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In this paper, a generative design approach is proposed that involves the users’ psychological aspect in the design space exploration stage to create distinct design alternatives. Users’ perceptual judgment about designs is extracted as a psycho-physical distance metric, which is then integrated into the design exploration step to generate design alternatives for the parametric computer-aided design (CAD) shapes. To do this, a CAD model is first parametrized by defining geometric parameters and determining ranges of these parameters. Initial design alternatives for the CAD model are generated using Euclidean distance-based sampling teaching–learning-based optimization (S-TLBO), which is recently proposed and can sample N space-filling design alternatives in the design space. Similar designs are then clustered, and a user study is conducted to capture the subjects’ perceptual response for the dissimilarities between the cluster pairs. In addition, a furthest-point-sorting technique is introduced to equalize the number of designs in the clusters, which are being compared by the subjects in the user study. Afterward, nonlinear regression analyses are carried out to construct a mathematical correlation between the subjects’ perceptual response and geometric parameters in the form of a psycho-physical distance metric. Finally, a psycho-physical distance metric obtained is utilized to explore distinct design alternatives for the CAD model. Another user study is designed to compare the diversification between the designs when the Euclidean and the suggested psycho-physical distance metrics are utilized. According to the user study, designs generated with the latter metric are more distinct.

Recently proposed quad-meshing techniques allow the generation of high-quality semi-regular quadrilateral meshes. This paper outlines the generation of quadrilateral segments using such meshes. Quadrilateral segments are advantageous in reverse engineering because they do not require surface trimming or surface parameterization. The motorcycle graph algorithm of Eppstein et al. produces the motorcycle graph of a given quadrilateral mesh consisting of quadrilateral segments. These graphs are preferable to base complexes, because the mesh can be represented with a smaller number of segments, as T-joints (where the intersection of two neighboring segments does not involve the whole edge or the vertex) are allowed in quadrilateral segmentation. The proposed approach in this study enumerates all motorcycle graphs of a given quadrilateral mesh and optimum graph for reverse engineering is then selected. Due to the high computational cost of enumerating all these graphs, the mesh is cut into several sub-meshes whose motorcycle graphs are enumerated separately. The optimum graph is then selected based on a cost function that produces low values for graphs whose edges trace a large number of highly curved regions in the model. By applying several successive enumeration steps for each sub-mesh, a motorcycle graph for the given mesh is found. We also outline a method for the extraction of feature curves (sets of highly curved edges) and their integration into the proposed algorithm. Quadrilateral segments generated using the proposed techniques are validated by B-spline surfaces.

Today's quad-meshing techniques generate high-quality quadrilateral meshes whose extraordinary vertices (i.e., not four-valence vertices except on the boundary) are generally located in highly curved regions. The motorcycle graph (MCG) algorithm of Eppstein et al. can be used to generate structured partitions of such quadrilateral meshes. However, it is not always possible for it to capture feature curves in the highly-curved parts of the model on the partition boundaries because model geometry is not taken into account. This study investigated feature-aware algorithms representing extensions of the MCG algorithm. Initial partitioning is first performed using a speed control algorithm identical to the MCG algorithm except that it assigns variable rather than constant speed to particles. Partition boundaries are then improved via local path flipping operations. The MCG algorithm and the speed control algorithm are intended to trace as many feature curves as possible, but do not necessarily trace all of them. For this reason, feature curves are extracted and integrated into the proposed framework by adding seeds located at ordinary vertices in addition to extraordinary seeds. The proposed algorithm generates partitions that are still structured, and has been tested with quadrilateral mesh models generated using the mixed integer quadrangulation technique of Bommes et al.

This paper outlines a simple method for computing outermost-surface polygon data from CT images. The concept involves manipulating CT values of object void structures and the subsequent application of isosurface extraction algorithms. To identify void structures, a morphological closing operator is applied to input images, and differences between the input and closed images are computed. The method enables the creation of topologically simple isosurfaces because polygonization of the internal structure is prevented. In addition, sub-voxel accuracy is guaranteed thanks to the application of common methods for polygonization.

