Constructing<i>G</i><sup>1</sup>continuous curve on a free-form surface with normal projection

Wang, Xiaoping; Zhang, Weizhong; Zhou, Laishui; Zhang, Liyan

doi:10.1080/00207160802624349

Cited by 3 publications

(2 citation statements)

References 19 publications

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“…Although the related theory is complicated compared to the first order method, this second order method is claimed to be faster than the first order method. Wang et al in [47] and [48] proposed algorithms for G 1 and G 2 continuous curve construction on a free-form surface using normal projection, respectively. The condition of normal projection in [17] was employed with different formulation of a set of differential equations for the normal projection curves.…”

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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“…Under this construction, difficulties lie in the determination of accurate initial points and the robustness of the iteration process. For designing G 1 curves on surfaces, Wang et al [18] interpolated data points and corresponding tangent vectors lying on a freeform surface using a first-order differential equation method analogous to that in [14]. Improvements for designing G 2 curves are made in [20].…”

Section: Introductionmentioning

confidence: 99%

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

Fang

Tam

et al. 2012

International Journal of Computer Mathematics

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Repeated use of point projection to find the projection of a curve on a surface is rather inefficient as the iteration procedures in point projection is typically slow. A novel curve projection scheme is proposed for computing the orthogonal projection of a progenitor curve onto a parametric surface. Under this scheme, the projection curve is parameterized using the parameter of the progenitor curve. Differential geometric characteristics of the projection curve are analysed. A marching method with error adjustment is used to calculate the projection curve. Several examples are presented and comparisons are made to demonstrate the effectiveness of the proposed scheme.

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