Ending Position Research Articles

중국어권 학습자의 종결표현 ‘-(으)ㄹ 텐데’ 사용 양상 연구

Objectives The purposes of this study were to investigate Chinese-speaking learners’ usage and perception of ’-eultende’, which is used at the end of the sentence, and compared them with the usage and perception of native speakers.
 Methods First, we looked at the explanation of ‘-eultende’ appearing in dictionaries, grammar books, Korean textbooks, and papers. Next, analyze the usage of ‘-eultende’, which is used in the ending position in the learner corpus of the National Institute of the Korean Language. Last, reveal the usage and the perception patterns of ‘-eultende’, which is used in the ending position of the Chinese learners’ usage through a survey.
 Results The result shows that first, Chinese-speaking learners could discriminate the semantic functions of ‘regret’ and ‘regret’ of ‘-eultende’. Second, we found that some Chinese-speaking learners confused expressions of regret and expressions of hope. In particular, in the fill-in-the-blank question, Chinese learners responded with the expression ‘-(었/았/였)으면 좋겠다’which is known as expression of ‘hope’, in a situation expressing ‘regret’, and showed a higher usage rate than native speakers. In addition, we also found that there were some Chinese-speaking learners regarded ‘-eultende’ as the speaker's ‘hope’ or ‘wish’ and ‘-(었/았/였)으면 좋겠다’ as ​​the speaker's ‘regret’. Third, it was shown that in a situation expressing ‘worry’, native speakers preferred ‘-eultende’ more than Chinese-speaking learners. Fourth, problems with tense and honorifics were found in the responses of Chinese-speaking learners.
 Conclusions In conclusion, first, the situation that Chinese language learners consider ‘-eultende’ as the speaker's ‘hope’ or ‘wish’ and ‘-(었/았/였)으면 좋겠다’ as ​​the speaker's ‘regret’ raised the topic of the need for a comparative study of regret expressions for Chinese learners in Korean language education, and a study of discourse and pragmatic discrimination between expressions of regret and hope. Second, it is thought that the factor of the textbook is also an important cause that Chinese learners are not accustomed to using -eultende’, which indicates ‘worry’. At the same time, this also raised the topic of the necessity of integrating the presentation form and explanation of ‘-eultende’.

Influence of the ending position of controllable speed casing on a transonic compressor rotor tip leakage flow

Abstract The controllable speed casing is a novel casing treatment approach that makes partial casing rotate at adjustable and proper speed to achieve stability expansion. Structural parameters of casing treatment are found to influence the effect of stability expansion by many studies. In this paper, the effect of the ending position of the rotatable ring in controllable speed casing on the tip leakage flow and the stability expansion was studied numerically. The results show that when the rotatable ring rotates at 30 % and 50 % rotor design speed, the controllable speed casing achieves the stability expansion of the compressor rotor no matter where the ending position is. The upstream movement of the ending position decreases the axial pressure gradient in the middle and rear of the tip passage. It pushes the shock wave downstream, which reduces blockage region at tip leading edge. The upstream movement of the ending position contributes to an approximately linear increase in the stable operating margin.

Predictability and Effectiveness of Nuvola® Aligners in Dentoalveolar Transverse Changes: A Retrospective Study.

Nowadays, many people use clear aligners to address their dental issues. The efficacy of transparent dental aligners must be investigated even though they are more aesthetically pleasing, easy to use, and tidy than permanent tools. Thirty-five patients in this study's sample group who used Nuvola® clear aligners for their orthodontic therapy were prospectively observed. Initial, simulated, and final digital scans were analysed with a digital calliper. The actual results were compared with the prescribed ending position to evaluate the efficacy of transversal dentoalveolar expansion. Aligner treatments in Groups A (12) and B (24), particularly in the dental tip measures, demonstrated high adherence to the prescription. On the other hand, the gingival measures exhibited a greater level of bias, and the differences were statistically significant. However, there was no difference in the outcomes between the two groups (12 vs. 24). Within specific parameters, the evaluated aligners were shown to be helpful in predicting movements in the transverse plane, particularly when considering movements linked to the vestibular-palatal inclination of the dental elements. This article compares the expansion effectiveness of Nuvola® aligners compared with other work in the literature using competitor companies.

