A second-order algorithm for curve orthogonal projection onto parametric surface

Xu, Hai-Yin; Fang, Xiongbing; Tam, Hwa Yaw; Wu, Xiaofeng; Hu, Li'an

doi:10.1080/00207160.2011.628385

Cited by 5 publications

(4 citation statements)

References 18 publications

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“…The condition of normal projection in [17] was employed with different formulation of a set of differential equations for the normal projection curves. Xu et al [49] proposed a method of orthogonal projection of a curve on a parametric surface using a second order approximation scheme. The central difference of others is that the projected curve on the surface is parameterized with the parameter of the curve.…”

Section: Extension Of Orthogonal Projection Of Pointsmentioning

confidence: 99%

Orthogonal projection of points in CAD/CAM applications: an overview

Sakkalis

2014

Journal of Computational Design and Engineering

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This paper aims to review methods for computing orthogonal projection of points onto curves and surfaces, which are given in implicit or parametric form or as point clouds. Special emphasis is place on orthogonal projection onto conics along with reviews on orthogonal projection of points onto curves and surfaces in implicit and parametric form. Except for conics, computation methods are classified into two groups based on the core approaches: iterative and subdivision based. An extension of orthogonal projection of points to orthogonal projection of curves onto surfaces is briefly explored. Next, the discussion continues toward orthogonal projection of points onto point clouds, which spawns a different branch of algorithms in the context of orthogonal projection. The paper concludes with comments on guidance for an appropriate choice of methods for various applications.

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Section: Extension Of Orthogonal Projection Of Pointsmentioning

confidence: 99%

Orthogonal projection of points in CAD/CAM applications: an overview

Sakkalis

2014

Journal of Computational Design and Engineering

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“…Curves lying on surfaces show many applications related to design and manufacture, such as surface trimming [1], surface blending [2], NC tool path generation [3,4], and so on. According to the designing manner, curves on a surface can be the offset of a given curve on a surface [3], the intersection curve of two surfaces [4], the projection curve of a spatial curve onto a surface [5][6][7], or the image of a curve in the parametric domain of a parametric surface [1,2].…”

Section: Introductionmentioning

confidence: 99%

Solving the Boundary Value Problem of Curves With Prescribed Geodesic Curvature Based on a Cubic B-Spline Element Method

et al. 2021

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Composite manufacturing processes such as ATP and FW put forward specific requirements for the geodesic curvature along the layup paths of the composite tows and tapes. In the present paper, a nonuniform cubic b-spline element method is considered for solving the boundary value problem of curves with prescribed geodesic curvature. The differential equation system of the target curve is discretized through the point collocation method, and a quasi-Newton iteration scheme is adopted to approach the real solution from an initial approximation. The proposed method is proved to have third order accuracy, which shows more superiorities than existing numerical methods. The performance of our approach is investigated on a series of parametric surfaces, and experimental results demonstrate that the method is efficient.The proposed method could cope with the BVP for curves no matter their geodesic curvature vanishes or not. At the same time, the computed curves are natural and smooth, and no interpolation technique is needed to ensure the continuity of target curves. One potential application of this method is trajectory optimization for automated tape placement process.

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“…Jingyu et al (2019) presented some methods for multi-point inversion and multi-ray surface intersection by combining Newton-Raphson iteration and the Runge-Kutta ordinary differential equation (ODE) solver. Xu et al (2012) described a marching method with error adjustment to calculate the projection curve. Fu et al (2018) proposed an efficient algorithm to find the intersections between two ball B-spline curves, providing accurate intersection curves of boundary surfaces.…”

Section: Introductionmentioning

confidence: 99%

New methods for projecting a 3D object onto a free-form surface

Pei

Wang

Zhang

et al. 2020

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Purpose This paper aims to provide a series of new methods for projecting a three-dimensional (3D) object onto a free-form surface. The projection algorithms presented can be divided into three types, namely, orthogonal, perspective and parallel projection. Design/methodology/approach For parametric surfaces, the computing strategy of the algorithm is to obtain an approximate solution by using a geometric algorithm, then improve the accuracy of the approximate solution using the Newton–Raphson iteration. For perspective projection and parallel projection on an implicit surface, the strategy replaces Newton–Raphson iteration by multi-segment tracing. The implementation takes two mesh objects as an example of calculating an image projected onto parametric and implicit surfaces. Moreover, a comparison is made for orthogonal projections with Hu’s and Liu’s methods. Findings The results show that the new method can solve the 3D objects projection problem in an effective manner. For orthogonal projection, the time taken by the new method is substantially less than that required for Hu’s method. The new method is also more accurate and faster than Liu’s approach, particularly when the 3D object has a large number of points. Originality/value The algorithms presented in this paper can be applied in many industrial applications such as computer aided design, computer graphics and computer vision.

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A second-order algorithm for curve orthogonal projection onto parametric surface

Cited by 5 publications

References 18 publications

Orthogonal projection of points in CAD/CAM applications: an overview

Orthogonal projection of points in CAD/CAM applications: an overview

Solving the Boundary Value Problem of Curves With Prescribed Geodesic Curvature Based on a Cubic B-Spline Element Method

New methods for projecting a 3D object onto a free-form surface

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