Control Points Research Articles

Adaptive B-spline curve fitting with minimal control points using an improved sparrow search algorithm for geometric modeling of aero-engine blades

Adaptive B-spline curve fitting with minimal control points using an improved sparrow search algorithm for geometric modeling of aero-engine blades

Development of rational compositions for multicomponent juices based on melon crops

This study objects are juices from melon, watermelon, and pumpkin, as well as additives from apples, plums, pears, bell peppers, beets, carrots, aloe, melissa, and nettle. The problem addressed is minimizing melon crop losses. The research relevance stems from the need to reduce these losses. The development of multicomponent juices is aimed at the more efficient utilization of melon crops, contributing to the minimization of crop losses. Optimal component proportions were determined using sensory evaluation of organoleptic characteristics on a 5-point scale. The results showed that juice compositions with optimal component proportions have high organoleptic qualities and functional orientation. For melon juice, the optimal ratio was as follows: melon juice – 55 %, apple juice – 30 %, green bell pepper juice – 10 %, aloe juice – 5 %. For watermelon juice: watermelon juice – 65 %, plum juice – 25 %, beet juice – 5 %, melissa juice – 5 %. For pumpkin juice: pumpkin juice – 60 %, pear juice – 20 %, carrot juice – 15 %, nettle juice – 5 %. Critical control point (CCP) analysis was conducted at each production stage, from raw material acceptance to packaging and storage of the final product. This analysis identified potential risks and established control measures to minimize them. Developing multicomponent juices based on melon crops with plant-based enriching additives allows the creation of products with high organoleptic qualities and functional orientation, contributing to efficient use of melon crops and reducing crop losses. Implementing the HACCP system at all production stages ensures product safety and high quality. This research offers a practical approach for the food industry to produce high-quality, functional beverages that maximize crop yields and ensure consumer safety

Analyzing the Combined Effects of Axial Loads and Bending Moments on Unequal-Angle Steel Members

Angle steel is commonly used in inclined bracing components such as transmission towers. Due to its inherent section characteristics, unequal angle steel undergoes angular rotation when subjected to eccentric axial pressure, resulting in a change in the direction of action along the X and Y axes. In comparison to equal angle steel, the analysis of unequal angle steel is more complex. In design, particular attention should be given to whether the angle steel section is compact or noncompact, with a significant emphasis on the impact of the width-to-thickness ratio on strength. In study analyzed nine different angle steel sections, revealing that two of them exhibit a phenomenon known as control point transfer. This is especially prone to occur with shorter lengths of angle steel components, leading to Leg Local Buckling. In contrast, longer components are more susceptible to Lateral-Torsional Buckling. Summarizing the research findings, it is recommended to exercise caution when using non-compact section angle steel in design, and a preference for compact sections is advised to ensure the safety of the structure. Furthermore, it is advised to pay attention to the parameter βw in the AISC unequal angle steel calculation formula and adhere to relevant specifications to enhance the accuracy and reliability of structural design.

The post-viral GPNMB+ immune niche persists in long-term Covid, asthma, and COPD.

Epithelial injury calls for a regenerative response from a coordinated network of epithelial stem cells and immune cells. Defining this network is key to preserving the repair process for acute resolution, but also for preventing a remodeling process with chronic dysfunction. We recently identified an immune niche for basal-epithelial stem cells using mouse models of injury after respiratory viral infection. Niche function depended on an early sentinel population of monocyte-derived dendritic cells (moDCs) that provided ligand GPNMB to basal-ESC receptor CD44 for reprogramming towards chronic lung disease. These same cell and molecular control points worked directly in mouse and human basal-ESC organoids, but the findings were not yet validated in vivo in human disease. Further, persistence of GPNMB expression in moDCs and M2-macrophages in mouse models suggested utility as a long-term disease biomarker in humans. Here we show increased expression of GPNMB localized to moDC-macrophage populations in lung tissue samples from long-term Covid, asthma, and COPD. The findings thereby provide initial evidence of a persistent and correctable pathway from acute injury to chronic disease with implications for cellular reprogramming and inflammatory memory.