The model of ring-spun slub yarn based on random fiber arrangement and its application: Part 1. Study on the relationship between fiber distribution and the length of the transitional segment of slub yarn

In this paper, the research on the transitional segment of slub yarn mainly focuses on the length of the transitional segment. Slub yarn was simulated by randomly determining the fiber position with the Monte Carlo method according to the draft principle of ring spinning for slub yarn. The length of the transitional segment was obtained by determining its starting and ending position according to the mass curves of the simulated and real-spun slub yarns. According to the data analysis, the fiber length, acceleration and deceleration time on draft rollers’ velocity, and slub multiple affect the length of the transitional segment. Both the lengths of the left and right transitional segments are all equal. The maximum error rate of the simulated value to the measured value of the length of the transitional segment is approximately 12%. The empirical formula has been established to estimate the length of the transitional segment. Compared with those of the simulated and real spun slub yarns, the error rate of the length of the transitional segment calculated by the empirical formula is less than 10%. The research content of this paper provides a basis for studying the appearance and properties of slub yarn.

Impact of the ending position of controllable speed casing on the flow stability in a transonic compressor rotor

The structure of casing treatment has a significant influence on the stability expansion effect. The ending position of the rotatable ring is one of the important structural parameters in the controllable speed casing. The impact of ending position of the rotatable ring rotating at the same speed as the rotor on the stability expansion and stability expansion mechanism was studied in this paper. The results show that, when the ending position of rotatable ring expands downstream in the range of 20% to 60% axial chord length, because of the improvement in the tip leakage vortex trajectory and main flow/leakage flow interface, the stability expansion effect rises gradually. The further downstream expansion of ending position from 60% axial chord length, however, has a slight impact on tip flow, bringing out a steady stability expansion effect around 52.5%. The best stability expansion effect of ending position occurs at 60% axial chord length where the stable operating margin increases by 53.5%.

Strategies for Improving Text Reading Ability Based on Human-Computer Interaction in Artificial Intelligence.

In order to improve text reading ability, a human-computer interaction method based on artificial intelligence (AI) human-computer interaction is proposed. Firstly, the design of the AI human-computer interaction model is constructed, which includes the Stanford Question Answering Dataset (SQuAD) and the designed baseline model. There are three components: the coding layer is based on a cyclic neural network (recurrent neural network [RNN] encoder layer), which aims to encode the problem and text into a hidden state; the interaction layer is used to integrate problems and text representation; the output layer connects two independent soft Max layers after a fully connected layer, one is used to obtain the starting position of the answer in the text and the other is used to obtain the ending position. In the interaction layer of the model, this manuscript uses hierarchical attention and aggregation mechanism to improve text coding. The traditional model interaction layer has a simple structure, which leads to weak relevance between text and problems, and poor understanding ability of the model. Finally, the self-attention model is used to further enhance the feature representation of text. The experimental results show that the improved model in this manuscript is compared with the public AI human-computer interaction reading comprehension model. According to the data in the table, the accuracy of the model in this manuscript is better than that of the baseline model, in which the exact match (EM) value is increased by 1.4% and the F1 value is increased by 2.7%. However, compared with improvement point 2, the EM and F1 values of the model have decreased by 0.7%. It shows that the output layer has a certain impact on the effect of the model, and the improvement and optimization of the output layer can also improve the performance of the model. It is proved that AI human-computer interaction can effectively improve text reading ability.

UTILIZATION OF THE INFLUENCE LINE OF DISPLACEMENT TO IDENTIFY A DECLINE IN THE STIFFNESS OF BEAMS

The purpose of this work is to offer a method for detecting structural damage utilizing the standardized index of the beam’s deflection influence line difference as input data for the evaluation procedure. The displacement influence line used in the evaluation is calculated using the findings of the behavior analysis of the reinforced concrete beam’s finite element model when subjected to a moving load. SAP2000 software is used to simulate reinforced concrete beams. The mobile load is then assigned to move along the beam from its starting position to its ending position. For each mobile load example, the displacement at each survey node will be output to draw the influence line. The displacement analysis of the beams is compared before and after assuming damage for each mobile load instance in order to determine the location of the stiffness drop. From then, the findings of beam damage diagnosis are reviewed and evaluated, as well as the methods’ practicality in real implementations.

Neural correlates of acoustic dissonance in music: The role of musicianship, schematic and veridical expectations.

