Constructing up to G 2 continuous curve on freeform surface

Wang, Xiaoping; Meng, Yaqin; Wang, Zhiguo; Zhang, Liyan

doi:10.1007/s00371-010-0462-x

Cited by 5 publications

(10 citation statements)

References 22 publications

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“…For any i ¼ 0; 1; Á Á Á ; N − 1, the equations (Wang et al, 2010). The similar conclusions hold for parameter q iþ1 .…”

Section: G 2 Continuous Curvessupporting

confidence: 64%

“…(16) is the key to successfully construct G1 or G2 continuous curve on S. For detailed proof, please refer to Wang et al . (2010).…”

Section: Implementation and Discussionmentioning

confidence: 99%

“…We need to note that even if we use Bezier curve, spline curve or their interpolation form as the projected curve C(t) when using Azariadis's method, the final target curve Q(t) on the point-cloud surface S cannot achieve G2 continuity. This is because the curve Q(t) obtained via projection and the designed space curve C(t) must satisfy Theorem 1 in Wang et al . (2010).…”

Section: Implementation and Discussionmentioning

confidence: 99%

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Construction of G2 continuous curve on point-cloud surface

Wang,

Wang

2023

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PurposeThe curve construction on surfaces is becoming more and more important in computer-aided design (CAD), computer graphics (CG) and the other related fields. This problem is often encountered in NC machining, tool path generation, automated fiber placement and so on. However, designing curves on curved surfaces is quite different from constructing a curve in Euclidean space. Therefore, the traditional methods of curve design are not suitable for constructing a continuous curve on surface. The authors need to perform interpolation directly on surface so that the final target curve is embedded into the given surface and also meets the continuous conditions.Design/methodology/approachFirstly, adopting a series of Hermite blending functions, the authors design a space curve passing the given knots on the point-cloud surface. Then, the authors construct a class of directrixes that are adopted to determine vector fields for projection. Finally, a complete G2 continuous curve embedded in point-cloud surfaces is constructed by solving the first-order ordinary differential equations (ODEs).Findings The authors’ main contribution is to overcome the problem of constructing G1 and G2 continuous curves on point-cloud surfaces and the authors’ schemes are based on the projection moving least square (MLS) surfaces and traditional differential geometric.Originality/valueBased on the framework of projection MLS surfaces, a novel method to overcome the problem of constructing G2 continuous curves on point-cloud surfaces is proposed.

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“…For any i ¼ 0; 1; Á Á Á ; N − 1, the equations (Wang et al, 2010). The similar conclusions hold for parameter q iþ1 .…”

Section: G 2 Continuous Curvessupporting

confidence: 64%

“…(16) is the key to successfully construct G1 or G2 continuous curve on S. For detailed proof, please refer to Wang et al . (2010).…”

Section: Implementation and Discussionmentioning

confidence: 99%

Section: Implementation and Discussionmentioning

confidence: 99%

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Construction of G2 continuous curve on point-cloud surface

Wang,

Wang

2023

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“…(4) Calculate the perpendicularity error ε using Equation (20) and make corrections using Equation (24) once the error is above a specified threshold. (7), (13) and (14) to calculate …”

Section: Outline Of Our Curve Projection Algorithmmentioning

confidence: 99%

“…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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