Non-Deterministic and Risk Based Security Services

This paper presents a comprehensive framework to address these challenges. Understanding various social engineering tactics is crucial for effective prevention and detection. Trust based models in entities enable many business objectives that may include speed to market, scalability, decentralization etc However, they also increase the attack surface due to "loose boundaries" between enforcement points or corresponding resource authorization servers and the service orchestration layer. The control points of enforcement are generally static across a spectrum of threat vectors such as Identity, Fraud, Authentication, Authorization, Cyber security and physical security etc. in this paper we propose a "Trust based security framework aka " Interdiction Services" that fundamentally is non-deterministic and risk based. This paper presents a converged security framework towards a comprehensive prevention and detection controls mechanism. The paper proposes a converged security framework that allows various parties from fraud, cyber, and physical security to collaborate but operate independently through a common framework of Interdiction Services.

First-Generation Antihistamines and Seizures in Young Children

The widespread use of antihistamines in children for treatment of common cold symptoms and their central nervous system effects, like drowsiness, underscore the importance of being aware of the associated risks. To assess associations between prescriptions of first-generation antihistamines and seizures in children using a comprehensive and nationwide dataset. This cohort study used a self-controlled case-crossover design. Data were obtained from the National Health Insurance Service database in Korea. Children born between January 1, 2002, and December 31, 2005, who visited the emergency department for seizure events (International Statistical Classification of Diseases and Related Health Problems, Tenth Revision, codes R56.8, G40, and G41) during the follow-up period were included. Follow-up was completed on December 31, 2019, and data were analyzed from June 3, 2023, to January 30, 2024. First-generation antihistamine prescription. Primary outcome consisted of an index seizure event. Odds ratios (ORs) for seizure events were estimated using a conditional logistic regression model, comparing first-generation antihistamine prescription 1 to 15 days before seizure (hazard period) against control period 1 (31-45 days before the event) and control period 2 (61-75 days before the event) using the same period windows. Stratified analyses were conducted to examine the association with individual participant characteristics. Of 11 729 children who had a seizure event, 3178 (1776 [55.9%] boys) were identified as having been prescribed antihistamines during the hazard or the control period, but not both. Seizure events were predominantly observed in children aged 6 to 24 months (985 [31.0%]) and 25 months to 6 years (1445 [45.5%]). During the hazard period, 1476 first-generation antihistamine prescriptions were recorded, in contrast to 1239 and 1278 prescriptions during control periods 1 and 2, respectively. After multiple confounder adjustments, first-generation antihistamine prescription was associated with an increased seizure event risk during the hazard period (adjusted OR [AOR], 1.22 [95% CI, 1.13-1.31]). Stratified subgroup analyses showed consistent results, particularly in children aged 6 to 24 months who were prescribed first-generation antihistamines having a higher risk (AOR, 1.49 [95% CI, 1.31-1.70]) than children aged 25 months to 6 years (AOR, 1.11 [95% CI, 1.00-1.24]; P = .04 for interaction). Furthermore, sensitivity analyses, including adjustment for exposure window periods, evaluation of new first-generation antihistamine prescriptions, comparison of control points from the same period 1 year prior, and exclusion of individuals using combination drugs, confirmed a similarly high risk. In this cohort study, prescriptions for first-generation antihistamines were associated with a 22.0% higher seizure risk in children, especially in those aged 6 to 24 months. These findings emphasize the need for careful and judicious prescription of first-generation antihistamines in young children and underline the need for further research to elucidate associations between antihistamine prescriptions and seizure risk.

Improving mechanical properties of lattice structures using nonuniform hollow struts

In contrast to constant-strut lattices, the introduction of innovative strut designs has the potential to enhance the mechanical properties of lattice structures. This study presents a Bézier curve-based nonuniform section design for body-centered cubic lattices with hollow struts (BCCH). Periodic boundary conditions are applied to the unit cells, and a finite element (FE) numerical homogenization method is employed to assess their elastic properties. A comprehensive dataset is generated through the FE model, which is subsequently divided into training, validation, and testing sets. The coordinates of the Bézier curve control points serve as inputs to deep learning networks, which are trained on the training dataset. Relative density and elastic properties are treated as two distinct networks, with the validation set utilized to prevent overfitting. The objective function consists of two weighted components: one aims to maximize the relative Young's modulus, while the other ensures that the relative density achieves a specified value. An evolutionary algorithm is employed to optimize the objective function, with variations in the control point coordinates constrained to specific ranges. By leveraging the fast inference ability of the deep learning model, the stiffness and orientation-dependent mechanical properties can be efficiently tailored. Our results demonstrate that the optimized structures demonstrate superior stiffness (+92.8 %) and distributed stress field compared to the benchmark lattice. The design method also enables tailoring of specific mechanical properties, including isotropic elasticity. 3D-printed lattice designs were fabricated and compression tests confirmed agreement with simulation results in terms of stiffness. Additionally, the optimized designs exhibit superior strength (+99.6 %) and toughness compared to the benchmark lattices.

