scholarly journals Visualization of Coalescence of Multiple Small Bubbles with Closed B-Spline Curve

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Fangfang Zhang ◽  
Hongjun Li
Keyword(s):  
Computer Games ◽  
Control Point ◽  
Main Idea ◽  
Surface Shape ◽  
Simulation Algorithm ◽  
Coalescence Process ◽  
B Spline ◽  
Bubble Deformation ◽  
Key Issues ◽  
Small Bubbles

The smoothness of surface shape is one of the key issues to simulate coalescence of underwater bubbles. In this paper, B-spline closed curve is used to realize the visual simulation of multibubble coalescence. The main idea of the proposed algorithm is to construct a continuous bubble deformation which is guided by the normal direction of each control point and weighted by the distance from the point to the geometry center of the contour. The advantages of this algorithm include the smoothness of the bubble contour in the processing of deformation and the randomness of dynamic process and coalescence process. Experiment results show that the simulation algorithm works well and can be used in 3D computer games and animations.

scholarly journals Trajectory optimization of the 6-degrees-of-freedom high-speed parallel robot based on B-spline curve

2019 ◽  
Vol 103 (1) ◽  
pp. 003685041988011
Author(s):  
Jiangping Mei ◽  
Fan Zhang ◽  
Jiawei Zang ◽  
Yanqin Zhao ◽  
Han Yan
Keyword(s):  
Trajectory Optimization ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Control Point ◽  
Parallel Robot ◽  
B Spline ◽  
Spline Curve ◽  
Deformation Problem ◽  
Point Subset ◽  
6 Degrees Of Freedom

According to the problem that the existing high-speed parallel robot cannot satisfy the operation requirements of non-planar industrial production line, a 6-degrees-of-freedom high-speed parallel robot is proposed to carry out the kinematic and dynamic analyses. Combining with the door-type trajectory commonly used by the parallel robot, it adopts 3-, 5-, and 7-time B-spline curve motion law to conduct the trajectory planning in operation space. Taking the average cumulative effect of joint jerky as the optimization target, a trajectory optimization method is proposed to improve the smoothness of robot end-effector motion with the selected motion law. Furthermore, to solve the deformation problem of the horizontal motion stage of the trajectory, a mapping model between the control point subset of B-spline and the motion point subset of trajectory is established. Based on the main diagonally dominant characteristic of the coefficient matrix, the trajectory deformation evaluation index is constructed to optimize the smoothness and minimum deformation of the robot motion trajectory. Finally, compared to without the optimization, the maximum robot joint jerk decreases by 69.4% and 72.3%, respectively, and the maximum torque decreases by 51.4% and 38.9%, respectively, under a suitable trajectory deformation.

Research on the Key Issues of Numerical Controlled Machine Layout Design

2014 ◽  
Vol 548-549 ◽  
pp. 968-973
Author(s):  
Zhi Gang Xu
Keyword(s):  
Recursive Formula ◽  
Layout Design ◽  
Basis Functions ◽  
Nurbs Curve ◽  
B Spline ◽  
Machine Layout ◽  
Spline Basis ◽  
Key Issues ◽  
Normal Vectors

Formulas for the derivatives and normal vectors of non-rational B-spline and NURBS are proved based on de BOOR’s recursive formula. Compared with the existing approaches targeting at the non-rational B-spline basis functions, these equations are directly targeted at the controlling points, so the algorithms and programs for NURBS curve and surface can also be applied to the derivatives and normals, the calculating performance is increased. A simplified equation is also proved in this paper.

Filling N-Sided Holes With Trimmed B-Spline Surfaces Based on Energy-Minimization Method

2015 ◽  
Vol 15 (1) ◽  
Author(s):  
Xiaodong Liu
Keyword(s):  
Energy Minimization ◽  
Computer Aided Design ◽  
Control Points ◽  
Minimization Method ◽  
B Spline ◽  
Spline Surface ◽  
Spline Surfaces ◽  
Key Issues ◽  
Complex Constraints ◽  
Aided Design

Using a trimmed rectangular B-Spline surface to fill an n-sided hole is a much desired operation in computer aided design (CAD), but few papers have addressed this issue. Based on an energy-minimization or variational B-Spline technique, the paper presents the technique of using one single trimmed rectangular B-Spline surface to fill an n-sided hole. The method is efficient and robust, and takes a fraction of a second to fill n-sided holes with high-quality waterproof B-Spline surfaces under complex constraints. As the foundation of filling n-sided holes, the paper also presents the framework and addresses the key issues on variational B-Spline technique. Without any precalculation, the variational B-Spline technique discussed in this paper can solve virtually any B-Spline surface with up to 20,000 control points in real time, which is much more efficient and powerful than previous work in the variational B-Spline field. Moreover, the result is accurate and satisfies CAD systems' high-precision requirements.

scholarly journals Control point insertion for B-spline curves

1988 ◽  
Vol 38 (2) ◽  
pp. 307-313 ◽  
Author(s):  
Heinz H. Gonska ◽  
Andreas Röth
Keyword(s):  
User Interface ◽  
Control Point ◽  
Point Of View ◽  
Control Points ◽  
Natural User Interface ◽  
B Spline ◽  
Spline Curves