In western music, harmonic expectations can be fulfilled or broken by unexpected chords. Musical irregularities in the absence of auditory deviance elicit well-studied neural responses (e.g. ERAN, P3, N5). These responses are sensitive to schematic expectations (induced by syntactic rules of chord succession) and veridical expectations about predictability (induced by experimental regularities). However, the cognitive and sensory contributions to these responses and their plasticity as a result of musical training remains under debate. In the present study, we explored whether the neural processing of pure acoustic violations is affected by schematic and veridical expectations. Moreover, we investigated whether these two factors interact with long-term musical training. In Experiment 1, we registered the ERPs elicited by dissonant clusters placed either at the middle or the ending position of chord cadences. In Experiment 2, we presented to the listeners with a high proportion of cadences ending in a dissonant chord. In both experiments, we compared the ERPs of musicians and non-musicians. Dissonant clusters elicited distinctive neural responses (an early negativity, the P3 and the N5). While the EN was not affected by syntactic rules, the P3a and P3b were larger for dissonant closures than for middle dissonant chords. Interestingly, these components were larger in musicians than in non-musicians, while the N5 was the opposite. Finally, the predictability of dissonant closures in our experiment did not modulate any of the ERPs. Our study suggests that, at early time windows, dissonance is processed based on acoustic deviance independently of syntactic rules. However, at longer latencies, listeners may be able to engage integration mechanisms and further processes of attentional and structural analysis dependent on musical hierarchies, which are enhanced in musicians.

Mandarin adaptations of voiced alveolar fricative [z] in English loanwords

This paper explores the adaptation of English voiced fricative [z] E into Mandarin. The principal findings are that the adaptation of [z] E depends on its position in the source word. If [z] E occupies the word initial or middle position, it tends to be borrowed as Mandarin [ts] M or [s] M . If [z] E is in the ending position, more variations would be observed as it may correspond to [ts] M , [s] M , [ʈʂ] M or [ʂ] M . Moreover, adapting [z] E into Mandarin is also heavily influenced by the orthography. The English [z] E can be spelled with <s> or <z>. The letters of <s> and <z> are also listed in Mandarin Pinyin , a Romanization system that transcribes the sounds of Chinese characters using Roman alphabets. Specifically, <s> is pronounced as [s] M , while [z] is pronounced as [ts] M . It turns out that [s] M sounds different from [z] E , while [ts] M is perceptually similar to [z] E . Generally, there emerged two major adaptation patterns, that is, <z> [z] E " <z> [ts] M and <s> [z] E " <s> [s] M . The latter is based on the spelling similarity, rather than perceptual similarity. It is therefore concluded that the loanword adaptation is not only determined by the speech perception, phonology and legitimacy of sound structures, but also systematically interfered with the orthography, that is, the source-loan spelling similarity.

A unified and simple control strategy for a class of n-link vertical underactuated manipulator

In this paper, we propose a unified and simple trajectory planning-based control strategy for the n-link (n≥2⋂n∈Z) vertical underactuated manipulator (VUM) with an underactuated joint. The proposed method does not need to partition the entire motion space like the traditional methods, and can quickly realize the control objective of swinging the endpoint of the system up from the vertical downward starting position and stabilizing it at the vertical upward ending position. The trajectory planned for each active link includes two stages. The first stage is to make the first active link and passive link reach the intermediate states, and other active links reach the ending states. The second stage is to move the first active link and the passive link to the ending states, while other active links keep at the ending states. Considering the above targets of two stages, the trajectory of each active link is designed and the trajectory parameters are optimized via utilizing the differential evolution algorithm. Then, the tracking controllers and stabilization controllers are designed to track the two-stage trajectories and to stay the endpoint at the ending position. Finally, the numerical simulations are carried out to show the feasibility and superiority of the proposed method.

Evolution Mechanism of Transient Strain and Residual Stress Distribution in Al 6061 Laser Welding

Considering the harm that residual stress causes to the mechanical properties of a weld joint, the evolution mechanisms of transient strain and residual stress distribution are investigated in laser welding of Al 6061, considering that these originate from non-uniform temperature distribution and are intensified further by the unbalanced procedure of melting and solidification. Thermal-elastic-plastic finite element method is developed and analyzed, while the actual weld profile is novel fitted by a B-spline curve. Transient strain is extracted by strain gauges. Longitudinal strain starts from a fluctuating compressive state and progresses to an ultimate residual tension state at the starting and ending welding positions, respectively. The maximum fitting deviation of the weld profile is 0.13 mm. Experimental and simulation results of residual strain are 842.0 μ and 826.8 μ, with a relative error of 1.805% at the starting position and −17.986% at the ending position. Near the weld center, mechanical behavior is complexly influenced by thermal expansion and contraction in the weld zone and the reaction binding force of the solid metal. Within a distance between −10 mm and 10 mm, and longitudinal stress is in a tension state, transverse stress fluctuates with a high gradient (~100 MPa).

