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Properties Of Concrete

The power crust is a construction which takes a sample of points from the surface of a three-dimensional object and produces a surface mesh and an approximate medial axis. The approach is to first approximate the medial axis transform (MAT) of the object. We then use an inverse transform to produce the surface representation from the MAT.This idea leads to a simple algorithm with theoretical guarantees comparable to those of other surface reconstruction and medial axis approximation algorithms. It also comes with a guarantee that does not depend in any way on the quality of the input point sample. Any input gives an output surface which is the `watertight' boundary of a three-dimensional polyhedral solid: the solid described by the approximate MAT. This unconditional guarantee makes the algorithm quite robust and eliminates the polygonalization, hole-filling or manifold extraction post-processing steps required in previous surface reconstruction algorithms.In this paper, we use the theory to develop a power crust implementation which is indeed robust for realistic and even difficult samples. We describe the careful design of a key subroutine which labels parts of the MAT as inside or outside of the object, easy in theory but non-trivial in practice. We find that we can handle areas in which the input sampling is scanty or noisy by simply discarding the unreliable parts of the MAT approximation. We demonstrate good empirical results on inputs including models with sharp corners, sparse and unevenly distributed point samples, holes, and noise, both natural and synthetic.We also demonstrate some simple extensions: intentionally leaving holes where there is no data, producing approximate offset surfaces, and simplifying the approximate MAT in a principled way to preserve stable features.

The power crust

The medial axis transform (or MAT) is a representation of an object as an infinite union of balls. We consider approximating the MAT of a three-dimensional object, and its complement, with a finite union of balls. Using this approximate MAT we define a new piecewise-linear approximation to the object surface, which we call the power crust. We assume that we are given as input a sufficiently dense sample of points from the object surface. We select a subset of the Voronoi balls of the sample, the polar balls, as the union of balls representation. We bound the geometric error of the union, and of the corresponding power crust, and show that both representations are topologically correct as well. Thus, our results provide a new algorithm for surface reconstruction from sample points. By construction, the power crust is always the boundary of a polyhedral solid, so we avoid the polygonization, hole-filling or manifold extraction steps used in previous algorithms. The union of balls representation and the power crust have corresponding piecewise-linear dual representations, which in some sense approximate the medial axis. We show a geometric relationship between these duals and the medial axis by proving that, as the sampling density goes to infinity, the set of poles, the centers of the polar balls, converges to the medial axis.

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The power crust, unions of balls, and the medial axis transform

We present a new approach for computing generalized 2D and 3D Voronoi diagrams using interpolation-based polygon rasterization hardware. We compute a discrete Voronoi diagram by rendering a three dimensional distance mesh for each Voronoi site. The polygonal mesh is a bounded-error approximation of a (possibly) non-linear function of the distance between a site and a 2D planar grid of sample points. For each sample point, we compute the closest site and the distance to that site using polygon scan-conversion and the Z-buffer depth comparison. We construct distance meshes for points, line segments, polygons, polyhedra, curves, and curved surfaces in 2D and 3D. We generalize to weighted and farthest-site Voronoi diagrams, and present efficient techniques for computing the Voronoi boundaries, Voronoi neighbors, and the Delaunay triangulation of points. We also show how to adaptively refine the solution through a simple windowing operation. The algorithm has been implemented on SGI workstations and PCs using OpenGL, and applied to complex datasets. We demonstrate the application of our algorithm to fast motion planning in static and dynamic environments, selection in complex user-interfaces, and creation of dynamic mosaic effects. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling; I.3.3 [Computer Graphics]: Picture/Image Generation. Additional

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Fast computation of generalized Voronoi diagrams using graphics hardware

The medial surface is a skeletal abstraction of a solid that provides useful shape information, which compliments existing model representation schemes. The medial surface and its associated topological entities are defined, and an algorithm for computing the medial surface of a large class of B-rep solids is then presented. The algorithm is based on the domain Delaunay triangulation of a relatively sparse distribution of points, which are generated on the boundary of the object. This strategy is adaptive in that the boundary point set is refined to guarantee a correct topological representation of the medial surface.

Shape description by medial surface construction

Bridge weigh in motion (B-WIM) uses accurate sensing systems to transform an existing bridge into a mechanism to determine actual traffic loading. This information on traffic loading can enable efficient and economical management of transport networks and is becoming a valuable tool for bridge safety assessment. B-WIM can provide site-specific traffic loading on deteriorating bridges, which can be used to determine if the reduced capacity is still sufficient to allow the structure to remain operational and minimise unnecessary replacement or rehabilitation costs and prevent disruption to traffic. There have been numerous reports on the accuracy classifications of existing B-WIM installations and some common issues have emerged. This paper details some of the recent developments in B-WIM which were aimed at overcoming these issues. A new system has been developed at Queens University Belfast using fibre optic sensors to provide accurate axle detection and improved accuracy overall. The results presented in this paper show that the fibre optic system provided much more accurate results than conventional WIM systems, as the FOS provide clearer signals at high scanning rates which require less filtering and less post-processing. A major disadvantage of existing B-WIM systems is the inability to deal with more than one vehicle on the bridge at the same time; sensor strips have been proposed to overcome this issue. A bridge can be considered safe if the probability that load exceeds resistance is acceptably low, hence B-WIM information from advanced sensors can provide confidence in our ageing structures.

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Recent developments in bridge weigh in motion (B-WIM)

In many finite element analysis models it would be desirable to combine reduced- or lower-dimensional element types with higher-dimensional element types in a single model. In order to achieve compatibility of displacements and stress equilibrium at the junction or interface between the differing element types, it is important in such cases to integrate into the analysis some scheme for coupling the element types. A novel and effective scheme for establishing compatibility and equilibrium at the dimensional interface is described and its merits and capabilities are demonstrated. Copyright © 2000 John Wiley & Sons, Ltd.

Desmond Robinson

Papers

Shape description by medial surface construction

Recent developments in bridge weigh in motion (B-WIM)

Mixed‐dimensional coupling in finite element models

Computing the medial surface of a solid from a domain Delaunay triangulation

A review of the equations used to predict the velocity distribution within a ship’s propeller jet