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Thickening Freeform Surfaces for Solid Fabrication
"... Purpose: Given an intersectionfree mesh surface S, we introduce a method to thicken S into a solid H located at one side of S. By such a surfacetosolid conversion operation, industrial users are able to fabricate a designed (or reconstructed) surface by rapid prototyping. Design/methodology/appro ..."
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Purpose: Given an intersectionfree mesh surface S, we introduce a method to thicken S into a solid H located at one side of S. By such a surfacetosolid conversion operation, industrial users are able to fabricate a designed (or reconstructed) surface by rapid prototyping. Design/methodology/approach: In this paper, we first investigate an implicit representation of the thickened solid H according to an extension of signed distance function. After that, a partial surface reconstruction algorithm is proposed to generate the boundary surface ∂H of H, which remains the given surface S on the resultant surface. Finding: Experimental tests show that the thickening results generated by our method give nearly uniform thickness and meanwhile do not present shape approximation error at the region of input surface S. These two good properties are important to the industrial applications of solid fabrication. Research limitation/implications: The input polygonal model is assumed to be intersectionfree, where models containing selfintersection will lead to invalid thickening results. Originality/value: A novel robust operation to convert a freeform open surface into a solid by introducing no shape approximation error. A new implicit function that gives a compact mathematical representation, which can easily handle the topological change on the thickened solids. A new polygonization algorithm that generates faces for the boundary of thickened solid meanwhile retaining faces on the input open mesh.
Efficient Exact CollisionChecking of 3D Rigid Body Motions using Linear Transformations and Distance Computations in Workspace
"... AbstractThis paper presents a new method for efficient and exact collisionchecking of linear motions of 3D rigid bodies. 3D rigid bodies have 6D configuration spaces (three degrees of freedom for position and three for orientation), and constitute an important subclass of motion planning probl ..."
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AbstractThis paper presents a new method for efficient and exact collisionchecking of linear motions of 3D rigid bodies. 3D rigid bodies have 6D configuration spaces (three degrees of freedom for position and three for orientation), and constitute an important subclass of motion planning problems. Our method can be used with any collisionchecker that is capable of performing linear transformations and distance computations on 3D geometry. As previous work has shown, computing the distance between the rigid body in some configuration and the workspace obstacles immediately determines the collisionstatus of surrounding configurations. Using a recursive procedure one can then determine exactly whether an entire motion of the rigid body is collisionfree. In this paper, we will show that by performing an optimally selected linear transformation on the workspace, the collisionstatus of rigid body motions can be determined using significantly fewer (costly) distance computations. Since collisionchecking is often the computational bottleneck in samplingbased motion planning, our approach allows for significant performance improvements of algorithms such as PRM and RRT when planning for 3D rigid bodies. We demonstrate the benefit of our approach when used in combination with RRT to construct a planning tree in an illustrative benchmark motion planning scenario.
High Precision Conservative Surface Mesh Generation for Swept Volumes
"... Abstract—We present a novel, efficient and flexible scheme to generate a high quality mesh that approximates the outer boundary of a swept volume. Our approach comes with two guarantees. First, the approximation is conservative, i.e., the swept volume is enclosed by the generated mesh. Second, the o ..."
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Abstract—We present a novel, efficient and flexible scheme to generate a high quality mesh that approximates the outer boundary of a swept volume. Our approach comes with two guarantees. First, the approximation is conservative, i.e., the swept volume is enclosed by the generated mesh. Second, the onesided Hausdorff distance of the generated mesh to the swept volume is upper bounded by a user defined tolerance. Exploiting this tolerance the algorithm generates a mesh that is adapted to the local complexity of the swept volume boundary, keeping the overall output complexity remarkably low. The algorithm is twophased: the actual sweep and the mesh generation. In the sweeping phase we introduce a general framework to compute a compressed voxelization. The phase is tailored for an easy application of parallelization techniques. We show this for our exemplary implementation and provide a multicore solution as
High Quality Conservative Surface Mesh Generation for Swept Volumes
"... Abstract — We present a novel, efficient and flexible scheme to generate a high quality mesh that approximates the outer boundary of a swept volume. Our approach comes with two guarantees. First, the approximation is conservative, i.e., the swept volume is enclosed by the generated mesh. Second, the ..."
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Abstract — We present a novel, efficient and flexible scheme to generate a high quality mesh that approximates the outer boundary of a swept volume. Our approach comes with two guarantees. First, the approximation is conservative, i.e., the swept volume is enclosed by the generated mesh. Second, the onesided Hausdorff distance of the generated mesh to the swept volume is upper bounded by a user defined tolerance. Exploiting this tolerance the algorithm generates a mesh that is adapted to the local complexity of the swept volume boundary, keeping the overall output complexity remarkably low. The algorithm is twophased: the actual sweep and the mesh generation. In the sweeping phase we introduce a general framework to compute a compressed voxelization. The phase is tailored for an easy application of parallelization techniques. We show this for our exemplary implementation and provide a multicore solution as well as a GPU based solution using CUDA. The meshing phase utilizes Delaunay refinement which we carefully modified such that required guarantees are met. The approach is able to handle inputs of very high complexity at desired precision, which we demonstrate on real industrial data sets. I.
Nested Cages
"... and fully encloses it without intersections. A slice through all layers (left), shows a tightly encaged Bunny. Many tasks in geometry processing and physical simulation benefit from multiresolution hierarchies. One important characteristic across a variety of applications is that coarser layers str ..."
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and fully encloses it without intersections. A slice through all layers (left), shows a tightly encaged Bunny. Many tasks in geometry processing and physical simulation benefit from multiresolution hierarchies. One important characteristic across a variety of applications is that coarser layers strictly encage finer layers, nesting one another. Existing techniques such as surface mesh decimation, voxelization, or contouring distance level sets do not provide sufficient control over the quality of the output surfaces while maintaining strict nesting. We propose a solution that enables use of applicationspecific decimation and quality metrics. The method constructs each nextcoarsest level of the hierarchy, using a sequence of decimation, flow, and contactaware optimization steps. From coarse to fine, each layer then fully encages the next while retaining a snug fit. The method is applicable to a wide variety of shapes of complex geometry and topology. We demonstrate the effectiveness of our nested cages not only for multigrid solvers, but also for conservative collision detection, domain discretization for elastic simulation, and cagebased geometric modeling.
REGARDING AN ALTERNATIVE METHOD FOR TRANSLATIONAL SINGLEITEM CONTAINMENT
, 2011
"... The longstanding application of the Minkowski sum for translational packing requires the use of the complement operator. Current implementations which make use of exact arithmetic use convex decomposition to produce the Minkowski sum. In this situation, manipulation of unbounded point sets must be ..."
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The longstanding application of the Minkowski sum for translational packing requires the use of the complement operator. Current implementations which make use of exact arithmetic use convex decomposition to produce the Minkowski sum. In this situation, manipulation of unbounded point sets must be specifically accounted for. Although this can be handled by setting finite space boundaries, or through the use of infimaximal boxes described by Mehlhorn and Seel, we present an alternative formulation, unrestricted in dimension, that eliminates the use of unbounded sets. The idea for this work comes from personal correspondence with Peter Hachenberger, and also from Althaus et al. Our work is to show that this alternative does produce the same result as the standard singleitem packing algorithm, as well as the limitations of its validity. Finally, we build on this to provide a solution for the packing of two objects into a container while continuing to avoid unbounded sets.