How does a superior quality sign guarantee the quality of lamb meat? The Label Rouge case

Owing to the social, environmental and health changes in Europe, meat quality is becoming a critical issue for the long-term future of livestock farming. Label Rouge (LR) is a quality label owned by the French government that identifies food products produced inside or outside the European Union. This label guarantees the superior quality of a product compared with a standard product. This superior quality is guaranteed throughout the production process by specifications negotiated between the Institut National de l’Origine et de la Qualité (INAO) and operators in the sector. These specifications comprise two documents: first, common production conditions that apply to all specifications in a sector, and second, a book of specifications (BoSs). These two documents, which form the qualification mechanism, are divided into several parts: product name, product description, traceability, production method, labelling and the main control points. This study aims to understand how the LR defines lamb meat quality in the 11 existing BoSs using the seven dimensions of quality of animal-source foods (nutritional, sensory, commercial, technological, safety, convenience and image). We performed a computerised qualitative transversal analysis of the commitments associated with the production method and description of the product. This analysis was enriched by five semi-structured interviews with INAO members. We show that although LR is committed to all aspects of lamb meat quality, the sensory, image and carcass commercial quality attributes are predominant. However, the image attribute of quality is so ubiquitous that it required refinement to provide a better understanding of the construction of quality in terms of its environmental, ethical and cultural components.

Microbial co-cultivation: Reaction dynamics of combustible gases bioremediation in goaf

The accumulation of combustible gases in goaf is a key and difficult point in mine disaster prevention and control, which can easily lead to coal mine accidents and seriously safety production. Methanotrophs (S2, T7) and carboxydotrophic bacteria (M13) were extracted from mine environment to cocultivation. The cultivation conditions such as inoculation, temperature, and pH were selected to explore the effects of the growth and metabolic characteristics, and reveal the reaction kinetics of mixed strains (S2/M13, T7/M13). The results showed that the optimal inoculation amount for mixed strains was 5 %, and the maximum range of mixed carbon source inoculation for S2/M13 and T7/M13 were 9.69 % CH4+(7.27–9.69 % CO) and 9.69 % CH4+(4.35–7.27 % CO), the optimal cultivation temperatures were 25, 30 ℃, respectively, and the optimal pH was 7. In addition, the CH4 metabolic rates of S2/M13 and T7/M13 were 72.4 % and 85.4 %, respectively, and the CO metabolic rate reached over 95 % under the above optimal conditions, the processes of growth and metabolism of the mix cultures remained consistent. Moreover, the growth curves of the S2/M13 and T7/M13 conformed to the Logistic model, and whose attenuation coefficients (b) were 0.035, −0.215 d−1, the maximum specific growth rates (umax) were 0.524, 0.862 d−1, respectively. At the same time, the reaction rate of combustible gases showed high consistency in the logarithmic and stationary phases of the mixed strains, and exhibited a good linear relationship with the consumption rate of O2, the inhibitory kinetics of mixed strains on the reaction rate of combustible gases under different cultivation conditions were determined. The research results have vital theoretical and practical significance for the prevention and control of combustible gases and the safe mining in coal mines.

A scoping review on control strategies for Echinococcus granulosus sensu lato.

