scholarly journals Computing the Closest Approach Distance of Two Ellipsoids

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1302
Author(s):  
Min Gyu Choi
Keyword(s):  
Computer Games ◽  
Contact Point ◽  
Normal Vector ◽  
Bisection Method ◽  
Stopping Criterion ◽  
Approach Distance ◽  
Collision Handling ◽  
Deformable Bodies ◽  
Real Time Applications ◽  
Center Distance

This paper presents two practical methods for computing the closest approach distance of two ellipsoids in their inter-center direction. The closest approach distance is crucial for collision handling in the dynamic simulation of rigid and deformable bodies approximated with ellipsoids. To find the closest approach distance, we formulate a set of equations for two ellipsoids contacting each other externally in terms of the inter-center distance, contact point, and normal vector. The equations are solved robustly and efficiently using a hybrid of the fixed-point iteration method and bisection method with root bracketing, and a hybrid of Newton’s method and the bisection method. In addition to a stopping criterion expressed with the progress of the solution, we introduce a novel criterion expressed in terms of the error in distance. This criterion can be effectively employed in real-time applications such as computer games by allowing an unnoticeable error. Experimental results demonstrate the robustness and efficiency of the proposed methods in various experiments.

Choosing the Optimal Contact Force Distribution for Multi-Limbed Mobile Robots With Three Feet Contact

2003 ◽  
Author(s):  
Dennis W. Hong ◽  
Raymond J. Cipra
Keyword(s):  
Contact Force ◽  
Dimensional Space ◽  
Contact Point ◽  
Optimal Solution ◽  
Solution Space ◽  
Contact Forces ◽  
Force Distribution ◽  
Normal Vector ◽  
Optimization Criteria ◽  
Contact Force Distribution

One of the inherent problems of multi-limbed mobile robotic systems is the problem of multi-contact force distribution; the contact forces and moments at the feet required to support it and those required by its tasks are indeterminate. A new strategy for choosing an optimal solution for the contact force distribution of multi-limbed robots with three feet in contact with the environment in three-dimensional space is presented. The optimal solution is found using a two-step approach: first finding the description of the entire solution space for the contact force distribution for a statically stable stance under friction constraints, and then choosing an optimal solution in this solution space which maximizes the objectives given by the chosen optimization criteria. An incremental strategy of opening up the friction cones is developed to produce the optimal solution which is defined as the one whose foot contact force vector is closest to the surface normal vector for robustness against slipping. The procedure is aided by using the “force space graph” which indicates where this solution is positioned in the solution space to give insight into the quality of the chosen solution and to provide robustness against disturbances. The “margin against slip with contact point priority” approach is also presented which finds an optimal solution with different priorities given to each foot contact point for the case when one foot is more critical than the other. Examples are presented to illustrate certain aspects of the method and ideas for other optimization criteria are discussed.

The Detection Methods of Non-Level Road Based on OPCODE

2013 ◽  
Vol 765-767 ◽  
pp. 2189-2194
Author(s):  
Chun Guang Duan ◽  
Shu Yi Pang ◽  
Hsin Guan
Keyword(s):  
Vehicle Dynamics ◽  
Contact Point ◽  
Detection Methods ◽  
Normal Vector ◽  
Detection Accuracy ◽  
Road Detection ◽  
Vehicle Simulation ◽  
The Road ◽  
Detection Model ◽  
Calculation Step

The research of vehicle dynamics performance on the flat road has been more perfect at present. Around the world ,for lack of simulation environment, the analysis of vehicle driving and handling performance on non-level road is on an explorative stage. The paper established tire road detection model by using of open source code OPCODE. The ray given off from the wheel center intersects with the road model, and obtains the precise contact point and the road normal vector. Then wrote computer program based on the established detection model and embedded it into the complex vehicle model to simulate on longitudinal and lateral slope road. The simulation results show that: each detection time reach microsecond level and in the 1ms vehicle dynamics calculation step, road detection model meet the real-time simulation, and also the detection accuracy satisfy the requirements of the whole vehicle simulation.

scholarly journals The n-th section method: A modification of Bisection

2017 ◽  
Vol 13 (4) ◽  
pp. 728-731
Author(s):  
Mohd Rivaie Mohd Ali ◽  
Muhammad Imza Fakhri ◽  
Nujma Hayati ◽  
Nurul Atikah Ramli ◽  
Ibrahim Jusoh
Keyword(s):  
Iterative Sequence ◽  
Bisection Method ◽  
Stopping Criterion ◽  
Fourth Section ◽  
Section Method ◽  
Selected Functions ◽  
Number Of Iterations

Bisection method is the easiest method to find the root of a function. This method is based on the existence of a root on a specified interval. This interval is then halved or divided into two parts. The root is known to be laying in either one of these interval. The iterative sequence is continued until a desired stopping criterion is reached. In this research, a new modification of bisection method namely fourth section and sixth section methods are introduced. These methods are tested for several selected functions by using Maple software. The results are then analyzed based on the number of iterations and the CPU times. Based on the results, it is shown that when the interval increases, the CPU will also increase. However, the number of iterations is reduced significantly.