MRI evaluation of fetal tethered-cord syndrome: correlation with ultrasound findings and clinical follow-up after birth

The study aimed to describe the features of magnetic resonance imaging (MRI) in fetuses with tethered-cord syndrome (TCS) or lower spinal cord (LSC) and to analyse the clinical outcomes and complications during follow-up. This is a retrospective study of fetuses diagnosed with TCS or LSC using MRI from January 2015 to August 2019. The average gestational week (GW) at MRI examination was 25.46±4.73 GW (range: 21-39 GW). MRI was used1 to identify the anatomical landmarks of the spine2; to measure the width of the conus medullaris and record the ending position of the LSC3; and to analyse other neurological deformities. The diagnostic results between MRI and ultrasonography (US) were compared. A total of 38 fetuses with suspected intracranial or spinal lesions on US or MRI were included. Among all fetuses, 17 fetuses were diagnosed with LSC or TCS without associated anomalies. Twenty-one fetuses had complications of central nervous system (CNS) anomalies, one fetus also had a diagram hernia, and one fetus had an inverse foot. MRI provided more diagnoses than US in nine fetuses. Two cases of diastematomyelia detected on MRI were missed on US. The capability of MRI was comparable with that of US in terms of displaying spina bifida. In the present study, fetal MRI showed better performance than US for depicting TCS and related CNS abnormalities. MRI provided clinicians with additional information in terms of prenatal counselling and management.

Acute Effect of Chest Physical Therapy on Arterial Blood Gases for Mechanical Ventilated Patients

Abstract Background: Patients receiving mechanical ventilation have an increased risk of complications resulting in excess morbidity and mortality. Aim of Study: This study aimed to identify the acute effect of chest physical therapy on arterial blood gases of mechanically ventilated patients. Material and Methods: Sixty mechanically ventilated patients participated in the study. Their age ranged from 40 to 60 years. The patients were assigned into one study group including both sexes who received a chest physiotherapy protocol in form of (manual hyperinflation, vibration, percus-sion, suctioning, upper and lower limbs exercise and ending position) for one session. Arterial Blood Gases (ABG) includ-ing (pH, PaO2, SO2, PaCO2 and HCO3) were assessed by arterial blood sample analysis through the Laboratory GEM premier 3000 device. All the assessment was done for every patient pre and post chest physiotherapy protocol. Results: The results revealed a marked improvement in arterial blood gas exchange as compared to base line reflected by a highly significant statistical increase in PaO2 and SaO2 (p < 0.001) and a significant decrease in PaCO2 (p < 0.001) while with no significant changes regarding pH and HCO3 (p=0.36 and 0.15 respectively). Conclusion: Chest physiotherapy protocol is an effective method for improving arterial blood gases of mechanical ventilated patients acutely.

GSA-Net: gated scaled dot-product attention based neural network for reading comprehension

Reading Comprehension (RC) is concerned with building systems that automatically answer questions about a given context passage. The interactions between the context and question are very important to locate the correct answer. In this paper, we propose a Gated Scaled Dot-Product Attention based model for RC task. The character-level embedding is incorporated into the word embedding which is helpful to deal with Out-of-Vocabulary (OOV) tokens. The attention distribution is obtained by scaled dot product which captures the interaction between question and passage effectively. Further, self-matching attention mechanism is adopted to resolve the problem of long-distance dependency. These components provides more information for the prediction of the starting and ending position of the answer. We evaluate our method on Stanford Question Answering Dataset (SQuAD) and the results show that different components in the model boost the performance.

