Efficient point-projection to freeform curves and surfaces

Oh, Young‐Taek; Kim, Yong-Joon; Lee, Jieun; Kim, Myung-Soo; Elber, Gershon

doi:10.1016/j.cagd.2011.04.002

Cited by 23 publications

(11 citation statements)

References 15 publications

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“…This process is repeated until the termination condition is satisfied. Oh et al [41] employed the concept of the circle/sphere clipping method by [40] but introduced a more efficient technique using the separating axis and k-DOP type of bounding scheme for culling or clipping unnecessary part of curves or surfaces during the iteration. Moreover, through testing the uniqueness of the projection point in the subdivided regions the computational efficiency can be improved.…”

Section: Subdivision Of Curve or Surfacementioning

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: Subdivision Of Curve or Surfacementioning

confidence: 99%

“…Moreover, through testing the uniqueness of the projection point in the subdivided regions the computational efficiency can be improved. The method by Oh et al [41] was extended to compute projection of a moving query point onto a freeform curve [42].…”

Section: Subdivision Of Curve or Surfacementioning

confidence: 99%

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

Sakkalis

2014

Journal of Computational Design and Engineering

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“…After subdivision the surface segments located outside the sphere are repeatedly eliminated until the termination condition is satisfied. The concept of the clipping sphere method was further improved in Reference by using the separating axis and k‐DOP (discrete Orientation Polytopes) type of bounding scheme.…”

Section: Introductionmentioning

confidence: 99%

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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“…The computation problem of the minimum distance between a point and a curve is also called the point projection problem of the curve [1][2][3][4][5][6]. The distance information between a point and a curve is very important for interactively selecting curves and curve construction in geometric modeling, for collision detection and physical simulation in computer graphics and computer vision, for interference avoidance in CAD/CAM and NC verification [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

“…The distance information between a point and a curve is very important for interactively selecting curves and curve construction in geometric modeling, for collision detection and physical simulation in computer graphics and computer vision, for interference avoidance in CAD/CAM and NC verification [4][5][6]. However, most of the methods about this problem investigate the distance problem in the space R 3 , and only few methods study the distance problem on a curved space.…”

Section: Introductionmentioning

confidence: 99%

Computing the minimum distance between a point and a curve on mesh

Zhu

Liu

2015

JCM

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Computation of the distance between two objects is an important problem in computer aided geometric design. To make up the deficiencies in the existing algorithm, a calculation method of the closet distance between point and curve on mesh surfaces is proposed. The curves on surfaces are represented by geodesic B-spline, and the knot insertion algorithm in classic B-spline curve is expand to curved space, so that the geodesic B-spline curve can be decomposed into combination of sub-Bézier curves; using the intermediate results of the expand De Casteljau's algorithm, derivative of curve can be calculated. On this basis, the orthogonal projection point calculation algorithm, which is the projection point from point to curve, in Euclidean space is extended to curved space, and the point calculation method of the orthogonal projection on curved space is given, that is to say, the geodesic distance between point and its orthogonal projection point is the shortest distance from point to curve. Experimental results show that, the proposed method is robust, effective, and with a good adaptability to the shape variation of surface.

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Efficient point-projection to freeform curves and surfaces

Cited by 23 publications

References 15 publications

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

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

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

Computing the minimum distance between a point and a curve on mesh

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