scholarly journals An algebraic condition and an algorithm for the internal contact between two ellipsoids

2009 ◽  
Vol 26 (6) ◽  
pp. 635-644 ◽  
Author(s):  
Ibrahim Trabelsi ◽  
Maher Moakher ◽  
Cendrine Gatumel ◽  
Henri Berthiaux
Keyword(s):  
Contact Point ◽  
Detection Algorithm ◽  
Normal Vector ◽  
Contact Detection ◽  
Pharmaceutical Chemical ◽  
Algebraic Condition ◽  
Content Type ◽  
Food Industries ◽  
Internal Contact ◽  
Time Required

PurposeThe purpose of this paper is to present a new method for the detection and resolution of the contact point between two ellipsoids. Numerical simulations of ellipsoidal particles in a rotary cylinder are also presented.Design/methodology/approachAn algebraic condition is developed for the internal contact between two ellipsoids and an efficient contact detection algorithm for overlapping ellipsoids is implemented.FindingsThis method was found to have the advantages of effectiveness and speed in the detection and resolution of the contact point.Originality/valueThe dynamics of granular materials are of great importance in many industries dealing with powders and grains, such as pharmaceutical, chemical, and food industries. The main difficulty of such simulations is the excessive CPU time required for a large number of particles. In the discrete element method, contact detection between grains is the most expensive step in solving a nonlinear system for determination of the contact point, the normal vector and the overlap distance between ellipsoids. The numerical behavior and the optimization of the new algorithm presented in this paper are important also.

scholarly journals A Study on Interferential Tool Position Correcting Algorithm in Rough Machining of 3d Impeller Variable-axis Plunge Milling

2021 ◽  
Author(s):  
Lei Dong ◽  
Jie Wang
Keyword(s):  
Tool Path ◽  
Contact Point ◽  
Normal Vector ◽  
Sudden Increase ◽  
Rough Machining ◽  
Plunge Milling ◽  
Radial Depth ◽  
Milling Method ◽  
Tool Position ◽  
Cutter Position

Abstract The plunge milling method has remarkably improved the rough machining efficiency of 3D impeller channel. However, in conventional cutter position planning for plunge milling, interference at the end of every cutter position due to sudden increase of radial depth is inevitable, which may seriously compromise the service life of machine tool and cutter, as well as the cutting efficiency at the interferential phase. This study optimized the cutter axis vector for the tool path of conventional rough machining of 3D impeller variable -axis plunge milling to make the angle between the normal vector for workpiece surface at the cutter contact point and the cutter-axis vector of adjacent tool position increase gradually from outlet to inlet at the smallest scale. Based on this, an iterative algorithm for tool center position and safety height for the cutter was provided, thus making the hub allowance of the optimized tool path for plunge milling as small as possible without affecting the subsequent machining on the premise of avoiding the interferential phenomenon. Finally, the correctness of the proposed method was verified by relevant numerical examples.

On the Choice of the Contact Frame in Railroad Vehicle Dynamics

2009 ◽  
Author(s):  
Ali Afshari ◽  
Ahmed A. Shabana
Keyword(s):  
Angular Velocity ◽  
Contact Point ◽  
Rolling Direction ◽  
Contact Forces ◽  
Normal Vector ◽  
Principal Curvatures ◽  
Hertz Theory ◽  
Principal Directions ◽  
Railroad Vehicle ◽  
Contact Ellipse

In some of the wheel/rail creep theories used in railroad vehicle simulations, the direction of the tangential creep forces is assumed to be the wheel rolling direction (RD). When Hertz theory is used, an assumption is made that the rolling direction is the direction of one of the axes of the contact ellipse. In principle, the rolling direction depends on the wheel motion, while the direction of the axes of the contact ellipse (CE) are determined using the principal directions which depend only on the geometry of the wheel and rail surfaces and do not depend on the motion of the wheel. The RD and CE directions can also be different from the direction of the rail longitudinal tangent (LT) at the contact point. In this investigation, the differences between the contact frames that are based on the RD, LT, and CE directions, that enter into the calculation of the wheel/rail creep forces and moments, are discussed. The choice of the frame, in which the contact forces are defined, can be determined using one longitudinal vector and the normal to the rail at the contact point. While the normal vector is uniquely defined, different choices can be made for the longitudinal vector including the RD, LT, and CE directions. In the case of pure rolling or when the slipping is small, the RD direction can be defined using the cross product of the angular velocity vector and the vector that defines the location of the contact point. Therefore, this direction does not depend explicitly on the geometry of the wheel and rail surfaces at the contact point. The LT direction is defined as the direction of the longitudinal tangent obtained by differentiation of the rail surface equation with respect to the rail longitudinal parameter (arc length). Such a tangent does not depend explicitly on the direction of the wheel angular velocity nor does it depend on the wheel geometry. The CE direction is defined using the direction of the axes of the contact ellipse used in Hertz theory. In the Hertzian contact theory, the contact ellipse axes are determined using the principal directions associated with the principal curvatures. Therefore, the CE direction differs from the RD and LT directions in the sense that it is function of the geometry of the wheel and rail surfaces. In order to better understand the role of geometry in the formulation of the creep forces, the relationship between the principal curvatures of the rail surface and the curvatures of the rail profile and the rail space curve is discussed in this investigation. Numerical examples are presented in order to examine the differences in the results obtained using the RD, LT and CE contact frames.