Thanks to recent improvements, computational methods can now be used to convert triangular meshes into quadrilateral meshes so that the quadrilateral elements capture well the principal curvature directional fields of surfaces and intrinsically have surface parametric values. In this study, a quadrilateral mesh generated using the mixed integer quadrangulation technique of Bommes et al. is used for input. We first segment a quadrilateral mesh into four-sided patches. The feature curves inside these patches are then detected and are constrained to act as the patch boundaries. Finally, the patch configuration is improved to generate large patches. The proposed method produces bi-monotone patches, which are appropriate for use in reverse engineering to capture the surface details of an object. A shape control parameter that can be adjusted by the user during the patch generation process is also provided to support the creation of patches with good bi-monotone shapes. This study mainly targets shape models of mechanical parts consisting of major smooth surfaces with feature curves between them.

The authors present a method for extracting polygon data of endocranial surfaces from CT images of human crania. Based on the fact that the endocast is the largest empty space in the crania, we automate a procedure for endocast extraction by integrating several image processing techniques. Given CT images of human crania, the proposed method extracts endocranial surfaces by the following three steps. The first step is binarization in order to fill void structures, such as diploic space and cracks in the skull. We use a void detection method based on mathematical morphology. The second step is watershed-based segmentation of the endocranial part from the binary image of the CT image. Here, we introduce an automatic initial seed assignment method for the endocranial region using the distance field of the binary image. The final step is partial polygonization of the CT images using the segmentation results as mask images. The resulting polygons represent only the endocranial part, and the closed manifold surfaces are computed even though the endocast is not isolated in the cranium. Since only the isovalue threshold and the size of void structures are required, the procedure is not dependent on the experience of the user. The present paper also demonstrates that the proposed method can extract polygon data of endocasts from CT images of various crania.

Mesh generation from X-ray computed tomography (CT) images of mechanical parts is an important consideration in industrial application, and boundary surface meshes in multimaterial parts can be extracted by generating segmented meshes from segmented images. In this paper, the authors outline a new approach for achieving segmented mesh generation. The image is first subjected to centroidal Voronoi tessellation and Delaunay tessellation steered by a density map to create a triangular mesh while maintaining discontinuities between materials. Given an input domain and a number of initial sites, the energy function is minimized automatically by iteratively updating the Voronoi tessellation and relocating sites to produce optimized domain discretization and form the mesh. Thus, the mesh in question is effectively and quickly segmented into different parts via this new graph cut method. The proposed approach is considered more efficient because there are fewer triangles than pixels, which reduces computation time and memory usage.

Semi-landmarks play an important role in the analysis of the fossil crania. While anatomical landmarks can be located reliably, locating semi-landmarks consistently is difficult because they are generally distributed around featureless regions and cannot be located using local shape descriptors.

Centroidal Voronoi tessellations can be constructed using iterative improvement methods such as Lloyd’s method. Using iterative improvement methods implies that the convergence speed and the quality of the results depend on the initialization methods. In this chapter, we briefly describe how to construct centroidal Voronoi tessellations on surface meshes and propose efficient initialization methods. The proposed methods try to make initial tessellations mimic the properties of the centroidal Voronoi tessellations. We compare our methods with other initialization methods: random sampling and farthest point sampling. The experimental results show that our methods have the faster convergence speed than farthest point sampling and outperform random sampling.

Centroidal Voronoi tessellations can be constructed using iterative improvement methods such as Lloyd?s method. Using iterative improvement methods implies that the convergence speed and the quality of the results depend on the initialization methods. In this paper, we propose an efficient initialization method for constructing centroidal Voronoi tessellations on surface meshes. The proposed method tries to make initial tessellations mimic the properties of the centroidal Voronoi tessellations. We compare our method with other initialization methods: random sampling, farthest point sampling and Ward?s method. The results show that our method and Ward?s method have the faster convergence speed than random sampling and farthest point sampling, and create better tessellations than random sampling.