A Universal Parametrization in B-Spline Curve and Surface Interpolation and Its Performance Evaluation.

The choice of a proper parametrization method is critical in curve and surface fitting using parametric B-splines. Conventional parametrization methods do not work well partly because they are based only on the geometric properties of given data points such as the distances between consecutive data points and the angles between consecutive line segments. The resulting interpolation curves don\u27t look natural and they are often not affine invariant. The conventional parametrization methods don\u27t work well for odd orders k. If a data point is altered, the effect is not limited locally at all with these methods. The localness property with respect to data points is critical in interactive modeling. We present a new parametrization based on the nature of the basis functions called B-splines. It assigns to each data point the parameter value at which the corresponding B-spline N\sb{ik}(t) is maximum. The new method overcomes all four problems mentioned above; (1) It works well for all orders k, (2) it generates affine invariant curves, (3) the resulting curves look more natural, in general, and (4) it has the semi-localness property with respect to data points. The new method is also computationally more efficient and the resulting curve has more regular behavior of the curvature. Fairness evaluation and knot removal are performed on curves obtained from various parametrizations. The results also show that the new parametrization is superior. Fairness is evaluated in terms of total curvature, total length, and curvature plot. The curvature plots are looking natural for the curves obtained from the new parametrization. For the curves obtained from the new method, knot removal is able to provide with the curves which are very close to the original curves. A more efficient and effective method is also presented for knot removal in B-spline curve. A global norm is utilized for approximation unlike other methods which are using some local norms. A geometrical view makes the computation more efficient

Perfectly normal type-2 fuzzy interpolation B-spline curve

In this paper, we proposed another new form of type-2 fuzzy data points(T2FDPs) that is perfectly normal type-2 data points(PNT2FDPs). These kinds of brand-new data were defined by using the existing type-2 fuzzy set theory(T2FST) and type-2 fuzzy number(T2FN) concept since we dealt with the problem of defining complex uncertainty data. Along with this restructuring, we included the fuzzification(alpha-cut operation), type-reduction and defuzzification processes against PNT2FDPs. In addition, we used interpolation B-soline curve function to demonstrate the PNT2FDPs.Comment: arXiv admin note: substantial text overlap with arXiv:1304.786

Non-uniform quaternion spline interpolation in vehicle kinematics

SGS-2022-00

Torso shape detection to improve lung monitoring

Newborns with lung immaturity often require continuous monitoring and treatment of their lung ventilation in intensive care units, especially if born preterm. Recent studies indicate that Electrical Impedance Tomography (EIT) is feasible in newborn
 infants and children, and can quantitatively identify changes in regional lung aeration and ventilation following alterations to respiratory conditions. Information on the patient-specic shape of the torso and its role in minimizing the artefacts in the
 reconstructed images can improve the accuracy of the clinical parameters obtained from EIT. Currently, only idealized models or those segmented from CT scans are usually adopted. This study presents and compares two methodologies that can
 detect the patient-specic torso shape by means of wearable devices based on: (1) previously reported bend sensor technology and (2) a novel approach based on the use of accelerometers. The reconstruction of different phantoms, taking into account
 anatomical asymmetries and different sizes, are produced for comparison. As a result, the accelerometers are more versatile than bend sensors, which cannot be used on bigger cross-sections. The computational study estimates the optimal number of
 accelerometers required in order to generate an image reconstruction comparable to the use of a CT scan as the forward model. Furthermore, since the patient position is crucial to monitoring lung ventilation, the orientation of the phantoms is automatically
 detected by the accelerometer-based method. [Abstract copyright: © 2018 Institute of Physics and Engineering in Medicine.

Torso shape detection to improve lung monitoring

Newborns with lung immaturity often require continuous monitoring and treatment of their lung ventilation in intensive care units, especially if born preterm. Recent studies indicate that Electrical Impedance Tomography (EIT) is feasible in newborn
 infants and children, and can quantitatively identify changes in regional lung aeration and ventilation following alterations to respiratory conditions. Information on the patient-specic shape of the torso and its role in minimizing the artefacts in the
 reconstructed images can improve the accuracy of the clinical parameters obtained from EIT. Currently, only idealized models or those segmented from CT scans are usually adopted. This study presents and compares two methodologies that can
 detect the patient-specic torso shape by means of wearable devices based on: (1) previously reported bend sensor technology and (2) a novel approach based on the use of accelerometers. The reconstruction of different phantoms, taking into account
 anatomical asymmetries and different sizes, are produced for comparison. As a result, the accelerometers are more versatile than bend sensors, which cannot be used on bigger cross-sections. The computational study estimates the optimal number of
 accelerometers required in order to generate an image reconstruction comparable to the use of a CT scan as the forward model. Furthermore, since the patient position is crucial to monitoring lung ventilation, the orientation of the phantoms is automatically
 detected by the accelerometer-based method. [Abstract copyright: © 2018 Institute of Physics and Engineering in Medicine.

