Hilbert's space-filling curve for regions with holes

Nair, Siddharth H.; Sinha, Arpita; Vachhani, Leena

doi:10.1109/cdc.2017.8263684

Cited by 9 publications

(9 citation statements)

References 13 publications

(24 reference statements)

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“…Hilbert curve [23], Sierpiński curve [24,25]). Using space-filling curves with varying degrees of subdivision level has been explored for purposes other than 3D printing, such as robotic exploration tasks [26], finite element analysis [27,28], paths for CNC milling [29]. In the context of 3D printing, Kumar et al [30] combined several square based space-filling curves (e.g.…”

Section: Space-filling Curves and Surfacesmentioning

confidence: 99%

CrossFill: Foam Structures with Graded Density for Continuous Material Extrusion

Kuipers

Wang

2019

Computer-Aided Design

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The fabrication flexibility of 3D printing has sparked a lot of interest in designing structures with spatially graded material properties. In this paper, we propose a new type of density graded structure that is particularly designed for 3D printing systems based on filament extrusion. In order to ensure high-quality fabrication results, extrusion-based 3D printing requires not only that the structures are self-supporting, but also that extrusion toolpaths are continuous and free of self-overlap. The structure proposed in this paper, called CrossFill, complies with these requirements. In particular, CrossFill is a self-supporting foam structure, for which each layer is fabricated by a single, continuous and overlap-free path of material extrusion. Our method for generating CrossFill is based on a space-filling surface that employs spatially varying subdivision levels. Dithering of the subdivision levels is performed to accurately reproduce a prescribed density distribution. We demonstrate the effectiveness of CrossFill on a number of experimental tests and applications.

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Section: Space-filling Curves and Surfacesmentioning

confidence: 99%

CrossFill: Foam Structures with Graded Density for Continuous Material Extrusion

Kuipers

Wang

2019

Computer-Aided Design

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“…On repeating this procedure infinitely, the complete HC is generated [2]. We use an approximated version of the HC [15] (Fig. 2).…”

Section: Preliminaries a Mathematical Preliminariesmentioning

confidence: 99%

“…We employ the HC in this endeavour. Such an online strategy is presented in [15], which divides the space into a grid based on the sensor resolution of the agent, and plans a path when the obstacle occupies one grid square. If there is a bigger obstacle, these strategies are unable to guarantee evasion (for eg.…”

Section: Introductionmentioning

confidence: 99%

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Modification of Hilbert's Space-Filling Curve to Avoid Obstacles: A Robotic Path-Planning Strategy

Joshi,

Bhatt,

Sinha

2019

Preprint

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This paper addresses the problem of exploring a region using Hilbert's space-filling curve in the presence of obstacles. No prior knowledge of the region being explored is assumed. An online algorithm is proposed which can implement evasive strategies to avoid up to two obstacles placed side by side and successfully explore the entire region. The strategies are specified changing the waypoint array followed by the robot, locally at the hole. The fractal nature of Hilbert's space-filling curve has been exploited in proving the validity of the solution. Extension of algorithm for bigger obstacles is briefly shown.

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“…Closer in spirit to our approach are the works based on well defined geometric curves such as raster scanning zigzag paths used in cell based schemes discussed in [5], [15], etc., and space filling curves such as the Hilbert curve for multi-agent coverage in [25], and for non-uniform priority based coverage in [22] and [20]. These curves often involve sharp turns and require additional path planning to return to the 'start' position to repeat the task.…”

Section: Literature Surveymentioning

confidence: 99%

Reconfigurable formations of quadrotors on Lissajous curves for surveillance applications

Borkar¹,

Hangal²,

Arya³

et al. 2018

Preprint

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This paper proposes trajectory planning strategies for online reconfiguration of a multi-agent formation on a Lissajous curve. In our earlier work [2], a multi-agent formation with constant parametric speed was proposed in order to address multiple objectives such as repeated collision-free surveillance and guaranteed sensor coverage of the area with ability for rogue target detection and trapping. This work addresses the issue of formation reconfiguration within this context. In particular, smooth parametric trajectories are designed for the purpose using calculus of variations. These trajectories have been employed in conjunction with a simple local cooperation scheme so as to achieve collision-free reconfiguration between different Lissajous curves. A detailed theoretical analysis of the proposed scheme is provided. These surveillance and reconfiguration strategies have also been validated through simulations in MATLAB ® for agents performing parametric motion along the curves, and by Software-In-The-Loop simulation for quadrotors. In addition, they are validated experimentally with a team of quadrotors flying in a motion capture environment.

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Hilbert's space-filling curve for regions with holes

Cited by 9 publications

References 13 publications

CrossFill: Foam Structures with Graded Density for Continuous Material Extrusion

CrossFill: Foam Structures with Graded Density for Continuous Material Extrusion

Modification of Hilbert's Space-Filling Curve to Avoid Obstacles: A Robotic Path-Planning Strategy

Reconfigurable formations of quadrotors on Lissajous curves for surveillance applications

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