. The proposed method completes the matching through the methodology of random sample consensus (RANSAC) and principal component analysis (PCA). Cylindrical pipe estimation is based on two mathematical models that compute the parameters and combine the results to predict spheres and lines. RANSAC fitting computes the center and radius of the sphere, which can be the radius of the cylinder axis and finds straight and curved areas through PCA. This allows fast matching without normal estimation and segmentation. Linear and curved regions are distinguished by a discriminant using eigenvalues. The linear region is the sum of the vectors of linear candidates, and the curved region is matched by a Catmull–Rom spline. The proposed method is expected to improve the work efficiency of the reverse design by matching linear and curved cylinder estimation without vertical/horizontal constraint and segmentation. It is also more than 10 times faster while maintaining the accuracy of the conventional method.

Automatic Annotation and Segmentation of Object Instances With Deep Active Curve Network

Object instance segmentation is a challenging task in computer vision research, and instance annotation is its key sub-task and a basic component of segmentation models. In this paper, we propose the Deep Active Curve Network (DACN) which combines powerful ResNet models with GCN-based active curves. This new method regards instance segmentation as a points/vertices, edges and object masks prediction task instead of only a pixel-labeling problem. The multi-scale encoder firstly predicts a coarse result through a combination of the edge and segmentation features in a multi-task learning framework, which is effective dealing with objects with rough boundaries. In order to generate an accurate object annotation, an iterative Graph Convolutional Network (GCN) is used to correct the encoder’s feature map and move all vertices of the predicted coarse result to the edge of the corresponding ground truth. A novel weighted loss function further estimates the location of points, edges, and segmented areas, and optimizes the annotation results. Finally, we use the improved 5-interpolation Catmull-Rom spline (CRS) algorithm which exploits key points to control the active curves around objects. In the experimental analysis, we demonstrate the effectiveness of our proposed method on three datasets in automatic mode, including Cityscapes, ADE20K and Rooftop. We further show the generalization ability of our approach on two novel cross-domain datasets.

Using 3D Mobile Mapping to Evaluate Intersection Design Through Drivers’ Visual Perception

At intersections, road features related to different maneuvers, such as left-turn, right-turn, and central channelization (i.e., guidelines and channelized islands), are widely used to decrease the traffic conflicts and improve the safety and mobility of traffic. However, there are several main problems related to channelization design at intersections, including poor recognizability, unreasonable entering speed, insufficient sight distance, and relatively low merging speed. To address these problems, this paper focused on developing a method to assess how to design intersection features by dividing the driving process through intersections into four stages: “appearance of channelization,” “beginning of channelization,” “middle of channelization,” and “end of channelization.” Drivers' visual lane models were established based on the Catmull-Rom spline to quantify visual road information perceived by drivers. Shape parameters and three characteristic regions were extracted from these models. The naturalistic driving experiments and 3D mobile mapping experiments were conducted at intersections with channelized islands or guidelines. Driving speed distributions in the four stages were found to obey normal distributions and could be calculated by shape parameters with Bayesian inference. Then, 3D mobile mapping was used as a substitute for extensive naturalistic driving experiments to obtain drivers' visual perception from all possible visual angles. An evaluation method on intersection design was built and used to identify which stage of channelization needs to be modified. This new method helps to enhance the safety and efficiency of intersections.

Curvature Variation Minimizing Cardinal Spline Curves

Since the free parameter and the two auxiliary points have effect on the shape of the Cardinal spline curves, a natural idea arises to find the optimal parameter and auxiliary points to obtain the smoothest curves. We use curvature variation minimization to achieve this goal in this paper. By minimizing an appropriate approximation of the curvature variation energy, the unique solution can be easily obtained. Some examples show that the Cardinal spline curves with minimum curvature variation are better than the Catmull-Rom spline curves in dealing with interpolation problems.