Cystic echinococcosis (CE) is a widespread neglected zoonotic disease caused by Echinococcus granulosus sensu lato (EG) with a global burden of control in the billions of dollars. E. granulosus' life cycle involves definitive, intermediate, and humans as dead-end hosts. Echinococcosis control programs use strategies that focus on any of these hosts. We aimed to provide a comprehensive and up-to-date overview of the EG control interventions worldwide. We conducted a scoping review by mapping all studies on interventions for EG control following the Arksey and O'Malley Framework. We screened identified articles, and charted and coded selected papers. We classified the data based on target host, type of study, and control mechanism. We described the efficacy or safety outcomes, and the associated barriers/facilitators for the intervention. Critical appraisal was conducted. From 7,853 screened studies, we analyzed 45: seven centered on human interventions, 21 on animals, and 17 on both. Studies on humans focused on educational strategies and human CE monitoring. The studies on animals were field trials and most were based on Praziquantel (PZQ) for dogs. Studies focused on both animals and humans had, in general, more participants, lasted longer, and covered larger geographical areas. Overall, the quality of studies was moderate to low. Available evidence suggests that long-term interventions aimed at both animals and humans can achieve significant reduction in EG transmission, particularly when PZQ treatment for dogs is included. Higher quality evidence, standardization of methodologies, and better reporting on post-intervention outcomes are necessary for drawing stronger conclusions. Further evidence is needed to assess the sustainability and scalability of control measures. Nonetheless, an integrative One Health approach is essential for overcoming the multiple challenges associated with sustaining long-term control efforts for Echinococcosis.

基于S-TEB算法的果园割草机人局部路径规划研究

This paper proposes a local path planning algorithm method named S-TEB (Smooth Time Elastic Band), aimed at fulfilling the requirement of full coverage for ORLMs (Orchard Robotic Lawn Mowers) during mowing operations. Firstly, by analyzing the tracking control mode of ORLMs in operational scenarios, control points are selected reasonably. Subsequently, utilizing B-spline curves, the path is optimized to generate the optimal trajectory and speed for ORLMs that satisfy multiple objectives and constraints. Finally, multiple simulations and field experiments were conducted in actual operational environments, with a speed of 0.6 m/s. Experimental results show that in scenarios involving obstacle avoidance, the minimum distance between the automatic lawnmower and the outer contour of obstacles is 4 cm. Compared to the traditional TEB planning algorithm, there is a 4.23% increase in mowing coverage area. These findings provide theoretical and technical support for local path planning in the operational scenarios of ORLMs.

Predicting bathymetry using multisource differential marine geodetic data with multilayer perceptron neural network

ABSTRACT We propose a method for enhancing the accuracy of bathymetry models based on a multilayer perceptron (MLP) neural network that integrates the differences in multisource marine geodetic data (MMGD) (longitude, latitude, reference bathymetry, slope, the meridional and prime components of vertical deflection, gravity anomaly, vertical gravity gradient, and mean dynamic topography). First, we use the MMGD differences between the shipborne sounding control points within 8′ × 8′ grid points and shipborne sounding control points as input data, as well as the differences between the topo_24.1 model and the measured bathymetric values at the control points as output data to train the MLP model. Second, we feed the input data from the central point of a 1′ × 1′ grid into the MLP model to obtain predictions, and then use the topo_24.1 model to recover the predicted bathymetry at the prediction point. We focus on the Caribbean Sea, and construct a Caribbean Bathymetric Chart of the Oceans (CBCO1) model using MLP neural network. The reliability of MMGD, a CBCO2 model using MMGD, and the reliability and effectiveness of the overall method are demonstrated through comparisons with the CBCO2, GEBCO_2022, topo_24.1, DTU18 models at the checkpoints.

Caputo Fabrizio Bézier Curve with Fractional and Shape Parameters

In recent research in computer-aided geometric design (CAGD), one of the most popular concerns has been the creation of new basis functions for the Bézier curve. Bézier curves with high degrees often overshoot, which makes it challenging to maintain control over the ideal length of the curved trajectory. To get around this restriction, free-form surfaces and curves can be created using the Caputo Fabrizio basis function. In this study, the Caputo Fabrizio fractional order derivative is used to construct the Caputo Fabrizio basis function, which contains fractional parameter and shape parameters. The Caputo Fabrizio Bézier curve and surface are defined using the Caputo Fabrizio basis function, and their geometric properties are examined. Using fractional and shape parameters in the implementation of the Caputo Fabrizio basis function offers an alternative perspective on how the Caputo Fabrizio basis function can construct complicated curves and surfaces beyond a limited formulation. Curves and surfaces can have additional shape and length control by adjusting a number of fractional and shape parameters without affecting their control points. The Caputo Fabrizio Bézier curve’s flexibility and versatility make it more effective in creating complex engineering curves and surfaces.