Exogenous GM1 Ganglioside Attenuates Ketamine-Induced Neurocognitive Impairment in the Developing Rat Brain

A prolonged exposure to ketamine triggers significant neurodegeneration and long-term neurocognitive deficits in the developing brain. Monosialotetrahexosylganglioside (GM1) can limit the neuronal damage from necrosis and apoptosis in neurodegenerative conditions. We aimed to assess whether GM1 can prevent ketamine-induced developmental neurotoxicity. Postnatal day 7 (P7) rat pups received 5 doses of intraperitoneal ketamine (20 mg/kg per dose) at 90-minute intervals for 6 hours. Cognitive functions, determined by using Morris water maze (MWM) including escape latency (at P32-36) and platform crossing (at P37), were compared among the ketamine-exposed pups treated with or without exogenous GM1 (30 mg/kg; n = 12/group). The effect of GM1 on apoptosis in hippocampus was determined by terminal deoxynucleotidyl transferase-mediated 2'-deoxyuridine 5'-triphosphate nick end labeling (TUNEL) staining and activated caspase 3 measurement. The hippocampal expression of brain-derived neurotrophic factor (BDNF), along with the phosphorylation of protein kinase B (AKT) and extracellular signal-related kinases 1 and 2 (ERK1/2), was detected by western blotting (n = 6/group). Anti-BDNF antibody (2 μg per rat) administered before GM1 treatment was applied to determine the neuroprotective mechanisms of GM1. The rats receiving ketamine exposure experinced cognitive impairment in MWM test compared to the control rats, indicated by prolonged escape latency at P34 (P = .006), P35 (P = .002), and P36 (P = .005). However, in GM1-pretreated rats, ketamine exposure did not induce prolonged escape latency. The exogenous GM1 increased the platform-crossing times at P37 (3.00 ± 2.22 times vs 5.40 ± 1.53 times, mean ± standard deviation; P = .041) and reduced the hippocampal TUNEL-positive cells and cleaved-caspase 3 expression in ketamine-exposed young rats. Ketamine decreased BDNF expression and phosphorylation of AKT and ERK in the hippocampus, whereas exogenous GM1 blocked these ketamine-caused effects. However, for the ketamine-exposed rat pups receiving exogenous GM1, compared to immunoglobulin Y (IgY) isotype control, the BDNF-neutralizing antibody treatment counteracted the exogenous GM1-induced improvement of the escape latency at P36 (41.32 ± 12.37 seconds vs 25.14 ± 8.97 seconds, mean ± standard deviation; P = .036), platform-crossing times at P37 (2.16 ± 1.12 times vs 3.92 ± 1.97 times, mean ± standard deviation; P < .036), apoptotic activity, as well as AKT and ERK1/2 phosphorylation in the hippocampus of ketamine-challenged young rats. Our data suggest that the exogenous GM1 acts on BDNF signaling pathway to ameliorate the cognitive impairment and hippocampal apoptosis induced by ketamine in young rats. Our study may indicate a potential use of GM1 in preventing the cognitive deficits induced by ketamine in the young per se.

Logic-based Benders decomposition for gantry crane scheduling with transferring position constraints in a rail–road container terminal

ABSTRACT Rail–road container terminals can be seen as buffers within a large logistics network encompassing hinterland distribution systems. They are used as temporary storage points for containers such that unloading operations from a train and loading operations onto a truck need not be synchronized. Container transferring operation implemented by gantry cranes is one of the most important issues to ensure efficient logistics. To enable efficient container transfer, this article considers the special features of container movement, and integrates the starting position and the ending position of container movement into the gantry crane scheduling problem. In order to solve the proposed problem, this article develops two models: first using mixed integer programming, and secondly using constraint programming (CP). Since the problem is computationally intractable for realistic sizes, this article also proposes a logic-based Benders decomposition (LBBD) methodology to solve it. This method exploits a natural decomposition of the studied problem into a relaxed master problem (RMP) solved by mixed integer programming (MIP), and a series of sub-problems, solved separately by MIP and CP. Computational experiments are performed on generated instances, the structures of which are designed to follow the practical application. The computational results show that the CP approach is better suited to solve the proposed problem with small-sized and medium-sized instances compared with MIP and LBBD. In addition, the LBBD framework is far superior to mixed integer programming on all but a few small instances, and it is highly effective in finding good-quality solutions for larger cases with up to 100 tasks within a reasonable runtime. Moreover, the results find that LBBD using constraint programming to solve the sub-problems usually outperforms LBBD with mixed integer programming on the instances tested.

