The compression of CAD models is a key technology for realizing Internet-based collaborative product development because big model sizes often prohibit us to achieve a rapid product information transmission. Although there exist some algorithms for compressing discrete CAD models, original precise CAD models are focused on in this paper. Here, the characteristics of hierarchical structures in CAD models and the distribution of their redundant data are exploited for developing a novel data encoding method. In the method, different encoding rules are applied to different types of data. Geometric data is a major concern for reducing model sizes. For geometric data, the control points of B-spline curves and surfaces are compressed with the second-order predictions in a local coordinate system. Based on analysis to the distortion induced by quantization, an efficient method for computation of the distortion is provided. The results indicate that the data size of CAD models can be decreased efficiently after compressed with the proposed method.

A topology optimization methodology, named "smooth boundary topology optimization," is proposed to overcome the shortcomings of cell-based methods. Material boundary is represented by B-spline curves and their control points are considered as design variables. The design is improved by either creating a hole or moving control points. To determine which is more beneficial, a selection criterion is defined. Once determined to create a hole, it is represented by a new B-spline and recognized as a new boundary. Because the proposed method deals with the control points of B-spline as design variables, their total number is much smaller than cell-based methods and it ensures smooth boundaries. Differences between our method and level set method are also discussed. It is shown that our method is a natural way of obtaining smooth boundary topology design effectively combining computer graphics technique and design sensitivity analysis.

The inverse offset method (IOM) is widely used for generating cutter paths from the point-based surface where the surface is characterised by a set of surface points rather than parametric polynomial surface equations. In the IOM, cutter path planning is carried out by specifying the grid sizes, called the step-forward and step-interval distances respectively in the forward and transverse cutting directions. The step-forward distance causes the chordal deviation and the step-forward distance produces the cusp. The chordal deviation and cusp are also functions of local surface slopes and curvatures. As the slopes and curvatures vary over the surface, different step-forward and step-interval distances are appropriate in different areas for obtaining the machined surface accurately and efficiently. In this paper, the chordal deviation and cusp height are calculated in consideration with the surface slopes and curvatures, and their combined effect is used to estimate the machined surface error. An adaptive grid generation algorithm is proposed, which enables the IOM to generate cutter paths adaptively using different step-forward and step-interval distances in different regions rather than constant step-forward and step-interval distances for entire surface.

Reverse engineering of reliefs aims to turn an existing relief superimposed on an underlying surface into a geometric model which may be applied to a different base surface. Steps in this process include segmenting the relief from the background, and describing it as an offset height field relative to the underlying surface. We have previously considered relief segmentation using a geometric snake. Here, we show how to use this initial segmentation to estimate the background surface lying under the relief, which can be used (i) to refine the segmentation and (ii) to express the relief as an offset field. Our approach fits a B-spline surface patch to the measured background data surrounding the relief, while tension terms ensure this background surface smoothly continues underneath the relief where there are no measured background data points to fit. After making an initial estimate of relief offset height everywhere within the patch, we use a support vector machine to refine the segmentation. Tests demonstrate that this approach can accurately model the background surface where it underlies the relief, providing more accurate segmentation, as well as relief height field estimation. In particular, this approach provides significant improvements for relief concavities with narrow mouths and can segment reliefs with small internal holes.

In density-based topology optimization, 0/1 solutions are sought. Discrete topological problems are often relaxed with continuous design variables so that they can be solved using continuous mathematical programming. Although the relaxed methods are practical, grey areas appear in the optimum topologies. SIMP (Solid Isotropic Microstructures with Penalization) employs penalty schemes to suppress the intermediate densities. SRV (the Sum of the Reciprocal Variables) drives the solution to a 0/1 layout with the SRV constraint. However, both methods cannot effectively remove all the grey areas. SRV has some numerical aspects. In this work, a new scheme SIMP-SRV is proposed by combining SIMP and SRV approaches, where SIMP is employed to generate an intermediate solution to initialize the design variables and SRV is then adopted to produce the final design. The new method turned out to be very effective in conjunction with the method of moving asymptotes (MMA) when using for the stiffness topology optimization of continuum structures for minimum compliance. The numerical examples show that the hybrid technique can effectively remove all grey areas and generate stiffer optimal designs characterized with a sharper boundary in contrast to SIMP and SRV.