Evalutionary algorithms for ship hull skinning approximation

Traditionally, the design process of a hull involves simulation using clay models. This must be done cautiously, accurately and efficiently in order to sustain the performance of ship. Presently, the current technology of Computer Aided Design, Manufacturing, Engineering and Computational Fluid Dynamic has enabled a 3D design and simulation of a hull be done at a lower cost and within a shorter period of time. Besides that, automated design tools allow the transformation of offset data in designing the hull be done automatically. One of the most common methods in constructing a hull from the offset data is the skinning method. Generally, the skinning method comprised of skinning interpolation and skinning approximation. Skinning interpolation constructs the surface perfectly but improper selection of parameterization methods may cause bumps, wiggles, or uneven surfaces on the generated surface. On the other hand, using the skinning surface approximation would mean that the surface can only be constructed closer to data points. Thus, the error between the generated surface and the data points must be minimized to increase the accuracy. Therefore, this study aims to solve the error minimization problem in order to produce a smoother and fairer surface by proposing Non Uniform Rational B-Spline surface using various evolutionary optimization algorithms, namely, Gravitational Search Algorithm, Particle Swarm Optimization and Genetic Algorithm. The proposed methods involve four procedures: extraction of offset data from line drawing plan; generation of control points; optimization of a surface; and validations of hull surfaces. Validation is done by analyzing the surface curvature and errors between the generated surface and the given data points. The experiments were implemented on both ship hull and free form models. The findings from the experiments are compared with interpolated skinning surface and conventional skinning surface approximation. The results show that the optimized skinning surfaces using the proposed methods yield a smaller error, less control points generation and feasible surfaces while maintaining the shape of the hull

Improving particle swarm optimization path planning through inclusion of flight mechanics

Military engagements are continuing the movement toward automated and unmanned vehicles for a variety of simple and complex tasks. This allows humans to stay away from dangerous situations and use their skills for more difficult tasks. One important piece of this strategy is the use of automated path planners for unmanned aerial vehicles (UAVs). Current UAV operation requires multiple individuals to control a single plane, tying up important human resources. Often paths are planned by creating waypoints for a vehicle to fly through, with the intention of doing reconnaissance while avoiding as much danger to the plane as possible. Path planners often plan routes without taking into consideration the UAV\u27s ability to perform the maneuvers required to fly the specified waypoints, instead relying upon them to fly as close as possible. This thesis presents a path planner solution incorporating vehicle mechanics to insure feasible flight paths. This path planner uses Particle Swarm Optimization (PSO) and digital pheromones to generate multiple three-dimensional flight paths for the operator to choose from. B-spline curves are generated using universal interpolation with each path waypoint representing a control point. The b-spline curve represents the flight path of the UAV. Each point along the curve is evaluated for fuel efficiency, threat avoidance, reconnaissance, terrain avoidance, and vehicle mechanics. Optimization of the flight path occurs based on operator defined performance characteristics, such as maximum threat avoidance or minimum vehicle dynamics cost. These performance characteristics can be defined for each unique aircraft, allowing the same formulation to be used for any aircraft. The vehicle mechanics conditions considered are pull-out, glide, climb, and steady, level, co-ordinate turns. Calculating the flight mechanics requires knowing the velocity and angle of the plane, calculated using the derivative of the point on the curve. The flight mechanics of the path allows the path planner to determine whether the path exceeds the maximum load factor (G-force), minimum velocity (stall velocity), or the minimum turning radius. Comparing the results between PSO Path Planner with flight mechanics and PSO Path Planner without flight mechanics over five scenarios indicates an increase in the feasibility of the returned paths. Visualizing the flight paths was improved by changing the original waypoint based visualization to a b-spline curve representation. Using b-spline curves allows for an accurate representation of the actual UAV flight path especially when considering turns. Operators no longer must create a mental representation of the flight path to match the waypoints