Avaliação da precisão da técnica Structure from Motion aplicada ao Mapeamento Fotogramétrico de Corredores

The advantages offered by the use of RPA technology combined with the algorithms implemented by the SfM technique and its variants have made Photogrammetry supported by RPA and SfM an economical, fast and widely used solution in various branches of Engineering. Despite many studies on the accuracy achieved in digital cartographic products generated through these technologies, little is discussed about the case of corridors. In this context, the objective of this work is to investigate the positional accuracy achieved in the mapping of a 1.3 km long corridor through the adoption of different amounts of control points and different amounts of lanes. Accuracy assessment was performed based on the Mean Square Error (NDE) values of the checkpoints and trend analysis. The experiments showed that the adoption of control points positioned every five and ten photogrammetric bases can achieve accuracy between 2-2.6 GSD and eliminate planimetric and altimetric statistical trends in the RMSE values of the checkpoints that adopt two or three bands. In addition, the experiments performed showed that increasing the number of bands does not necessarily imply a decrease in the NDE values of checkpoint discrepancies.

Precise Positioning in Nitrogen Fertility Sensing in Maize (Zea mays L.).

This study documented the contribution of precise positioning involving a global navigation satellite system (GNSS) and a real-time kinematic (RTK) system in unmanned aerial vehicle (UAV) photogrammetry, particularly for establishing the coordinate data of ground control points (GCPs). Without augmentation, GNSS positioning solutions are inaccurate and pose a high degree of uncertainty if such data are used in UAV data processing for mapping. The evaluation included a comparative assessment of sample coordinates involving RTK and an ordinary GPS device and the application of precise GCP data for UAV photogrammetry in field crop research, monitoring nitrogen deficiency stress in maize. This study confirmed the superior performance of the RTK system in providing positional data, with 4 cm bias as compared to 311 cm with the non-augmented GNSS technique, making it suitable for use in agronomic research involving row crops. Precise GCP data in this study allow the UAV-based Normalized Difference Red-Edge Index (NDRE) data to effectively characterize maize crop responses to N nutrition during the growing season, with detailed analyses revealing the causal relationship in that a compromised optimum canopy chlorophyll content under limiting nitrogen environment was the reason for reduced canopy cover under an N-deficiency environment. Without RTK-based GCPs, different and, to some degree, misleading results were evident, and therefore, this study warrants the requirement of precise GCP data for scientific research investigations attempting to use UAV photogrammetry for agronomic field crop study.

A modified basis of cubic B-spline with free parameter for linear second order boundary value problems: Application to engineering problems

The traditional cubic B-spline method offers limited local control over the curve solution. Adjusting the position of a control point affects the entire curve, making it challenging to make localized changes, e.g., smoothness. Moreover, the basis functions vanish on one side by the cubic B-spline method near the end conditions where the initial and boundary conditions are applied. To address these limitations, this research proposes a new basis by including a free parameter γ with the purpose of modifying the weights of nearby control points. This free parameter γ can influence the curve’s behavior in specific regions as well as the entire curve. This modification of the cubic B-spline method was used to approximate the second-order derivative at each collocation point. The convergence test showed that the proposed method was second-order convergent. Numerical examples of ordinary differential equations were used with different step values to evaluate the accuracy of the proposed method. The findings persistently indicated that the proposed technique provided better error estimates as compared to the other methods discussed in the literatures.

Enhancing Regional Quasi-Geoid Refinement Precision: An Analytical Approach Employing ADS80 Tri-Linear Array Stereoscopic Imagery and GNSS Gravity-Potential Leveling

This research investigates precision enhancement in regional quasi-geoid refinement through ADS80 tri-linear array scanning stereoscopic imagery for aerial triangulation coupled with GNSS gravity-potential modeling. By acquiring stereoscopic imagery and analyzing triangulation accuracy using an ADS80 camera, we performed this study over the Qinghai–Tibet Plateau’s elevated, desolate terrain, collecting 593 GNSS points following high-precision stereoscopic imagery modeling. By utilizing 12 gravity satellite models, we computed geoid heights and China’s 1985 Yellow Sea elevations for 28 benchmarks and GNSS points, thereby refining the Qinghai Province Quasi-Geoid Model (QPQM) using geometric techniques. The findings reveal that POS-assisted ADS80 stereoscopic imagery yields high-precision triangulation with maximal horizontal and elevation accuracies of 0.083/0.116 cm and 0.053/0.09 cm, respectively, across five control point arrangements. The RMSE of normal heights for 1985, processed via these GNSS points, achieved decimeter precision. By applying error corrections from benchmarks to the 1985 elevation data from gravity satellites and performing weighted averaging, the precision of EGM2008, SGG-UGM-2, and SGG-UGM-1 models improved to 8.61 cm, 9.09 cm, and 9.38 cm, respectively, surpassing the QPQM by 9.22 cm to 9.99 cm. This research demonstrates that the proposed methods can significantly enhance the precision of regional quasi-geoid surfaces. Additionally, these methods offer a novel approach for rapidly establishing regional quasi-geoid models in the uninhabited areas of the Qinghai–Tibet Plateau.