Inserting new knots into B-spline curves is a well-known technique in CAGD to gain extra flexibility for design purposes. However, from a user's point of view, the insertion of knots is somewhat unsatisfactory since the newly generated control points sometimes show up in unexpected locations. The aim of this note is to show that these problems can be circumvented by inserting the control vertices directly, thus also providing a more natural user interface.

scholarly journals Real Time Animation of Trees Based on BBSC in Computer Games

2009 ◽  
Vol 2009 ◽  
pp. 1-8 ◽  
Author(s):  
Xuefeng Ao ◽  
Zhongke Wu ◽  
Mingquan Zhou
Keyword(s):  
Real Time ◽  
Computer Games ◽  
3D Model ◽  
Physical Simulation ◽  
High Demand ◽  
Complicated Structure ◽  
Tree Model ◽  
Model Trees ◽  
B Spline ◽  
Spline Curves

That researchers in the field of computer games usually find it is difficult to simulate the motion of actual 3D model trees lies in the fact that the tree model itself has very complicated structure, and many sophisticated factors need to be considered during the simulation. Though there are some works on simulating 3D tree and its motion, few of them are used in computer games due to the high demand for real-time in computer games. In this paper, an approach of animating trees in computer games based on a novel tree model representation—Ball B-Spline Curves (BBSCs) are proposed. By taking advantage of the good features of the BBSC-based model, physical simulation of the motion of leafless trees with wind blowing becomes easier and more efficient. The method can generate realistic 3D tree animation in real-time, which meets the high requirement for real time in computer games.

Filling N-Sided Holes Using Trimmed B-Spline Surfaces

2012 ◽  
Author(s):  
Xiaodong Liu
Keyword(s):  
Energy Minimization ◽  
Control Points ◽  
Variational Technique ◽  
High Quality ◽  
B Spline ◽  
Cad Systems ◽  
Spline Surface ◽  
Spline Surfaces ◽  
Key Issues ◽  
Complex Constraints

Using one single trimmed B-Spline surface to fill an n-sided hole is a much desired operation in CAD, but few papers have addressed this issue. The paper presents the method of using trimmed B-Spline surfaces to fill n-sided holes based on energy minimization or variational technique. The method is efficient and robust, and takes less than one second to fill n-sided holes with high quality B-Spline surfaces under complex constraints. As the foundation of filling n-sided holes, some key issues on variational B-Spline technique are also discussed. The variational technique discussed is significantly much more efficient and powerful than previous research, and the result is very accurate to satisfy CAD systems’ high-precision requirements. We demonstrate that, without any pre-calculation, the discussed technique is efficient enough to solve a B-Spline surface with up to 20,000 control points in real time while satisfying an arbitrary combination of point and curve constraints.

Sticking Paint Replacement Films on Ship Hull Surfaced based on Lines of Curvature

2019 ◽  
Author(s):  
M Takezawa ◽  
K Matsuo
Keyword(s):  
Shape Optimization ◽  
Nonlinear Optimization ◽  
Thin Sheet ◽  
Ship Hull ◽  
Surface Shape ◽  
Bulk Carrier ◽  
B Spline ◽  
Original Surface ◽  
Lines Of Curvature ◽  
Curvature Lines

In this paper, we propose a new concept of using the paint replacement films covering a ship-hull surface instead of paint based on lines of curvature. Firstly, we correct the B-spline hull surface within the prescribed deviation from the original surface shape based on nonlinear optimization to smooth the flow of curvature lines. After shape optimization, we adjust the position and the number of curvature lines so that it becomes the surface developments suitable for applying to thin sheet films. Using our method, it is possible to stick the films on the hull surface with few wrinkles. Finally, we applied proposed techniques to a bow of a bulk carrier to demonstrate the effectiveness of our algorithms.

Curve and Surface Representation by Iterative B-Spline Fit to a Data Point Set

1987 ◽  
Vol 16 (1) ◽  
pp. 29-35 ◽  
Author(s):  
Marilyn Lord
Keyword(s):  
Computer Aided Design ◽  
Control Point ◽  
The Body ◽  
B Spline ◽  
B Splines ◽  
Spline Surface ◽  
Data Points ◽  
Point Set ◽  
Support Surfaces ◽  
Aided Design

The method of B-splines provides a very powerful way of representing curves and curved surfaces. The definition is ideally suited to applications in Computer Aided Design (CAD) where the designer is required to remodel the surface by reference to interactive graphics. This particular facility can be advantageous in CAD of body support surfaces, such as design of sockets of limb prostheses, shoe insoles, and custom seating. The B-spline surface is defined by a polygon of control points which in general do not lie on the surface, but which form a convex hull enclosing the surface. Each control point can be adjusted to remodel the surface locally. The resultant curves are well behaved. However, in these biomedical applications the original surface prior to modification is usually defined by a limited set of point measurements from the body segment in question. Thus there is a need initially to define a B-spline surface which interpolates this set of data points. In this paper, a computer-iterative method of fitting a B-spline surface to a given set of data points is outlined, and the technique is demonstrated for a curve. Extension to a surface is conceptually straightforward.

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