Algorithms for projecting points onto conics

Chernov, N.; Wijewickrema, Sudanthi

doi:10.1016/j.cam.2013.03.031

Cited by 22 publications

(28 citation statements)

References 24 publications

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“…In general, this problem is addressed in the context of least squares fitting of quadratic geometric entities, and orthogonal projection is a critical operation in the fitting process. Chernov and Wijewickrema [18] addressed the problem of point projection onto quadratic curves. Their emphasis is placed on the robustness and practical aspects of the solution algorithms with good accuracy and simplicity.…”

Section: Orthogonal Projection Onto Conicsmentioning

confidence: 99%

“…Although several approaches were discussed, which are relatively fast such as [12], [13] and [14], only a few methods are theoretically proven to be robust [16], [19] and [20]. These methods were analyzed, and a modified algorithm of [19] was presented in [18].…”

Section: Orthogonal Projection Onto Conicsmentioning

confidence: 99%

“…from which Newton's method can be employed to obtain the accurate root. An improved version of Eberly's method was proposed by [18]. They followed the similar process to Eberly's with modified coordinate transformation and proposed a process that can be applied to all conic types.…”

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confidence: 99%

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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: Orthogonal Projection Onto Conicsmentioning

confidence: 99%

Section: Orthogonal Projection Onto Conicsmentioning

confidence: 99%

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

Sakkalis

2014

Journal of Computational Design and Engineering

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“…The work in [8] proposed a second-order tracing method for calculating the orthogonal projection of parametric curves onto B-spline surfaces. The work in [9] focused on projecting points onto conics. The work in [10] developed a secondorder algorithm for orthogonal projection onto curves and surfaces.…”

Section: Introductionmentioning

confidence: 99%

Symbolic Computation of the Orthogonal Projection of Rational Curves onto Rational Parameterized Surfaces

Gan

Zhou

2015

Mathematical Problems in Engineering

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This paper focuses on the orthogonal projection of rational curves onto rational parameterized surface. Three symbolic algorithms are developed and studied. One of them, based on regular systems, is able to compute the exact parametric loci of projection. The one based on Gröbner basis can compute the minimal variety that contains the parametric loci. The remaining one computes a variety that contains the parametric loci via resultant. Examples show that our algorithms are efficient and valuable.

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“…For the example given in Eq (13). and p 5 = 6 the trajectory of p t with t = 69 20 is illustrated in (a) as the intersection curve of E t and the sphere Φ t centered in P t .…”

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confidence: 99%

On the Line-Symmetry of Self-motions of Linear Pentapods

Nawratil

2017

Advances in Robot Kinematics 2016

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We show that all self-motions of pentapods with linear platform of Type 1 and Type 2 can be generated by line-symmetric motions. Thus this paper closes a gap between the more than 100 year old works of Duporcq and Borel and the extensive study of line-symmetric motions done by Krames in the 1930's. As a consequence we also get a new solution set for the Borel Bricard problem. Moreover we discuss the reality of self-motions and give a sufficient condition for the design of linear pentapods of Type 1 and Type 2, which have a self-motion free workspace.

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Algorithms for projecting points onto conics

Cited by 22 publications

References 24 publications

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

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

Symbolic Computation of the Orthogonal Projection of Rational Curves onto Rational Parameterized Surfaces

On the Line-Symmetry of Self-motions of Linear Pentapods

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