Geometry based triangulation of multiple trimmed NURBS surfaces

Kumar, G. Vijay; Srinivasan, Prabha; Shastry, K.; Prakash, B.G.

doi:10.1016/s0010-4485(00)00095-6

Cited by 21 publications

(4 citation statements)

References 13 publications

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“…However, the multiple surface has no natural parameter domain, and the initial grid cannot be generated through mapping. To establish a planar domain for both single surface and multiple surface, surface discretization technique [35] and mesh parameterization technique [36] are used.…”

Section: Initial Grid Generationmentioning

confidence: 99%

Digital and automatic design of free-form single-layer grid structures

Gao

et al. 2022

Automation in Construction

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Section: Initial Grid Generationmentioning

confidence: 99%

Digital and automatic design of free-form single-layer grid structures

Gao

et al. 2022

Automation in Construction

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“…. (8) For this equation system, R11 is obtained by the sum of terms of the right hand of Eq. ( 5) except the terms [10(1-v11)…”

Section: Basic Theorymentioning

confidence: 99%

“…For this equation, Wij are the weights and Ni p (u) Nj q (v) are the B-spline basis functions [4]. The weights Wij are calculated by means of the knot vector, which adds points to move the surface toward the control points [8]. For a surface with degree (p, q), there are at most (p+1)x(q+1) non-zero functions to be computed [15].…”

Section: Basic Theorymentioning

confidence: 99%

Improving the Modeling of the Plantar Surface via Bezier Networks and Laser Projection

Rodríguez

2014

ITC

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An automatic technique to improve the plantar surface model via Bezier networks is presented. This technique generates the foot sole model via Bezier networks based on surface points, which are retrieved via line projection. The surface model is defined by means of network weights and the control points, which are measured via line position by a Bezier network. Thus, the model represents the plantar surface with high accuracy. It is because the model passes through by all control points of the physical surface. Furthermore, the network reduces operations and memory size to calculate the surface. It is because the model is implemented with less mathematical terms than the traditional models. Also, the calibration of vision parameters is performed via laser line to avoid external calibration, which determines vision parameters outside of the vision system and increases the surface representation inaccuracy. Additionally, the shoe-last bottom is adjusted to plantar surface model. The viability of the proposed surface modeling is corroborated by an evaluation based on the speed, accuracy and memory size of the traditional surface models. Thus, the contribution of the proposed technique is elucidated.

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“…[14] presents a novel approach using super-surfaces to decrease the number of triangles in the tessellation, but this approach needs a priori connectivity information. Another recent publication is [13], but it only deals with very specific configuration of NURBS surfaces that are stacked on top of each other.…”

Section: Previous Workmentioning

confidence: 99%

Multiresolution rendering by sewing trimmed NURBS surfaces

Kahlesz¹,

Balázs²,

Klein³

2002

Proceedings of the Seventh ACM Symposium on Solid Modeling and Applications - SMA '02

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Most of the industrial parts are designed as trimmed NURBS. For their efficient rendering multiresolution models are needed. To create such models without artifacts at the trimming curves, one needs to sew parts together along the common boundaries. Due to the problem of determining the geometric places in 3D space along the trimming curves where sewing should be done, current approaches need to have a priori neighbourhood information of the patches and this way they do not provide an automatic solution to create large connected models just from a set of surfaces. In this paper we describe a method, which automatically determines common boundaries of trimmed NURBS surfaces and sews along them. Such a method provides us a non-manifold or manifold structure, which can be handled using standard multi-resolution techniques. Several examples of industrial data demonstrate the efficiency and applicability of our new method. The introduced techniques will also be included into the OpenSG scenegraph API [8] as the basic tool for NURBS rendering.

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Geometry based triangulation of multiple trimmed NURBS surfaces

Cited by 21 publications

References 13 publications

Digital and automatic design of free-form single-layer grid structures

Digital and automatic design of free-form single-layer grid structures

Improving the Modeling of the Plantar Surface via Bezier Networks and Laser Projection

Multiresolution rendering by sewing trimmed NURBS surfaces

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