Generalized Fractional Bézier Curve with Shape Parameters

The construction of new basis functions for the Bézier or B-spline curve has been one of the most popular themes in recent studies in Computer Aided Geometric Design (CAGD). Implementing the new basis functions with shape parameters provides a different viewpoint on how new types of basis functions can develop complex curves and surfaces beyond restricted formulation. The wide selection of shape parameters allows more control over the shape of the curves and surfaces without altering their control points. However, interpolated parametric curves with higher degrees tend to overshoot in the process of curve fitting, making it difficult to control the optimal length of the curved trajectory. Thus, a new parameter needs to be created to overcome this constraint to produce free-form shapes of curves and surfaces while still preserving the basic properties of the Bézier curve. In this work, a general fractional Bézier curve with shape parameters and a fractional parameter is presented. Furthermore, parametric and geometric continuity between two generalized fractional Bézier curves is discussed in this paper, as well as demonstrating the effect of the fractional parameter of curves and surfaces. However, the conventional parametric and geometric continuity can only be applied to connect curves at the endpoints. Hence, a new type of continuity called fractional continuity is proposed to overcome this limitation. Thus, with the curve flexibility and adjustability provided by the generalized fractional Bézier curve, the construction of complex engineering curves and surfaces will be more efficient.

Evaluation of driver visual demand at different traffic volumes on complex two-dimensional multi-lane highway alignments.

This research focuses on evaluating driver visual demand at different traffic volumes along with geometric design features for two-dimensional (2D) multi-lane highways consisting of horizontal and vertical alignments which is a crucial part of highway design consistency research. Three such alignments, with simple and complex curves were designed to generate desired traffic volume levels. A driving simulator was used to collect date from twenty drivers that participated in roadway alignment experiments at Ryerson University. Statistical Analysis Software (SAS) was used to analyze and process output data. Models were developed for visual demand and volume/capacity ratios, and geometric characteristics of the road, where visual demand was the only dependent variable. The research found that a relationship exists between visual demand and different traffic volumes along with geometric characteristics of the road.

Evaluation of driver visual demand at different traffic volumes on complex two-dimensional multi-lane highway alignments.

This research focuses on evaluating driver visual demand at different traffic volumes along with geometric design features for two-dimensional (2D) multi-lane highways consisting of horizontal and vertical alignments which is a crucial part of highway design consistency research. Three such alignments, with simple and complex curves were designed to generate desired traffic volume levels. A driving simulator was used to collect date from twenty drivers that participated in roadway alignment experiments at Ryerson University. Statistical Analysis Software (SAS) was used to analyze and process output data. Models were developed for visual demand and volume/capacity ratios, and geometric characteristics of the road, where visual demand was the only dependent variable. The research found that a relationship exists between visual demand and different traffic volumes along with geometric characteristics of the road.

Evaluation of driver visual demand in complex two dimensional rural highway alignments

Transportation has proven to be one of the most important infrastructures in the economic development of any country. Safe and effective traffic operations support growth of the economy and help in future developments. Highway alignment design plays a crucial role in implementing safer traffic operation and management. Road accidents not only jeopardize safety, but also have a major effect on the national economy. These accidents can be divided in three classes, grouped according to their severity. Statistics in North America and Europe show that one of the major reasons for such road accidents is driver error. Wrong decisions during navigation may be the primary reason for such errors. Wrong decisions occur when a driver is unable to process the range of visual information available in a complex highway situation. Drivers need to have sufficient visual information in guiding and controlling vehicles along the correct path. Drivers scan the roadway to collect visual information. This visual information consists mainly of the traffic situation, roadway signs, and the information from the highway alignment itself. The information from the highway alignment plays a major role in decision-making during maneuvering. All drivers, therefore, need sufficient visual information for perfect navigating, and for guiding and controlling their vehicles on the road. The main focus of this research study was on evaluating visual demands on two-dimensional highway alignments with an emphasis on determining the effect of complex curves on visual demand. Complex curves are defined as combinations of simple, compound, and reverse curves in a series. Eighteen hypothetical alignments for two-lane rural highways have been developed following the standard guidelines of the Transportation Association of Canada (TAC) and American Association of State Highway Transportation Officials (AASHTO). These alignments were simulated in a low-cost driving simulator. A series of experiments was carried out using the visual occlusion method. Nine subject drivers drove in the simulator, and the output data related to visual demand information and positioning of the subject vehicle were connected. The data relating to visual demand information and lateral positioning on curves and tangents were processed using Microsoft ExceFM and analyzed using SAS, a statistical software. The turning directions, characteristics of preceding elements, and the combination of curve to curve, tangent to curve, or curve to tangent have been considered as nominal variables and analyzed as independent variables with visual demand. It has been observed that visual demand varies widely with the inverse of radius of curvature of the preceding and current elements, and the characteristics of the combination of the current and the preceding element. Visual demand also varies on identical tangents, depending on the deflection angle, inverse of radius, and turning direction of the preceding curve. The standard deviation of lateral positioning of the subject vehicle was evaluated with respect to the centre-line of the driving lane. This was supposed to have a considerable impact on visual demand evaluation, but it has been observed that this does not bear any significant relationship to visual demand. In addition to curves, tangents, as preceding elements have an immense impact on visual demand evaluation on following curves. Besides, visual demand on tangents has also been observed as highly dependent on the preceding curve and their turning directions.

