Quart-parametric interpolations for intersecting paths

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

doi:10.1016/j.cad.2009.01.007

Cited by 2 publications

(2 citation statements)

References 19 publications

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“…The differences on the accuracy and time costs of the four approaches are demonstrated in Table. 4. The Results of comparison on efficiency are illustrated in Fig.…”

Section: Validationmentioning

confidence: 99%

“…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%

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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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“…The differences on the accuracy and time costs of the four approaches are demonstrated in Table. 4. The Results of comparison on efficiency are illustrated in Fig.…”

Section: Validationmentioning

confidence: 99%