A torus patch approximation approach for point projection on surfaces

Liu, Xiaoming; Yang, Lei; Yong, Jun-Hai; Gu, He-Jin; Sun, Jun

doi:10.1016/j.cagd.2009.01.004

Cited by 41 publications

(45 citation statements)

References 14 publications

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“…In Table 1, the mean running time of the first-order iterative method is 134,760, 141,798, 41,033, 140,051, 137,059, and 42,399 nanoseconds for six different initial iterative values, respectively. In the end, the overall average running time in Table 1 is 106183.33 nanoseconds (≈0.10618 ms), while the overall average running time of Tables 1 and 2 in [18] is 0.3565 ms. So the First-Order method is faster than the algorithm in [18].…”

Section: Numerical Examples Examplementioning

confidence: 98%

“…In the end, the overall average running time in Table 1 is 106183.33 nanoseconds (≈0.10618 ms), while the overall average running time of Tables 1 and 2 in [18] is 0.3565 ms. So the First-Order method is faster than the algorithm in [18]. (See Figure 3).…”

Section: Numerical Examples Examplementioning

confidence: 98%

“…In the end, the overall average running time is 1,043,700 nanoseconds(≈1.0437 ms), while the overall average running time of the Example 2 for the algorithm in [18] is 1.705624977 ms under the same initial iteration condition. So the hybrid second-order algorithm is faster than the algorithm proposed in [18]. On the other hand, from Table 4 In Tables 3 and 4, the convergence tolerance, the decimal place of approximate zero and the computation environment are set as those in Tables 1 and 2.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…The overall average running time of 0.336222 ms in Examples 1 and 2 for their algorithm [18] means the First-Order method is faster than the algorithm in [18]. In [18], authors point out that their algorithm is faster than that in [8], which means the First-Order method is faster than the one in [8]. At the same time, the overall average running time of 61.81167 ms in three Examples for their algorithm [26] is obtained, then the First-Order method is faster than the algorithm in [26].…”

Section: Numerical Examples Examplementioning

confidence: 99%

“…Based on the subdividing concept [16], Piegl and Tiller (1995) [17] present an algorithm for point projection on NURBS surfaces by subdividing a NURBS surface into quadrilaterals, projecting the test point onto the closest quadrilateral, and then recover the parameter from the closest quadrilateral. Liu et al (2009) [18] propose a local surface approximation technique-torus patch approximation-and prove that the approximation torus patch and the original surface are second-order osculating. By using the tangent line and the rectifying plane, Li et al (2013) [19] present an algorithm for finding the intersection between the two spatial parametric curves.…”

Section: Introductionmentioning

confidence: 99%

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Hybrid Second-Order Iterative Algorithm for Orthogonal Projection onto a Parametric Surface

Wang

et al. 2017

Symmetry

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Abstract:To compute the minimum distance between a point and a parametric surface, three well-known first-order algorithms have been proposed by Hartmann (1999), Hoschek, et al. (1993 and Hu, et al. (2000) (hereafter, the First-Order method). In this paper, we prove the method's first-order convergence and its independence of the initial value. We also give some numerical examples to illustrate its faster convergence than the existing methods. For some special cases where the First-Order method does not converge, we combine it with Newton's second-order iterative method to present the hybrid second-order algorithm. Our method essentially exploits hybrid iteration, thus it performs very well with a second-order convergence, it is faster than the existing methods and it is independent of the initial value. Some numerical examples confirm our conclusion.

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Section: Numerical Examples Examplementioning

confidence: 98%

Section: Numerical Examples Examplementioning

confidence: 98%

Section: Numerical Experimentsmentioning

confidence: 99%

Section: Numerical Examples Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Hybrid Second-Order Iterative Algorithm for Orthogonal Projection onto a Parametric Surface

Wang

et al. 2017

Symmetry

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Assessment of methods for computing the closest point projection, penetration, and gap functions in contact searching problems

Kopačka

Gabriel

Plešek

et al. 2015

Int. J. Numer. Meth. Engng

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Summary In computational contact mechanics problems, local searching requires calculation of the closest point projection of a contactor point onto a given target segment. It is generally supposed that the contact boundary is locally described by a convex region. However, because this assumption is not valid for a general curved segment of a three‐dimensional quadratic serendipity element, an iterative numerical procedure may not converge to the nearest local minimum. To this end, several unconstrained optimization methods are tested: the Newton–Raphson method, the least square projection, the sphere and torus approximation method, the steepest descent method, the Broyden method, the Broyden–Fletcher–Goldfarb–Shanno method, and the simplex method. The effectiveness and robustness of these methods are tested by means of a proposed benchmark problem. It is concluded that the Newton–Raphson method in conjunction with the simplex method significantly increases the robustness of the local contact search procedure of pure penalty contact methods, whereas the torus approximation method can be recommended for contact searching algorithms, which employ the Lagrange method or the augmented Lagrangian method. Copyright © 2015 John Wiley & Sons, Ltd.

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Efficient Point Projection to Freeform Curves and Surfaces

Kim

Lee

et al. 2010

Lecture Notes in Computer Science

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A torus patch approximation approach for point projection on surfaces

Cited by 41 publications

References 14 publications

Hybrid Second-Order Iterative Algorithm for Orthogonal Projection onto a Parametric Surface

Hybrid Second-Order Iterative Algorithm for Orthogonal Projection onto a Parametric Surface

Assessment of methods for computing the closest point projection, penetration, and gap functions in contact searching problems

Efficient Point Projection to Freeform Curves and Surfaces

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