An improved signal envelope estimation method for analysis of acoustic signals emitted by remotely piloted helicopters

This study presents a new signal envelope estimation method in order to improve the performance of the Empirical Mode Decomposition (EMD), especially in dealing with transient signals. An important application of this method is the analysis of signals containing spikes such as acoustic signals. For this purpose, both the spline interpolation and control point selection algorithm are adapted. To construct signal envelopes, the Catmull-Rom spline interpolation is employed due to its desired features. Also, a new algorithm is utilized in order to select control points prior to the iterative sifting process. Afterward, the proposed method is verified by some benchmark signals. Performance indices indicate that the proposed EMD outperforms the traditional one in handling transient signals. Finally, the proposed method is applied to acoustic signals gathered during some flight tests of a remotely piloted helicopter. The results demonstrate that the proposed method is able to isolate acoustic signals emitted by dissimilar sources.

A Novel WebVR-Based Lightweight Framework for Virtual Visualization of Blood Vasculum

With the arrival of the Web 2.0 era and the rapid development of virtual reality (VR) technology in recent years, WebVR technology has emerged as the combination of Web 2.0 and VR. Moreover, the concept of “WebVR + medical science” is also proposed to advance medical applications. However, due to the limited storage space and low computing capability of Web browsers, it is difficult to achieve real-time rendering of large-scale medical vascular models on the Web, let alone large-scale vascular animation simulations. The framework proposed in this paper can achieve virtual display of the medical blood vasculum, including lightweight processing of the vasculum and virtual realization of blood flow. This innovative framework presents a simulation algorithm for the virtual blood path based on the Catmull–Rom spline. The mechanisms of progressive compression and online recovery of the lightweight vascular structure are further proposed. The experimental results show that our framework has a shorter browser-side response time than existing methods and achieves efficient real-time simulation.

Rapid Construction of Virtual Scenes for Large-Scale Crops Distribution

With the development of computer hardware and virtual reality technology and its head-mounted display (HMD), the scale of the virtual environment that it can simulate is also growing, and related fields include forest simulation, virtual agriculture simulation and so on. However, it is urgent to solve the problem of slow construction speed of the scenes which include different kinds of three-dimensional models in the engineering practice. Aiming at the problem of crops planting by blocks in regular regions, a virtual scene construction method based on improved K-means clustering algorithm is proposed. For crops planting problems in irregular regions, we adapt the idea of visually adjusting the key points in regional boundaries to determine the region of planting crops in the virtual environment, proposing a rapid construction method of virtual scene based on Catmull-Rom Spline and Even-Odd Algorithm.

The Synchronization of Data Collection for Real-time Group Recognition

It is commonplace for people to perform various kinds of activities in groups. The recognition of groups is of importance in many applications including crowd evacuation, teamwork coordination, and advertising for groups. Existing group recognition approaches require snapshots of human trajectories, which is often impossible in real life situation due to the differences of data collection start time and frequency. This paper proposes an approach to synchronize the trajectory data of people by interpolation based on Catmull-Rom Spline. The optimal interpolating points are computed based on our proposed error function. Moreover, we propose an approach to assign the groups proper colors and then uses the hot map to show the dynamic changes of groups graphically. A real-life data set is used to validate the effectiveness of the proposed approach. The results show that 97.9% accuracy of group recognition can be achieved and the dynamic changes of groups is well shown.

Automatic Spine Tissue Segmentation from MRI Data Based on Cascade of Boosted Classifiers and Active Appearance Model.

The study introduces a novel method for automatic segmentation of vertebral column tissue from MRI images. The paper describes a method that combines multiple stages of Machine Learning techniques to recognize and separate different tissues of the human spine. For the needs of this paper, 50 MRI examinations presenting lumbosacral spine of patients with low back pain were selected. After the initial filtration, automatic vertebrae recognition using Cascade Classifier takes place. Afterwards the main segmentation process using the patch based Active Appearance Model is performed. Obtained results are interpolated using centripetal Catmull–Rom splines. The method was tested on previously unseen vertebrae images segmented manually by 5 physicians. A test validating algorithm convergence per iteration was performed and the Intraclass Correlation Coefficient was calculated. Additionally, the 10-fold cross-validation analysis has been done. Presented method proved to be comparable to the physicians (FF = 90.19 ± 1.01%). Moreover results confirmed a proper algorithm convergence. Automatically segmented area correlated well with manual segmentation for single measurements () and for average measurements () with p = 0.05. The 10-fold cross-validation analysis (FF = 91.37 ± 1.13%) confirmed a good model generalization resulting in practical performance.