This paper presents an algorithm of optimal cutting tool selection for machining of the point-based surface that is defined by a set of surface points rather than parametric polynomial surface equations. As the ball-end and fillet-end mills are generally used for finish machining in a 3-axis computer numerical control machine, the algorithm is applicable for both cutters. The optimum tool would be as large as possible in terms of the cutter radius and/or corner radius which maximise (s) the material removal rate (i.e., minimise (s) the machining time), while still being able to machine the entire point-based surface without gouging any surface point. The gouging are two types: local and global. In this paper, the distance between the cutter bottom and surface points is used to check the local gouging whereas the shortest distance between the surface points and cutter axis is effectively used to check the global gouging. The selection procedure begins with a cutter from the tool library, which has the largest cutter radius and/or corner radius, and then adequacy of the point-density is checked to limit the accuracy of the cutter selection for the point-based surface within tolerance prior to the gouge checking. When the entire surface is gouge-free with a chosen cutting tool then the tool becomes the optimum cutting tool for a list of cutters available in the tool library. The effectiveness of the algorithm is demonstrated considering two examples.

The objective of this work is to integrate reliability analysis into topology optimization problems. We introduce the reliability constraint in the topology optimization formulation, and the new model is called Reliability-Based Topology Optimization (RBTO). The application of the RBTO model gives a different topology relative to the classical topology optimization that should be deterministic. When comparing the structures resulting from the deterministic topology optimization and from the RBTO model, the RBTO model yields structures that are more reliable than the deterministic ones (for the same weight). Several applications show the importance of this integration.

Recently, feature-based solid modeling systems have been widely used in product design. However, for engineering analysis of a product model, an ed CAD model composed of mid-surfaces is desirable for conditions in which the ed model does not affect analysis result seriously. To meet this requirement, a variety of solid ion methods such as MAT (medial axis transformation) have been proposed to provide an ed CAE model from a solid design model. The algorithm of the MAT approach can be applied to any complicated solid model. However, additional work to trim and extend some parts of the result is required to obtain a practically useful CAE model because the inscribed sphere used in the MAT method generates insufficient surfaces with branches. On the other hand, the mid-surface ion approach supports a practical method for generating a two-dimensional ed model, even though it has difficulties in creating a mid-surface from some complicated parts. In this paper, we propose a dimension reduction approach on solid models based on the midsurface abstraction approach. This approach simplifies the solid model by abbreviating or removing trivial features first such as the fillet, mounting, or protrusion. The geometry of each face is replaced with mid-patches from the simplified model, and then unnecessary topological entities are deleted to generate a clean ed model. Also, additional work, such as extending and stitching mid-patches, completes the generation of a mid-surface model from the patches.

As the modular production is an important issue in globalized manufacturing industries, sub modules or parts of the final product are provided by many suppliers. Some part suppliers design their own products for themselves. In some cases, part supplier may provide the same type product to multiple 1-tier companies. Because all suppliers and 1-tier companies can not use the same CAD system in general case, the engineering change in the CAD model of one company could not propagate to related CAD models of other companies directly. Although they use the same CAD system, it is hard to share their CAD model with each other because of company security policy. In this paper, the neutral reference model, which consists of the neutral skeleton model and the external reference model, is proposed to apply a global top-down modeling approach to collaborating companies.

To understand the structure of molecules, various computational methodologies have been extensively investigated such as the Voronoi diagram of the centers of atoms in molecule and the power diagram for the weighted points where the weights are related to the radii of the atoms. For a more improved efficiency, constructs like an $\alpha$-shape or a weighted $\alpha$-shape have been developed and used frequently in a systematic analysis of the morphology of molecules. However, it has been recently shown that $\alpha$-shapes and weighted $\alpha$-shapes lack the fidelity to Euclidean distance for molecules with polysized spherical atoms. We present the theory as well as algorithms of $\beta$-shape and $\beta$-complex in $\mathbb{R}^3$ which reflects the size difference among atoms in their full Euclidean metric. We show that these new concepts are more natural for most applications and therefore will have a significant impact on applications based on particles, in particular in molecular biology. The theory will be equivalently useful for other application areas such as computer graphics, geometric modeling, chemistry, physics, and material science.

This paper presents a practical approach for surface reconstruction from unoriented point clouds. Instead of estimating local surface orientation, we first generate a set of depth images from the input point clouds, and a coarse mesh is then generated based on them by space carving techniques. The resultant mesh is progressively refined by local mesh refinement and optimization according to surface distance measure. A manifold mesh approximating the input points within an given tolerance is finally obtained. Our approach is easy to implement, but has the ability to outputs high quality meshes in different resolutions. We show that the proposed approach is not sensitive to several types of data disfigurement and is able to reconstruct models robustly from variance input data.

Sketch based query plays an important role in shape matching for 3D shape retrieval system. Some researchers suggest the sketch based query interfaces. It is more effective to capture the needs of users rather than query by example. In this paper, we propose a new 2D sketch based query interface with coarse filters for shape matching. Coarse filtering enables to eliminate unfavorable shapes from shapes in DB. For the purpose of coarse filtering, we use two filters with the topological and geometric patterns. For the validity of our method, we show the experimental results.