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In this paper we present a shape approximation method which yields accurate and unique polygonal approximations. The approach first looks for arcs with two or three runs along the shape boundary whose arc-to-chord deviations are not only the smallest in their local areas but also smaller than a tolerance value. These arcs are then replaced by their respective chords. This process goes on iteratively until no arc can be reduced for the given tolerance.

Birefringence characteristics of polished and D-shape fibers have been studied using the rectangular-core waveguide model. It is found that if an elliptical core fiber is polished parallel to the major axis of the core, the shape birefringence always increases with the polishing depth while if the fiber is polished parallel to the minor axis, the birefringence first decreases, becomes zero at one point and then increases sharply in the reverse direction.

A modified moire topographic technique has been developed to measure the surface shape of precise mechanical metal parts smoothly finished with shaving or grinding. By this technique, the difference of 3-D shape of curved surfaces from a standard surface can be measured with a fringe sensitivity of several microns. The change of the sensitivity is analysed and the feasibility of the technique is demonstrated by applying to the measurement of a tooth surface of a spur gear.

A method is developed for solving analytically the tidal equations for oceanic basins of uniform depth which are composed of an arbitrary number of adjoining rectangles. The method is applied to the solution of the semidiurnal K 2 tide in rectangular and cross-shaped basins. It is found that in the case of flat basins of dimensions of up to 1000 km , the dynamic amplification is small. In the case of the cross-shaped oceanic basin, shown in figure 8, which has an area of close to half a hemisphere, we found a dynamic amplification factor of 41. The condition of resonance to the K 2 tide of an ocean of this size an d shape is correlated with a state of resonance found previously (Accad & Pekeris 1963) in similar ocean basins. The convergence of the solution in the case of a cross-shaped basin is not as good as in the case of a rectangular basin, the slowest convergence occurring near the blunt edges.

We propose new techniques for 2-D shape/contour completion, which is one of the important research topics related to shape analysis and computer vision, e.g. the detection of incomplete objects due to occlusion and noises. The purpose of shape completion is to find the optimal curve segments that fill the missing contour parts, so as to acquire the best estimation of the original complete object shapes. Unlike the previous work using local smoothness or minimum curvature priors, we solve the problem under a Bayesian formulation taking advantage of global shape prior knowledge. With the priors, our methods are expert in recovering significant shape structures and dealing with large occlusion cases. There are two different priors adopted in this paper: (i) A generic prior model that prefers minimal global shape transformation (including non-rigid deformation and affine transformation with respect to a reference object shape) of the recovered complete shape; and (ii) a class-specific shape prior model learned from training examples of an object category, which prefers the reconstructed shape to follow the learned shape variation models of the category. Efficient contour completion algorithms are suggested corresponding to the two types of priors. Our experimental results demonstrate the advantage of the proposed shape completion approaches compared to the existing techniques, especially for objects with complex structure under severe occlusion.

A new perimeter for shapes composed of cells is defined. This perimeter is called the contact perimeter, which corresponds to the sum of the boundaries of neighboring cells of the shape. Also, a relation between the perimeter of the shape and the contact perimeter is presented. The contact perimeter corresponds to the measure of compactness proposed here called discrete compactness. In this case, the term compactness does not refer to point-set topology, but is related to intrinsic properties of objects.

A design work on a thin-double-wall vacuum vessel has been performed for JT-60U (an upgraded machine of JT-60), which has a larger plasma current up to 7MA and a larger plasma volume (∼100 m 3 ). The JT-60U vacuum vessel with a D-shaped cross section of only circular arcs will be fabricated by pressing Inconel plates. The structural analysis has been performed on magnetic loads induced by a plasma disruption and thermal loads during a plasma discharge. The maximum stress is obtained within allowable stresses of Inconel 625, so that it is concluded that this type of the D-shaped vacuum vessel is suitable for JT-60U. A full-scale mock-up was fabricated successfully.

A 3-D shape analysis system using moire topography technique is described and its application in 3-D measurement of the face is presented. With this system 80 moire patterns of a human face with normal morphology are analyzed and the statistical parameters on a number of feature points on the face are obtained. Some important problems encountered in this application are discussed. >

Following the selection of a working set of parameters for NET, it has become possible to elaborate on the design of the toroidal field coil system. The coils have basically a vertically elongated D shape. In the toroidal assembly of 16 coils the straight legs of the coils form a vault. This vault is subjected to the NET centering forces of the coils and balances the lateral forces acting on the straight leg. The conductor is force flow cooled A15 type superconductor, with a steel jacket to reinforce the winding pack. The insulation is glass fibre reinforced epoxy resin, the ground insulation may contain layers of Kapton.

The vacuum vessel of the JAERI Tokamak-60 Upgrade (JT-60U) has a multiarced D-shaped cross section, and an Inconel 625 thin-double-wall structure is used as the main structure of the vessel. The electromagnetic forces introduced by disruption of moving plasma were analyzed by the MATEX code system using a three-dimensional 10 degrees sector model. Structural analyses were also conducted by FEM (finite-element method) code systems. A three-dimensional fine-meshed model of a 20 degrees sector was used for static stress analyses and dynamic response analyses. In this model, the thin double wall was changed to a single shell with the equivalent anisotropic stiffness calculated by FEM analyses. Local stresses of the thin double wall were analyzed with zooming models, and fatigue life was evaluated and confirmed by comparing the results of the FEM analyses and fatigue life experiments. The average dynamic factor (i.e. ratio of the dynamic result to the static result) was about 1.5 for stresses and reaction forces at supports. Based on the analyses and evaluation, the integrity of the JT-60U vacuum vessel was determined, and the results are reflected in the structural design and fabrication of the vessel. >

Here we describe a sensor capable of perceiving complex one-dimensional (1-D) shape of an underlying substrate in a static and dynamic manner. The sensor consists of seven, serially connected, hyper-flexible strain gauges, manufactured using stretchable-gold-conductordeposited-on-PDMS technology. The custom designed read-out scheme allows decoupling strain-sensitive resistances of the strain-gauges from the parasitic pressure- and temperature-sensitive resistances of the connectors. The developed prototype device confirms full operation within the tested deflections ranging from 0 o to 35 o, showing an average sensitivity of 36 !/o and an average resolution of 0.22 o. The read-out frequency of 100 Hz allows quick scanning of the whole sensor array.