Group morphology with convolution algebras

Lysenko, Mikola; Nelaturi, Saigopal; Shapiro, Vadim

doi:10.1145/1839778.1839781

Cited by 17 publications

(34 citation statements)

References 32 publications

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“…However, the computations can be dramatically simplified by sampling-based approximations [42]. It has been shown that collision measures can be obtained as convolutions of indicator functions of the two bodies [43], and computed rapidly via fast Fourier transform (FFT) if these functions are sampled over uniform grids (i.e., voxelization) [44]. The convolution field provides an implicit representation of the C−obstacle as its 0−superlevel set.…”

Section: Related Workmentioning

confidence: 99%

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Topology optimization with accessibility constraint for multi-axis machining

Mirzendehdel

Behandish

Nelaturi

2020

Computer-Aided Design

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In this paper, we present a topology optimization (TO) framework to enable automated design of mechanical components while ensuring the result can be manufactured using multi-axis machining. Although TO improves the part's performance, the as-designed model is often geometrically too complex to be machined and the as-manufactured model can significantly vary due to machining constraints that are not accounted for during TO. In other words, many of the optimized design features cannot be accessed by a machine tool without colliding with the part (or fixtures). The subsequent post-processing to make the part machinable with the given setup requires trial-and-error without guarantees on preserving the optimized performance. Our proposed approach is based on the well-established accessibility analysis formulation using convolutions in configuration space that is extensively used in spatial planning and robotics. We define an inaccessibility measure field (IMF) over the design domain to identify non-manufacturable features and quantify their contribution to non-manufacturability. The IMF is used to penalize the sensitivity field of performance objectives and constraints to prevent formation of inaccessible regions. Unlike existing discrete formulations, our IMF provides a continuous spatial field that is desirable for TO convergence. Our approach applies to arbitrary geometric complexity of the part, tools, and fixtures, and is highly parallelizable on multi-core architecture. We demonstrate the effectiveness of our framework on benchmark and realistic examples in 2D and 3D. We also show that it is possible to directly construct manufacturing plans for the optimized designs based on the accessibility information.

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Section: Related Workmentioning

confidence: 99%

“…Both sweeps and C−obstacles can be expressed in terms of Minkowski products in C−space, and, in turn, as unions of the more familiar Minkowski sums in R 3 if the rotations are factored out as follows [43]:…”

Section: Morphological Definition Of Accessibilitymentioning

confidence: 99%

Topology optimization with accessibility constraint for multi-axis machining

Mirzendehdel

Behandish

Nelaturi

2020

Computer-Aided Design

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“…Several filters, including the ones introduced in [2], are used to cull out points that are not on the Minkowski sum boundary. Lysenko et al proposed converting the Minkowski sum to a convolution and computing the convolution using a fast Fourier transform (FFT) [20].…”

Section: Minkowski Sumsmentioning

confidence: 99%

Voxelized Minkowski sum computation on the GPU with robust culling

McMains

2011

Computer-Aided Design

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We present a new approach for computing the voxelized Minkowski sum (excluding any enclosed voids) of two polyhedral objects using programmable Graphics Processing Units (GPUs). We first cull out surface primitives that will not contribute to the final boundary of the Minkowski sum, analyzing and adaptively bounding the rounding errors of the culling algorithm to solve the floating point error problem. The remaining surface primitives are then rendered to depth textures along six orthogonal directions to generate an initial solid voxelization of the Minkowski sum. Finally we employ fast flood fill to find all the outside voxels. We generate both solid and surface voxelizations of Minkowski sums without enclosed voids and support high volumetric resolution of 1024 3 with low video memory cost. The whole algorithm runs on the GPU and is at least one order of magnitude faster than existing boundary representation (B-rep) based algorithms. It avoids the large number of 3D Boolean operations needed in most existing algorithms and is easy to implement. The voxelized Minkowski sums can be used in a variety of applications including motion planning and penetration depth computation.

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“…An interesting approach to configuration space analysis and similar problems was presented recently by Lysenko et al, who reformulated the framework of group morphology in terms of group convolution algebras [27].…”

Section: Path Planning and Configuration Space Analysismentioning

confidence: 99%

“…The same theory can be applied for symmetry detection of convex polyhedra, see for example [48]. Also, group convolution algebras have been applied for this purpose [27].…”

Section: Shape Comparison and Symmetry Detectionmentioning

confidence: 99%

Mathematical Morphology in Computer Graphics, Scientific Visualization and Visual Exploration

Roerdink

2011

Mathematical Morphology and Its Applications to Image and Signal Processing

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Abstract. Historically, mathematical morphology has primarily focused on the processing and analysis of two-dimensional image data. In this paper, we survey a number of other areas where mathematical morphology finds fruitful application, such as computer graphics and solid modeling; path planning; filtering, segmentation and visualization of volume data; or visual exploration of high-dimensional data. We also mention techniques for accelerating morphological computations by using graphics hardware (GPU computing).

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Group morphology with convolution algebras

Cited by 17 publications

References 32 publications

Topology optimization with accessibility constraint for multi-axis machining

Topology optimization with accessibility constraint for multi-axis machining

Voxelized Minkowski sum computation on the GPU with robust culling

Mathematical Morphology in Computer Graphics, Scientific Visualization and Visual Exploration

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