3D Garment Real-Time Simulation in Character Animation

2010 ◽  
Vol 108-111 ◽  
pp. 753-758 ◽  
Author(s):  
Yang Liu
Keyword(s):  
Real Time ◽  
Character Animation ◽  
Virtual Character ◽  
Real Time Simulation ◽  
Time Simulation ◽  
Mass Spring Model ◽  
Collision Handling ◽  
Physically Based ◽  
Deformable Bodies ◽  
Mass Spring

In this paper, a framework of 3D Real-time Garment Simulation System for character animation is presented .For the problem of computational efficiency and stability for cloth physical modeling, we proposed a cloth mass-spring model based on constraint. Take geometry sphere and cylinder as example to explaining the whole strategy which used to dealing with cloth deformable bodies colliding with environment object. We described the procedure of physically based simulation, and illustrated the result and analysis of the experiment. By using the technique of parameterized human body modelling, virtual try-on was realized with the different shape of virtual character. Finally, integrating the techniques of character animation, physically based cloth simulation and non-precise deformable object collision handling, we create the real-time simulation animation of virtual character.

Directions of the Tangential Creep Forces in Railroad Vehicle Dynamics

2010 ◽  
Vol 5 (2) ◽  
Author(s):  
Ali Afshari ◽  
Ahmed A. Shabana
Keyword(s):  
Angular Velocity ◽  
Contact Point ◽  
Rolling Direction ◽  
Contact Forces ◽  
Normal Vector ◽  
Principal Curvatures ◽  
Hertz Theory ◽  
Principal Directions ◽  
Railroad Vehicle ◽  
Contact Ellipse

In some of the wheel/rail creep theories used in railroad vehicle simulations, the direction of the tangential creep forces is assumed to be the wheel rolling direction (RD). When the Hertz theory is used, an assumption is made that the rolling direction is the direction of one of the axes of the contact ellipse. In principle, the rolling direction depends on the wheel motion while the direction of the axes of the contact ellipse (CE) are determined using the principal directions, which depend only on the geometry of the wheel and rail surfaces and do not depend on the motion of the wheel. The RD and CE directions can also be different from the direction of the rail longitudinal tangent (LT) at the contact point. In this investigation, the differences between the contact frames that are based on the RD, LT, and CE directions that enter into the calculation of the wheel/rail creep forces and moments are discussed. The choice of the frame in which the contact forces are defined can be determined using one longitudinal vector and the normal to the rail at the contact point. While the normal vector is uniquely defined, different choices can be made for the longitudinal vector including the RD, LT, and CE directions. In the case of pure rolling or when the slipping is small, the RD direction can be defined using the cross product of the angular velocity vector and the vector that defines the location of the contact point. Therefore, this direction does not depend explicitly on the geometry of the wheel and rail surfaces at the contact point. The LT direction is defined as the direction of the longitudinal tangent obtained by differentiation of the rail surface equation with respect to the rail longitudinal parameter (arc length). Such a tangent does not depend explicitly on the direction of the wheel angular velocity nor does it depend on the wheel geometry. The CE direction is defined using the direction of the axes of the contact ellipse used in Hertz theory. In the Hertzian contact theory, the contact ellipse axes are determined using the principal directions associated with the principal curvatures. Therefore, the CE direction differs from the RD and LT directions in the sense that it is function of the geometry of the wheel and rail surfaces. In order to better understand the role of geometry in the formulation of the creep forces, the relationship between the principal curvatures of the rail surface and the curvatures of the rail profile and the rail space curve is discussed in this investigation. Numerical examples are presented in order to examine the differences in the results obtained using the RD, LT and CE contact frames.

Real-Time Acoustic Phenomena Modelling for Computer Games Audio Engine

2015 ◽  
Vol 40 (2) ◽  
pp. 205-211 ◽  
Author(s):  
Bartłomiej Miga ◽  
Bartosz Ziółko
Keyword(s):  
Real Time ◽  
Efficient Method ◽  
Computer Games ◽  
Digital Filters ◽  
Digital Audio ◽  
Simplified Models ◽  
Audio Processing ◽  
Real Time Applications

Abstract This article presents an efficient method of modelling acoustic phenomena for real-time applications such as computer games. Simplified models of reflections, transmission, and medium attenuation are described along with assessments conducted by a professional sound designer. The article introduces representation of sound phenomena using digital filters for further digital audio processing.

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