Microbiological safety assessment of restaurants and HACCP-certified kitchens in hotels: A study in eastern China

The Hazard Analysis and Critical Control Point (HACCP) system plays a crucial role in ensuring food safety within food service establishments, effectively reducing the risk of foodborne diseases. This study focused on assessing the risk of microbe contamination in poultry-based cook-served food during meal preparation in four restaurants and five selected HACCP-certified hotels in eastern China. We examined samples collected from 26 poultry-based cooked dishes, 248 food contact surfaces, 252 non-food contact surfaces, and 121 hand swabs. Our findings indicated a favorable trend of compliance with Chinese national standards, as Escherichia coli and Campylobacter were not detected in any cooked food samples. However, the microbiological assessments revealed non-compliance with total plate count standards in 7 % of the cooked samples from restaurants. In contrast, both dine-in hotels and restaurants exhibited significant non-compliance with guidance concerning food and non-food contact surfaces. Furthermore, our study found that chefs' hand hygiene did not meet microbiological reference standards, even after washing. Notably, Campylobacter persisted at 27 % and 30 % on chefs' hands, posing a significant risk of cross-contamination and foodborne diseases. These findings emphasize the urgent necessity for enhanced supervision of hygiene procedures and process monitoring in the HACCP-certified establishments engaged in the preparation and serving of food. Targeted interventions and food safety education for different chef subgroups can enhance food handling practices and reduce the risk of foodborne diseases in independent food establishments.

Obesity-compromised immunity in post-COVID-19 condition: a critical control point of chronicity.

Post-COVID-19 condition is recognized as a multifactorial disorder, with persistent presence of viral antigens, discordant immunity, delayed viral clearance, and chronic inflammation. Obesity has emerged as an independent risk factor for both SARS-CoV-2 infection and its subsequent sequelae. In this study, we aimed to predict the molecular mechanisms linking obesity and post-COVID-19 distress. Viral antigen-exposed adipose tissues display remarkable levels of viral receptors, facilitating viral entry, deposition, and chronic release of inflammatory mediators and cells in patients. Subsequently, obesity-associated inflammatory insults are predicted to disturb cellular and humoral immunity by triggering abnormal cell differentiation and lymphocyte exhaustion. In particular, the decline in SARS-CoV-2 antibody titers and T-cell exhaustion due to chronic inflammation may account for delayed virus clearance and persistent activation of inflammatory responses. Taken together, obesity-associated defective immunity is a critical control point of intervention against post-COVID-19 progression, particularly in subjects with chronic metabolic distress.

Applied for Higher Order Bezier Curve using MATLAB

A Bézier curve is a parametric curve used in computer graphics and related fields. A set of discrete "control points" defines a smooth, continuous curve by means of a formula. The piecewise nature of a Bezier curve means that its representative equation is a linear combination of Bezier of particular degrees. The aim of this study is to infer Bézier curve graphs from higher orders using MATLAB. Where the applied analytical method was used I have reached .Will be clarified, and the following results have been reached is used in the linear curve association to express the distance ( on the line between the points and , In a second-order Bezier curve, we can create intermediate points such as and . These points have a value located in the interval , To obtain a Bezier curve for higher degrees, note that the idea in arriving at drawing the curve is to divide each line by placing a point on it and then connect the new points to each other (note that we get rid of a point at each stage), and we repeat the process until we have only one line left. So, we put ( on it and then we draw the curve. By comparing the manual solution and the solution using MATLAB, we find that the solution using MATLAB is faster and more accurate, especially at higher levels. And the study recommends the following : It is noted that the curve lies completely within the convex closure of the points, so these points are used with ease to form the required curve, it is also possible to apply geometric transformations (such as rotation and sliding) to the curve by applying this transformation to the control points of this curve.