Interactive design exploration for constrained meshes

In architectural design, surface shapes are commonly subject to geometric constraints imposed by material, fabrication or assembly. Rationalization algorithms can convert a freeform design into a form feasible for production, but often require design modifications that might not comply with the design intent. In addition, they only offer limited support for exploring alternative feasible shapes, due to the high complexity of the optimization algorithm.We address these shortcomings and present a computational framework for interactive shape exploration of discrete geometric structures in the context of freeform architectural design. Our method is formulated as a mesh optimization subject to shape constraints. Our formulation can enforce soft constraints and hard constraints at the same time, and handles equality constraints and inequality constraints in a unified way. We propose a novel numerical solver that splits the optimization into a sequence of simple subproblems that can be solved efficiently and accurately.Based on this algorithm, we develop a system that allows the user to explore designs satisfying geometric constraints. Our system offers full control over the exploration process, by providing direct access to the specification of the design space. At the same time, the complexity of the underlying optimization is hidden from the user, who communicates with the system through intuitive interfaces.     

Exit effect on hydrodynamics of the internal circulating fluidized bed riser

This is the first time an extensive investigation has been carried out regarding the effects of riser exit geometry on pressure drop and solid behaviour inside the Internal Circulating Fluidized Bed (ICFB) riser, using different riser exit geometries at several operating conditions.The Radioactive Particle-Tracking (RPT) technique was used for solid concentration measurements and solid residence time distribution at the exit zone. Experiments were conducted using Geldart B particles, in the gas superficial velocity range of 4 to 10 m/s. Axial solid hold-up, solid residence time distribution in the exit zone, and the reflux ratio factor k_m, (defined earlier by [E.H. Van der Meer, R.B. Thorpe, J.F. Davidson, Flow patterns in the square cross-section riser of a circulating fluidized bed and the effect of riser exit design, Chem. Eng. Sc. 55 (19) (2000) 4079-4099]), were the main criteria used to investigate the impact of gas-solid separator devices implemented at the ICFB riser exit.Solid residence time distribution results and axial solid hold-up profiles provided clear evidence that the separator device at the riser exit strongly influences the hydrodynamic structure of the ICFB riser. The V-shaped riser exit geometry was found to be the optimum of all the configurations studied.     

A new stereological principle for test lines in three-dimensional space

A new principle is presented to generate isotropic uniform random (IUR) test lines hitting a geometric structure in three-dimensional space (3D). The principle therefore concerns the estimation of surface area, volume, membrane thickness, etc., of arbitrary structures with piecewise smooth boundary. The principle states that a point-sampled test line on an isotropic plane through a fixed point in 3D is effectively an invariant test line in 3D. Particular attention is devoted to the stereology of particles, where an alternative to the surfactor method is obtained to estimate surface area. An interesting case arises when the particle is convex. The methods are illustrated with synthetic examples.     

Ready, Set, Go! The Voronoi diagram of moving points that start from a line

It is an outstanding open problem of computational geometry to prove a near-quadratic upper bound on the number of combinatorial changes in the Voronoi diagram of points moving at a common constant speed along linear trajectories in the plane. In this note we observe that this quantity is Θ(n²) if the points start their movement from a common line.     

Significance of the elastic peak stress evaluated by FE analyses at the point of singularity of sharp V-notched components

The paper presents an expression useful to estimate the notch stress intensity factor (NSIF) from finite element analyses carried out by using a mesh pattern with a constant element size. The evaluation of the NSIF from a numerical analysis of the local stress field usually requires very refined meshes and then large computational effort. The usefulness of the presented expression is that (i) only the elastic peak stress numerically evaluated at the V‐notch tip is needed and no longer the whole stress–distance set of data; (ii) the adopted meshes are rather coarse if compared to those necessary for the evaluation of the whole local stress field. The proposed expression needs the evaluation of a virtual V‐notch tip radius, i.e. the radius which would produce the same elastic peak stress than that calculated by FEM at the sharp V‐notch tip by means of a given mesh pattern. Once such a radius has been theoretically determined for a given geometry, the expression can be applied in a wide range of notch depths and opening angles.     

焊接试样的焊缝外形尺寸对爆炸试验的影响

选用水面舰艇用９４５钢和潜艇用９２１Ａ钢，研究了不同焊缝外形尺寸对爆炸试验中三缺口试样的中央缺口开裂行为的影响。通过大量的试验数据，确定了开裂判据ｅ≤ｅ_ｍ，为试验前预示中央缺口开裂与否提供了可靠的依据。     

小波变换用于影象分割的研究

将近年来兴起的小波理论应用于影象分割技术，提出了一种基于影象直方图小波变换的影象分割方法，并从理论上给出了使用该法所得分割门限的物理意义。实例表明，这种由粗到细引导的多分辨率分析方法，对于复杂影象的分割具有较强的鲁棒性和有效性，克服了传统分割方法中的参数需要人工确定的缺点。     

《周培德三角剖分不是最小权三角剖分》一文商榷——反例不成立

周培协三角剖分是否能得到最小权三角剖分，周培德在《周培德三角部分不是最小权三角剖分》一文撰写之前已有新的结论，本文还指出《周培德三角剖分不是最小权三角剖分》一文所举反例不成立。     

A generalized approach to the reconstruction of a restricted class of digitized planar curves

Reconstruction of an original continuous curve and the estimation of its parameters from the digitized version of the curve is a challenging problem, as quantization always causes some loss of information. In this paper, we have developed a scheme for reconstruction which is applicable to a class of curves having at the most two parameters. The class of curves for which the scheme works has also been characterized. We have shown that for one-parameter curves the exact domain of values of the parameter can be obtained. But in the two-parameter case, only the smallest rectangle containing the domain can be realised. The distinctive feature of our scheme is that it provides a unified approach to solve the reconstruction and the domain-finding problem for a class of curves.     

Rectilinear steiner tree heuristics and minimum spanning tree algorithms using geographic nearest neighbors

We study the application of the geographic nearest neighbor approach to two problems. The first problem is the construction of an approximately minimum length rectilinear Steiner tree for a set ofn points in the plane. For this problem, we introduce a variation of a subgraph of sizeO(n) used by YaO [31] for constructing minimum spanning trees. Using this subgraph, we improve the running times of the heuristics discussed by Bern [6] fromO(n ² log n) toO(n log² n). The second problem is the construction of a rectilinear minimum spanning tree for a set ofn noncrossing line segments in the plane. We present an optimalO(n logn) algorithm for this problem. The rectilinear minimum spanning tree for a set of points can thus be computed optimally without using the Voronoi diagram. This algorithm can also be extended to obtain a rectilinear minimum spanning tree for a set of nonintersecting simple polygons.The results in this paper are a part of Y. C. Yee's Ph.D. thesis done at SUNY at Albany. He was supported in part by NSF Grants IRI-8703430 and CCR-8805782. S. S. Ravi was supported in part by NSF Grants DCI-86-03318 and CCR-89-05296.