Evaluation of driver visual demand at different design speeds on complex two-dimensional rural highway alignments

Road crashes are a major cause of loss of human life, property and money throughout the world. One of the reasons behind these crashes is the interaction between drivers and road alignments. The need to understand the factors that affect drivers has become obvious and is now being addressed by researchers. Moreover, driver workload is gaining attention as a measure of highway-design consistency as it directly reveals design features to the driver. This research focuses on evaluating driver visual demand at different design speeds along with other geometric design features for two-dimensional rural horizontal roadway alignments. Twelve such alignments having simple and complex curves were designed following the standards of the American Association of Highway and Transportation Officials (AASHTO) and the Transportation Association of Canada (TAC). The driver simulator at Ryerson University, Toronto, recently modified after the integration of a car, was used for the simulation of roadway alignments. Scenario Definition Language (SDL) was used to develop Event files for simulation and to save the required data. Twelve drivers drove the simulated alignments. The output data relating to driver visual demand were processed using MS Notepad and MS Excel. The visual demand calculations for full-element length (VDF), half-element length (VDH) and the first 30 m of element length (VD30) for curve and tangent sections of alignments were done using MS Excel. Statistical Analysis Software (SAS) was used to anlayze and develop models for VDF, VDH and VD30 for curve and tangent sections, first considering design speed only as explanatory variable and then considering design speed along with other geometric design characteristics as explanatory variables. It has been observed that visual demand increases with the increase in design speed. Besides, the combined effect of design speed an other geometric design characteristics (e.g., the type of preceding element, the turning direction of a curve) has significant effect on visual demand. It was also found that visual demand followed a Log Normalized distribution which was also observed by previous research. The developed models were used to establish the visual demand profile for highway design consistency evaluation. The comparison of visual demand profile and operating speed profile has shown that the visual demand can be an acceptable measure for evaluating the highway design consistency.

Evaluation of driver visual demand in complex two dimensional rural highway alignments

Transportation has proven to be one of the most important infrastructures in the economic development of any country. Safe and effective traffic operations support growth of the economy and help in future developments. Highway alignment design plays a crucial role in implementing safer traffic operation and management. Road accidents not only jeopardize safety, but also have a major effect on the national economy. These accidents can be divided in three classes, grouped according to their severity. Statistics in North America and Europe show that one of the major reasons for such road accidents is driver error. Wrong decisions during navigation may be the primary reason for such errors. Wrong decisions occur when a driver is unable to process the range of visual information available in a complex highway situation. Drivers need to have sufficient visual information in guiding and controlling vehicles along the correct path. Drivers scan the roadway to collect visual information. This visual information consists mainly of the traffic situation, roadway signs, and the information from the highway alignment itself. The information from the highway alignment plays a major role in decision-making during maneuvering. All drivers, therefore, need sufficient visual information for perfect navigating, and for guiding and controlling their vehicles on the road. The main focus of this research study was on evaluating visual demands on two-dimensional highway alignments with an emphasis on determining the effect of complex curves on visual demand. Complex curves are defined as combinations of simple, compound, and reverse curves in a series. Eighteen hypothetical alignments for two-lane rural highways have been developed following the standard guidelines of the Transportation Association of Canada (TAC) and American Association of State Highway Transportation Officials (AASHTO). These alignments were simulated in a low-cost driving simulator. A series of experiments was carried out using the visual occlusion method. Nine subject drivers drove in the simulator, and the output data related to visual demand information and positioning of the subject vehicle were connected. The data relating to visual demand information and lateral positioning on curves and tangents were processed using Microsoft ExceFM and analyzed using SAS, a statistical software. The turning directions, characteristics of preceding elements, and the combination of curve to curve, tangent to curve, or curve to tangent have been considered as nominal variables and analyzed as independent variables with visual demand. It has been observed that visual demand varies widely with the inverse of radius of curvature of the preceding and current elements, and the characteristics of the combination of the current and the preceding element. Visual demand also varies on identical tangents, depending on the deflection angle, inverse of radius, and turning direction of the preceding curve. The standard deviation of lateral positioning of the subject vehicle was evaluated with respect to the centre-line of the driving lane. This was supposed to have a considerable impact on visual demand evaluation, but it has been observed that this does not bear any significant relationship to visual demand. In addition to curves, tangents, as preceding elements have an immense impact on visual demand evaluation on following curves. Besides, visual demand on tangents has also been observed as highly dependent on the preceding curve and their turning directions.

