Geodesic curve computations on surfaces

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

doi:10.1016/s0167-8396(03)00023-2

Cited by 45 publications

(19 citation statements)

References 3 publications

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“…By substituting Eqs. (5) and (6) into Eq. 1, the surface can be defined as a (1, ) n -Bézier surface as An example of (1, ) n -Bézier surface ( 3) n = is shown in Fig.…”

Section: Formulation Of Developable Surfacementioning

confidence: 99%

“…Since the membrane structure can be realized by connecting several planar sheets, it is desirable to design the cutting pattern so that uniform in-plane tension stress is generated in the membrane. The most conventional approach utilizes the geodesic line [5] to obtain approximate cutting patterns from the target curved surface [6,7]. Punurai et al [8] proposed an optimization approach using genetic algorithm.…”

Section: Introductionmentioning

confidence: 99%

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Shape Design of Curved Surface of Membrane Structure Using Developable Surface

Cui¹,

Ohsaki²

2018

Journal of the International Association for Shell and Spatial

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A method is presented for design of curved surface of frame supported membrane structures. Since a uniform stress state is desired, the minimal surface is often chosen as an ideal target curved surface. Another ideal shape is a developable surface that can be generated from a plane sheet. Therefore, in this paper, the minimal surface, the developable surface, and an intermediate surface between them are chosen as the target curved surface. The cutting patterns are generated by reducing the uniform stress from the plane sheet obtained from the curved surface, where correction coefficients are incorporated. In the numerical examples, the properties of selfequilibrium shape and its stress distribution are investigated for surfaces generated from the three kinds of target curved surfaces.

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“…By substituting Eqs. (5) and (6) into Eq. 1, the surface can be defined as a (1, ) n -Bézier surface as An example of (1, ) n -Bézier surface ( 3) n = is shown in Fig.…”

Section: Formulation Of Developable Surfacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Shape Design of Curved Surface of Membrane Structure Using Developable Surface

Cui¹,

Ohsaki²

2018

Journal of the International Association for Shell and Spatial

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“…There are many suggested methods to calculate discrete geodesics and it is still an active area of research investigation. [23][24][25] In this work, the simpler Dijkstra's algorithm 22 has been used to compute the discrete geodesics in the discretized structure.…”

Section: A Formulation-wave Propagation Approachmentioning

confidence: 99%

Acoustic emission source location in composite structure by Voronoi construction using geodesic curve evolution

Gangadharan

Prasanna

Bhat

et al. 2009

The Journal of the Acoustical Society of America

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Conventional analytical/numerical methods employing triangulation technique are suitable for locating acoustic emission (AE) source in a planar structure without structural discontinuities. But these methods cannot be extended to structures with complicated geometry, and, also, the problem gets compounded if the material of the structure is anisotropic warranting complex analytical velocity models. A geodesic approach using Voronoi construction is proposed in this work to locate the AE source in a composite structure. The approach is based on the fact that the wave takes minimum energy path to travel from the source to any other point in the connected domain. The geodesics are computed on the meshed surface of the structure using graph theory based on Dijkstra's algorithm. By propagating the waves in reverse virtually from these sensors along the geodesic path and by locating the first intersection point of these waves, one can get the AE source location. In this work, the geodesic approach is shown more suitable for a practicable source location solution in a composite structure with arbitrary surface containing finite discontinuities. Experiments have been conducted on composite plate specimens of simple and complex geometry to validate this method.

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“…A unique geodesic curve can be drawn through any point on a surface along a specified direction tangent to the surface. It can be shown that the geodesic curve segment joining start point and goal point on a surface has extremal length [2,3,4,20]. In the recent years, some geodesic development has Kasap [5] who used different method to solve the non-linear system of equation with boundary condition, Chen [25] proposes geodesic-like for find geodesic on surface and Gabriel [14] used geodesic distance for Riemannian metrics in computer vision and graphics.…”

Section: Introductionmentioning

confidence: 99%

3D path planning based on nonlinear geodesic equation

Lin

et al. 2014

11th IEEE International Conference on Control &Amp; Automation (ICCA)

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Abstract-A lot of methods have been proposed for 2D path planning of mobile robot, which could be a mobile platform or a wheelchair, in planar maps. This paper addresses a concept of the shortest path planning for a mobile robot to traverse a 3D surface, which is a parametrized regular surface that models the non-flat terrain on which the mobile robot traverses. Geodesic curve linking a given start to a given target that is locally shortest on non-flat terrain is used as path. Nonlinear geodesic equations are computed by a gradient descent method with energy function of geodesic, which is shown to converge to the geodesic path in a neighborhood of target position in which a certain Lipschitz condition holds. We present numerical simulations to illustrate the geodesic path planning on non-flat terrains.

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Geodesic curve computations on surfaces

Cited by 45 publications

References 3 publications

Shape Design of Curved Surface of Membrane Structure Using Developable Surface

Shape Design of Curved Surface of Membrane Structure Using Developable Surface

Acoustic emission source location in composite structure by Voronoi construction using geodesic curve evolution

3D path planning based on nonlinear geodesic equation

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