Min-jae Oh

Dimensions and bases of hierarchical tensor-product splines

We prove that the dimension of trivariate tensor-product spline space of tri-degree (m,m,m) with maximal order of smoothness over a three-dimensional domain coincides with the number of tensor-product B-spline basis functions acting effectively on the domain considered. A domain is required to belong to a certain class. This enables us to show that, for a certain assumption about the configuration of a hierarchical mesh, hierarchical B-splines span the spline space. This paper presents an extension to three-dimensional hierarchical meshes of results proposed recently by Giannelli and Juttler for two-dimensional hierarchical meshes.

Design of a teaching pendant program for a mobile shipbuilding welding robot using a PDA

Teaching pendant is a handheld device by which a human can control a robot. The main functions of a teaching pendant are moving the robot, teaching it about the locations, running robot programs, and jogging the axes. A teaching pendant is usually connected to the robot by a cable. The cable connection and the size of the teaching pendant generally do not pose a problem when the robot controller is separate from the robot. However, a large teaching pendant connected by a cable is not suitable for a self-propelled mobile robot with an internal controller. This paper describes the communication network of a personal data assistant (PDA) as a wireless teaching pendant for a mobile shipbuilding welding robot with embedded controller system that welds and moves autonomously inside the double hull structure of a ship. A double hull is a closed structure that has only a few access holes. It is very difficult and dangerous to weld components inside a double hull structure because of fumes, poisonous gas, and high temperatures. Using a wireless teaching pendant has the following advantages: (1) there are no limits to the welding activities that can take place, (2) the safety level increases because no workers are in close proximity to the robot, (3) workers are far away from the dangerous environmental conditions, (4) it is possible to reduce the weight of the cable connected to the robot, and (5) it is possible to reduce the weight of the robot because of the reduced load of the teaching pendant and the cable. We demonstrate the functionality and performance capabilities of our wireless teaching pendant through field-testing experiments.

Approximation of surface-to-surface intersection curves within a prescribed error bound satisfying G2 continuity

We present a new method of approximating the intersection curves of two parametric surfaces. Our approximation satisfies G2 continuity conditions, and is located within a prescribed distance from the exact intersection curve. First we identify the topology of the pre-image of the intersection in the domain of surface using extended [Grandine TA, Klein FW. A new approach to the surface intersection problem. Computer Aided Geometric Design 1997;14(2):111–34]’s topology determination method [Hur S, Oh M-J, Kim T-W. Classification and resolution of critical cases in Grandine–Klein’s topology determination using a perturbation method. Computer Aided Geometric Design (2008). in press [doi:10.1016/j.cagd.2008.03.003]]. Then, we choose a segment of the pre-image, identify the tangential directions and the signed curvatures at its two end-points, and construct a G2 Hermite interpolation using a rational cubic Bezier curve. We go on to find the exact maximum error of the approximation, and the point at which that error occurs, using the Hausdorff distance function. If the error is larger than a prescribed error bound e, we subdivide the segment at the point of maximum error, and apply the G2 interpolation process to the two new segments. We continue this recursive process until we have an approximation of the pre-image with an error smaller than e. We also find the maximum error bound of the approximation in the model space R3; and the bound on the distance, in model space, between the approximations which come from the domain of each surface. We verify our method with several examples.

Features Detection from Industrial Noisy 3D CT Data for Reverse Engineering

To detect features are significantly important for reconstructing a model in reverse engineering. In general, it is too difficult to find the features from the original industrial 3D CT data because the data have many noises. So it is necessary to reduce the noises for detecting features. This paper proposes a new method for detecting corner features and edge features from noisy 3D CT scanned data. First, we applied the level set method[18] to CT scanned image in order to segment the data. Next, in order to reduce noises, we exploited nonlocal means method[19] to the segmented surface. This helps to detect the edges and corners more accurately. Finally, corners and sharp edges are detected and extracted from the boundary of the shape. The corners are detected based on Sobel-like mask convolution processing with a marching cube. The sharp edges are detected based on Canny-like mask convolution with SUSAN method[13], which is for noises removal. In the paper, the result of detecting both features is presented.

Wireless Teaching Pendant for Mobile Welding Robot in Shipyard

Abstract The teach pendant is a hand-held robot control terminal that provides a convenient means to move the robot, teach locations, and run robot programs. Nowadays, almost teaching pendant is connected with a robot controller using cable. The cable connection and the size of teaching pendant are not problems because a robot controller is separated with robot. However, a large size and wired teaching pendant is not suitable for a self-deriving mobile welding robot which has a controller inside. In this paper, using a personal data assistant, the wireless teaching pendant is developed for the mobile welding robot which can weld and move autonomously in the double hull structure of the ship. We also verify the functions and performance of wireless teaching pendant from the experiments.

Iterative refinement of hierarchical T-meshes for bases of spline spaces with highest order smoothness

In this paper we propose a strategy for generating consistent hierarchical T-meshes which allow local refinement and offer a way to obtain spline basis functions with highest order smoothness incrementally. We describe the required ordering of line-segments during refinement and the construction of spline basis functions. We give our strategy for generating consistent hierarchical T-meshes over any shape of a two-dimensional domain.

Features Detection on Industrial 3D CT Data

Features are significantly used as design elements to reconstruct a model in reverse engineering. This paper proposes a new method for detecting corner features and edge features in 3D from CT scanned data. Firstly, the level set method is applied on CT scanned data to segment the data in the form of implicit function having two values, which mean inside and outside of the boundary of the shape. Next, corners and sharp edges are detected and extracted from the boundary of the shape. The corners are detected based on Sobel-like mask convolution processing with a marching cube. The sharp edges are detected based on Canny-like mask convolution. In this step, a noisy removal module is included. In the paper, the result of detecting both features is presented.