Evaluation of driver visual demand at different design speeds on complex two-dimensional rural highway alignments

Road crashes are a major cause of loss of human life, property and money throughout the world. One of the reasons behind these crashes is the interaction between drivers and road alignments. The need to understand the factors that affect drivers has become obvious and is now being addressed by researchers. Moreover, driver workload is gaining attention as a measure of highway-design consistency as it directly reveals design features to the driver. This research focuses on evaluating driver visual demand at different design speeds along with other geometric design features for two-dimensional rural horizontal roadway alignments. Twelve such alignments having simple and complex curves were designed following the standards of the American Association of Highway and Transportation Officials (AASHTO) and the Transportation Association of Canada (TAC). The driver simulator at Ryerson University, Toronto, recently modified after the integration of a car, was used for the simulation of roadway alignments. Scenario Definition Language (SDL) was used to develop Event files for simulation and to save the required data. Twelve drivers drove the simulated alignments. The output data relating to driver visual demand were processed using MS Notepad and MS Excel. The visual demand calculations for full-element length (VDF), half-element length (VDH) and the first 30 m of element length (VD30) for curve and tangent sections of alignments were done using MS Excel. Statistical Analysis Software (SAS) was used to anlayze and develop models for VDF, VDH and VD30 for curve and tangent sections, first considering design speed only as explanatory variable and then considering design speed along with other geometric design characteristics as explanatory variables. It has been observed that visual demand increases with the increase in design speed. Besides, the combined effect of design speed an other geometric design characteristics (e.g., the type of preceding element, the turning direction of a curve) has significant effect on visual demand. It was also found that visual demand followed a Log Normalized distribution which was also observed by previous research. The developed models were used to establish the visual demand profile for highway design consistency evaluation. The comparison of visual demand profile and operating speed profile has shown that the visual demand can be an acceptable measure for evaluating the highway design consistency.

Side Plank Pose Exercises for Adolescent Idiopathic Scoliosis Patients—Some Concerns About a Randomized Controlled Trial

In their recent article, Side Plank Pose Exercises for Adolescent Idiopathic Scoliosis Patients, Sarkisova, et. al. found no beneficial effect using the simple poses that Drs. Groessl, Sherman and I found successful in reversing adolescent idiopathic scoliosis (AIS) and degenerative scoliosis (DS). Although they tried to follow our protocol exactly, they did not. They did not distinguish thoracic from lumbar or thoracolumbar from complex (both thoracic and lumbar) curves, affecting the randomization. See Figure 2 in their study. The side plank is only intended to reverse lumbar and thoracolumbar curves, and actually exaggerates thoracic curves, and the thoracic component of complex curves. The vicissitudes of randomization placed 25 lumbar and thoracolumbar curves in the control and non-compliant groups, but no lumbar and only one thoracolumbar in the intervention group that did the side plank. This trial did not prove that the side plank does not reduce lumbar curves: none were tested.

The Method of High Accuracy Calculation of Robot Trajectory for the Complex Curves

The geometric model accuracy is crucial for product design. More complex surfaces are represented by the approximation methods. On the contrary, the approximation methods reduce the design quality. A new alternative calculation method is proposed. The new method can calculate both conical sections and more complex curves. The researcher is able to get an analytical solution and not a sequence of points with the destruction of the object semantics. The new method is based on permutation and other symmetries and should have an origin in the internal properties of the space. The classical method consists of finding transformation parameters for symmetrical conic profiles, however a new procedure for parameters of linear transformations determination was acquired by another method. The main steps of the new method are theoretically presented in the paper. Since a double result is obtained in most stages, the new calculation method is easy to verify. Geometric modeling in the AutoCAD environment is shown briefly. The new calculation method can be used for most complex curves and linear transformations. Theoretical and practical researches are required additionally.