Shape Modification of Parametric Curves

A technique of shape modification and deformation for parametric curvesthrough cosine extension function (CEF) is presented. First, a special extension function isdefined, based on which a shape operator matrix is constructed. Then combining such matrix with thecenter of extension and principal directions, two kinds of deformation matrices are defined.Finally, curve deformation is achieved through multiplying its position vector in a local coordinatesystem by deformation matrix or adding the multiplication of a vector field and quasi-deformationmatrix to its position vector in the original coordinate system. Since CEF contains several variableparameters, each of which generates a different effect of shape modification such as controllingthe degree of continuity of the modified part of curve with the unchanged part, ideal deformationeffects can be got fairly and easily. Examples of theoretical analysis show that the method ispotentially useful for geometric modeling, computer graphics and so on.

Quadratic Algebraic Curve Approximate Implicitization for Planar Parametric Curves

In this paper, a type of preserving GC1 quadratic algebraic polynomial curve approximate implicitization method for parametric curves is presented The coefficients of the implicit polynomial are determined by the GC1 continuity conditions and an optimal function's minimization Numerical examples show that this method is effective

Vanishing torsion of parametric curves

We consider the class of parametric curves that can be represented by combination of control points and basis func- tions. A control point is let vary while the rest is held fixed. It’s shown that the locus of the moving control point that yields points of zero torsion is the osculating plane of the corresponding discriminant curve at its point of the same parameter value. The special case is studied when the basis functions sum to one.

A SMOOTH C^1 INTERPOLATION FOR TWO-DIMENSIONAL CONTACT PROBLEMS USING PARAMETRIC CURVE TECHNIQUE

A smooth C^1 interpolation for two-dimensional contact problems using parametric curve technique was developed and implemented.The parametric curve can ensure C^1 continuity of the contact surfaces and provide a unique surface normal vector.Some numerical examples were used to illustrate the advantages of the newly developed representation of contact surface. The results reveal a significant improvement in the prediction of contact stresses and contact area.The predicted contact stresses are less sensitive to the mismatch in meshes of the different contacting bodies.

Adaptive estimation and nonlinear variable gain compensation of the contouring error for precise parametric curve following

Contour following is one of the most important issues faced by many computer-numerical-control(CNC) machine tools to achieve high machining precision. This paper presents a new real-time error compensation method aiming at reducing the contouring error caused by facts such as servo lag and dynamics mismatch in parametric curved contour-following tasks. Due to the lack of high-precision contouring-error estimation method for free-form parametric curved toolpath, the error can hardly be compensated effectively. Therefore, an adaptive accurate contouring-error estimation algorithm is proposed first, where a tangential-error backstepping method based on Taylor's expansion is developed to rapidly find the closest point on the parametric curve to the actual motion position. On this foundation, the contouring error is compensated using a proposed nonlinear variable-gain compensation method, where the compensation gain is obtained according to not only the contouring-error magnitude but also its direction variation. The stability of the system after compensation is analyzed afterwards according to the Jury stability criterion.By design of the compensator in accordance with the presented contouring-error compensation method as well as the stability analyzation result, the balance between the response speed and the contour control stability can be effectively made. Experimental tests demonstrate the feasibility of the presented methods in both contouring-error estimation and contour-accuracy improvement.Contributions of this research are significant for enhancing the contour-following performance of the CNC machine tools.

Graphics Evolutionary Computations in Higher Order Parametric Bezier Curves

This work demonstrates in practical terms the evolutionary concepts and computational applications of Parametric Curves.Specific cases were drawn from higher order parametric Bezier curves of degrees 2 and above.Bezier curves find real life applications in diverse areas of Engineering and Computer Science,such as computer graphics,robotics,animations,virtual reality,among others.Some of the evolutionary issues explored in this work are in the areas of parametric equations derivations,proof of related theorems,first and second order calculus related computations,among others.A Practical case is demonstrated using a graphical design,physical hand sketching,and programmatic implementation of two opposite-faced handless cups,all evolved using quadratic Bezier curves.The actual drawing was realized using web graphics canvas programming based on HTML 5 and JavaScript.This work will no doubt find relevance in computational researches in the areas of graphics,web programming,automated theorem proofs,robotic motions,among others.

Parametric curve with an implicit domain

In this paper we present a new representation of curve, named parametric curve with an implicit domain(PCID), which is a curve that exists in parametric form defined on an implicit domain. PCID provides a bridge between parametric curve and implicit curve because the conversion of parametric form or implicit form to PCID is very convenient and efficient. We propose a framework model for mapping given points to the implicit curve in a homeomorphic manner. The resulting map is continuous and does not overlap. This framework can be used for many applications such as compatible triangulation, image deformation and fisheye views. We also present some examples and experimental results to demonstrate the effectiveness of the framework of our proposed model.

Optimal parameterization of conic curves

Optimal parameterization of specified segment on the algebraic curves is a hot issue in CAGD and CG. Take the optimal approximation of arc-length parameterization as the criterion of optimal parameterization, and the optimal or close to optimal rational parameterization formula of any specified segment on the conic curves is obtained. The new method proposed in this paper has ad- vantage in quantity of calculation and has strong self-adaptability. Finally, a experimental comparison of the results obtained by this method and by the traditional parametric algorithm is conducted.

Optimal Rational Parameterization of Quadratic Curves Based on the Geographic Information of Both Ends

In this paper, we rewrote the equation of algebraic curve segmentswith the geometric informationonboth ends. The optimal or nearly optimal rationalparametric equation is determinedbythe principle that parametricspeedsat both endsareequal. Comparing withotherliteratures, the methodofthis paper has advantage in efficiency andiseasy to realize. The equation of optimal rational parameterization can be obtained directly by the information of both ends. Large numbers ofexperimental data show that our method hasbeen given withmore self-adaptability and accuracy than that ofotherliteratures, and if the parametricspeedat any end reaches its maximum or minimum value, the parameterization is optimal; otherwise itis close tooptimal rational parameterization.

A Review of Lane Detection Based on Deep Learning Methods

Lane detection is animportant aspect of autonomous driving,aiming to ensure that vehicles accurately understand road structures as well as improve their ability to drive in complex traffic environments.In recent years,lane detection tasks based on deep learning methods have made significant progress in detection accuracy.In this paper,we provide a comprehensive review of deep learning-based lane detection tasks in recent years.First,we introduce the background of the lane detection task,including lane detection,the lane datasets and the factors affecting lane detection.Second,we review the traditional and deep learning methods for lane detection,and analyze their features in detail while classifying the different methods.In the deep learning methods classification section,we explore five main categories,including segmentation-based,object detection,parametric curves,end-to-end,and keypoint-based methods.Then,some typical models are briefly compared and analyzed.Finally,in this paper,based on the comprehensive consideration of current lane detection methods,we put forward the current problems still faced,such as model generalization and computational cost.At the same time,possible future research directions are given for extreme scenarios,model generalization and other issues.

Nonlinear Vibration of A Loosely Supported Curved Pipe Conveying Pulsating Fluid under Principal Parametric Resonance

In this paper,the nonlinear dynamics of a curved pipe is investigated in the case of principal parametric resonance due to pulsating flow and impact with loose supports.The coupled in-plane and out-of-plane governing equations with the consideration of von Karman geometric nonUnearity are presented and discretized via the differential quadrature method（DQM）.The nonlinear dynamic responses are calculated numerically to demonstrate the influence of pulsating frequency.Finally,the impact is taken into consideration.The influence of clearance on frettingwear damage,such as normal work rate,contact ratio and impact force level,is demonstrated.