Detection, Location Estimation, and CRLB of a Streaking Target in an FPA With a Poisson Model

This paper deals with measurement extraction, from an optical sensor's Focal Plane Array (FPA), of a streaking target. We use a model that assumes pixels are separated by dead zones and model the streaking target's point spread function (PSF) as a Gaussian PSF that moves during the optical sensor's integration time. We make an assumption that the target has a constant velocity over the sampling interval and parametrize its motion with a starting and ending position. The noise model for a single pixel has variance proportional to its area, consistent with a Poisson model of the number of nontarget originated photons. We develop a maximum likelihood (ML) method of estimating the target motion parameter vector based on the set of pixel measurements from the optical sensor. This paper then derives the Cramer–Rao lower bound (CRLB) on the estimation error of the target motion parameter. We then present a matched filter (MF) based definition of the signal-to-noise ratio (SNR) to use as a basis for comparison of Monte Carlo simulation based location estimates to the calculated CRLB. It is shown that the ML estimator for the starting and ending positions of a streak in the FPA is efficient for MFSNR $\geq 12$ dB. We then provide a test statistic for target detection and propose approximate distributions to set the detection threshold for specific detection ( $P_D$ ) and false alarm probabilities ( $P_{\text{FA}}$ ), which are then verified via simulations. This paper's major contributions are the proposal of an ML/MF method for measurement extraction of streaking targets, confirmation that this method achieves the best accuracy possible for realistic FPA sensors, i.e., it attains the CRLB, the introduction of a statistically supported definition of SNR for these measurements, and an evaluation of the target measurement detection performance. Furthermore, this paper shows that, given our MFSNR definition, the streak length and direction of motion in the FPA have a negligible effect on performance compared to the SNR where we show that with a 4-dB change, the detection performance increases dramatically.

A Novel Method for Reconstructing Flatness Error Contour of Long Surface Based on a Laser Displacement Sensor

In order to solve the problem that the flatness error contour curve of the guideway mounting surface on machine tools can not be intuitive description, a novel method is proposed in this paper. The principle is to divide the measured surface with a certain length into several short surfaces with overlapping region, and the segmented surfaces are measured respectively, then the flatness error contours of the segmented surfaces can be obtained, finally, the segmented flatness error contours are spliced together to reconstruct the flatness error contour of the entire surface. On this basis, the detection instrument is designed, the detection principle is given, the benchmark plate is customized to identify the starting position and ending position of measurement, the reference surface and the measured surface are measured respectively in combination with the detection instrument and the benchmark plate. Then, an algorithm is developed to convert the distance difference between the reference surface and the measured surface into the flatness error contours of segmented surfaces. Next, using the geometric relationship between overlapping region of segmented flatness error contours, an algorithm is studied which can splice these segmented flatness error contours and reconstruct the flatness error contour of the entire surface. Meanwhile, mathematical models of the algorithms are established, and the measurement experiment is carried out. The results demonstrate that this method can reconstruct the flatness error contour of long surface accurately.

Dynamically integrated spatiotemporal‐based trajectory planning and control for autonomous vehicles

In the literature, the intensive research effort has been made on the trajectory planning for autonomous vehicles, while the integration of the trajectory planner with the trajectory controller is less focused. This study proposes the spatiotemporal-based trajectory planner and controller by a two-level dynamically integrated structure. In the upper level, the best trajectory is selected among a group of candidate time-parameterised trajectories, while the target vehicle ending position and velocity can be satisfied. Then the planned trajectory is evaluated by checking the feasibility when the actual vehicle dynamic motion constraints are considered. After that, the lower level trajectory controller based on the vehicle dynamics model will control the vehicle to follow the desired trajectory. Numerical simulations are used to validate the effectiveness of the proposed approach, where the scenario of an intersection and the scenario of overtaking are applied to show that the proposed trajectory controller can successfully achieve the control targets. In addition, compared with the potential field method, the proposed method based on the four-wheel independent steering and four-wheel independent driving electric vehicle shows great advantages in guaranteeing the vehicle handling and stability.

Path planning in distorted configuration space

SUMMARYAn effective algorithm for path planning is introduced based on a novel concept, the distorted configuration space (DC-space), where all obstacles deform into dimensionless geometric objects. Path planning in this space can be conducted by simply connecting the starting position and ending position with a straight line. This linear path in the DC-space is then mapped back into a feasible in the original C-space. The advantage of this approach is that no trial-and-error or iteration is needed while a feasible path can be found directly if it exists. An algorithm with general formulas is derived. Examples in 2D and 3D are provided to validate this concept and algorithm.