Filtered Medial Surface Based Approach for 3D Collision-Free Path Planning Problem by Karima Benzaid, Romain Marie, Noura Mansouri, Ouiddad Labbani-Igbida

“…Finally, an optimization process ensures the smoothness of the final path by fitting a set of 3D Bézier curves to the initial path. For a comparative study, the A-star algorithm is applied directly on the input environment representation and relevant comparative criteria are defined to assert the proposed approach using simulation results.…”
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Parking Space Detection and Path Planning Based on VIDAR by Yi Xu, Shanshang Gao, Guoxin Jiang, Xiaotong Gong, Hongxue Li, Xiaoqing Sang, Liming Wang, Ruoyu Zhu, Yuqiong Wang

“…In the path planning stage, the path optimization algorithm of the A∗ algorithm combined with the Bezier curve is used to generate smooth curves, and the environmental information is updated in real time based on VIDAR. …”
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Evaluation of parameters extracted from tissue residue functions in dynamic susceptibility contrast MRI: Healthy volunteers examined during normal breathing and spontaneous hyperve... by Ronnie Wirestam, Arthur Chakwizira, Peter Reinstrup

“…The corresponding whole-brain MTT estimates were 3.8 ± 0.7 s during normal breathing and 5.0 ± 1.3 s during hyperventilation (mean ± SD, n = 8). The applied Bézier curve deconvolution algorithm returned tissue residue functions of plausible shapes, i.e., without oscillations and negative values, and some indications that curve shape is relevant for improved assessment of oxygen extraction properties were demonstrated.…”
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TEACHING OF INTERPOLATION AND APPROXIMATION CURVES THROUGH COMPUTER SIMULATION by Norbert Annuš, Ondrej Takáč

“…In our study, we focused on three specific types of curves: the Hermite, Bézier and Coons curves. For universal use, students are able to simulate the curves concerned in nth-degree cases. …”
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Bivariate Generalized Shifted Gegenbauer Orthogonal System by Mohammad A. Alqudah, Maalee N. Almheidat, Tareq Hamadneh

“…Then, we construct a bivariate generalized shifted Gegenbauer orthogonal system ℭn,r,d∗λ,K0,K1u,v,w over a triangular domain T, with reference to a bivariate measure Wλ,γ,K0,K1u,v,w=Γ2λ+1/Γλ+1/22uλ−1/21−vλ−1/21−wγ−1Iu∈0,1−wIw∈0,1dudw+K0δ0u+K1δw−1u, which is given explicitly in the Bézier form as ℭn,r,d∗λ,K0,K1u,v,w=∑i+j+k=nai,j,kn,r,dBi,j,knu,v,w. …”
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Time-Optimal Trajectory Planning along Parametric Polynomial Lane-Change Curves with Bounded Velocity and Acceleration: Simulations for a Unicycle Based on Numerical Integration by Chien-Sheng Wu, Zih-Yun Chiu, Jing-Sin Liu

“…The rest-to-rest lane-change maneuvering simulations highlight the effect of the most relevant path geometric properties on minimal travel time: a faster lane-change curve such as a quintic Bezier curve followed by a unicycle tends to be shorter in route length and lower in maximum curvature to have achievable highest speed at the maximum curvature points. …”
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Data-driven prediction of critical diameter for deterministic lateral displacement devices: an integrated DPD-ML approach by Shuai Liu, Peng Zhang, Anbin Wang, Keke Tang, Shuo Chen, Chensen Lin

“…The study uses control parameters of Bézier curves to represent the arbitrary pillar shapes, along with the forces in the x and y directions of the fluid as input parameters. …”
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