• Korean Journal of Computational Design and Engineering
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• v.7 no.4
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• pp.269-279
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• 2002

Geometric shape morphing is an interesting geometric operation that interpolates two geometric shapes to generate in-betweens. It is well known that Minkowski operations can be used to test and build collision-free motion paths and to modify shapes in digital image processing. In this paper, we present a new geometric modeling technique to control the morphing on geometric shapes based on Minkowski sum. The basic idea develops from the linear interpolation on two geometric shapes where the traditional algebraic sum is replaced by Minkowski sum. We extend this scheme into a Bezier-like control structure with multiple control shapes, which enables the interactive control over the intermediate shapes during the morphing sequence as in the traditional CAGD curve/surface editing. Moreover, we apply the theory of blossoming to our control structure, whereby our control structure becomes even more flexible and general. In this paper, we present mathematical models of control structure, their properties, and computational issues with examples.

• Korean Journal of Computational Design and Engineering
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• v.8 no.4
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• pp.243-253
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• 2003

This paper presents a new geometric morphing algorithm for polygons based on a simple geometric structure called direction map, which is mainly composed of a circular list of direction vectors defined by two neighboring vertices of a polygon. To generate a sequence of intermediate morphing shapes, first we merge direction maps of given control shapes based on a certain ordering rule of direction vectors, and scale the length of each direction vectors using Bezier or blossom controls. We show that the proposed algorithm is an improvement of the previous methods based on Minkowski sum (or convolution) in th aspects of computational efficiency and geometric properties.

• International Journal of Aeronautical and Space Sciences
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• v.13 no.1
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• pp.58-63
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• 2012

In general, a conventional flap on an aircraft wing can reduce the aerodynamic efficiency due to geometric discontinuity. On the other hand, the aerodynamic performance can be improved by using a shape-morphing wing instead of a separate flap. In this research, a new flap morphing mechanism that can change the wing shape smoothly was devised to prevent aerodynamic losses. Moreover, a prototype wing was fabricated to demonstrate the morphing mechanism. A shape memory alloy (SMA) wire actuator was used for the morphing wing. The specific current range was measured to control the SMA actuator. The deflection angles at the trailing edge were also measured while various currents were applied to the SMA actuator. The trailing edge of the wing changed smoothly when the current was applied. Moreover, the deflection angle also increased as the current increased. The maximum frequency level was around 0.1 Hz. The aerodynamic performance of the deformed airfoil by the SMA wire was analyzed by using the commercial program GAMBIT and FLUENT. The results were compared with the results of an undeformed wing. It was demonstrated that the morphing mechanism changes the wing shape smoothly without the extension of the wing skin.

• Journal of the Korean Society for Precision Engineering
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• v.25 no.3
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• pp.147-156
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• 2008

A new approach based on cone prism intersection method combined with sorting algorithm is proposed for the fast and robust signed distance field computation. In the method, the space bounding the geometric model composed of triangular net is divided into multiple smaller cells. For the efficient calculation of distance fields, valid points among the triangular net which will generate minimum distances with current cell are selected by checking the intersection between current cell and cone prism generated at each point. The method is simple to implement and able to achieve an order of magnitude improvement in the computation time as compared to earlier approaches. Further the method is robust in handling the traditional sign problems. The validity of the suggested method was demonstrated by providing numerous examples including Boolean operation, shape deformation and morphing of complex geometric models.

• The KIPS Transactions:PartA
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• v.14A no.7
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• pp.435-442
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• 2007

This paper is concerned with the mesh segmentation problem that can be applied to diverse applications such as texture mapping, simplification, morphing, compression, and shape matching for 3D mesh models. The mesh segmentation is the process of dividing a given mesh into the disjoint set of sub-meshes. We propose a method for segmenting meshes by simultaneously reflecting global and local geometric characteristics of the meshes. First, we extract sharp vertices over mesh vertices by interpreting the curvatures and convexity of a given mesh, which are respectively contained in the local and global geometric characteristics of the mesh. Next, we partition the sharp vertices into the $\kappa$ number of clusters by adopting the $\kappa$-means clustering method [29] based on the Euclidean distances between all pairs of the sharp vertices. Other vertices excluding the sharp vertices are merged into the nearest clusters by Euclidean distances. Also we implement the proposed method and visualize its experimental results on several 3D mesh models.