A G1 connection around complicated curve meshes using C1 NURBS Boundary Gregory Patches

Konno, Kouichi; Tokuyama, Yoshimasa; Chiyokura, Hiroaki

doi:10.1016/s0010-4485(00)00087-7

Cited by 8 publications

(3 citation statements)

References 13 publications

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“…Since the left side of equation ( 12) becomes cubic, the degree of polynomial a i is limited to be quadratic. Therefore, when we assume a i using basis patch method [12], the unit vectors a 0 and a 2 are calculated from the boundary and a 1 is calculated using the equation ( 13):…”

Section: Cross Boundary Derivative Generationmentioning

confidence: 99%

Curve Mesh Modeling Method of Trimmed Surfaces for Direct Modeling

祐太¹,

晃市²,

喜政

et al. 2011

The Journal of the Society for Art and Science

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In the shape modeling with 3D CAD systems, the trimmed surface is quite popular. For instance, Japanese Industrial Standards (JIS) models contain a lot of notches, expressed using trimmed surfaces. Since trimmed surfaces are directly modified in direct modeling, it has a big restriction in the shape modification. It is effective to apply a new free-form surface to a closed region composed of the modified edges because the consistency of a trimmed surface can be maintained. This paper proposes the method of fitting a free-form surface by using the offset curve. To be more concrete, an offset curve is generated according to the tangent planes and a point cloud is generated. After that, a B-spline surface is generated using the generated point clouds and the boundary curves, so that a new trimmed surface is generated. Our method is effective for direct modeling that directly modifies the boundary edges of the trimmed surface representing a notch shape.

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Section: Cross Boundary Derivative Generationmentioning

confidence: 99%

Curve Mesh Modeling Method of Trimmed Surfaces for Direct Modeling

祐太¹,

晃市²,

喜政

et al. 2011

The Journal of the Society for Art and Science

Self Cite

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show abstract

“…Similarly, if two surfaces need to satisfy G 1 continuity, they should not only have a common boundary curve, but also have a common tangent plane at the common joint. In order to solve the problem mentioned above, many international scholars have done many studies on the related algorithms of geometric continuity conditions for different geometric models [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

“…As we all know, the geometric continuity conditions of traditional Bézier, rational Bézier and non-uniform rational B-spline (NURBS) surfaces, which can be used to produce engineering complex curves and surfaces, have been widely researched in [13][14][15][16][17][18][19]. Nowadays, the research on geometric continuity conditions of curves and surfaces with shape parameters is still a hot issue in the CAGD field.…”

Section: Introductionmentioning

confidence: 99%

Explicit Continuity Conditions for G1 Connection of S-λ Curves and Surfaces

Abbas

et al. 2020

Mathematics

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The S-λ model is one of the most useful tools for shape designs and geometric representations in computer-aided geometric design (CAGD), which is due to its good geometric properties such as symmetry, shape adjustable property. With the aim to solve the problem that complex S-λ curves and surfaces cannot be constructed by a single curve and surface, the explicit continuity conditions for G1 connection of S-λ curves and surfaces are investigated in this paper. On the basis of linear independence and terminal properties of S-λ basis functions, the conditions of G1 geometric continuity between two adjacent S-λ curves and surfaces are proposed, respectively. Modeling examples imply that the continuity conditions proposed in this paper are easy and effective, which indicate that the S-λ curves and surfaces can be used as a powerful supplement of complex curves and surfaces design in computer aided design/computer aided manufacturing (CAD/CAM) system.

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Continuity conditions for tensor product Q-Bézier surfaces of degree ($$m,\, n$$m,n)

Qin

2018

Comp. Appl. Math.

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A G1 connection around complicated curve meshes using C1 NURBS Boundary Gregory Patches

Cited by 8 publications

References 13 publications

Curve Mesh Modeling Method of Trimmed Surfaces for Direct Modeling

Curve Mesh Modeling Method of Trimmed Surfaces for Direct Modeling

Explicit Continuity Conditions for G1 Connection of S-λ Curves and Surfaces

Continuity conditions for tensor product Q-Bézier surfaces of degree ($$m,\, n$$m,n)

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