• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.235-246
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• 2005

We present an interpolating, univariate subdivision scheme which preserves the discrete curvature and tangent direction at each step of subdivision. Since the polygon have a geometric information of some original(in some sense) curve as a discrete curvature, we can expect that the limit curve has the same curvature at each vertex as the control polygon. We estimate the curvature bound of odd vertices and give an error estimate for restoring a curve from sampled vertices on curves.

• International Journal of CAD/CAM
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• v.13 no.1
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• pp.1-11
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• 2013

Just by adjusting the control points iteratively, progressive iterative approximation (PIA) presents an intuitive and straightforward scheme such that the resulting limit curve (surface) can interpolate the original data points. In order to obtain more flexibility, adjusting only a subset of the control points, a new method called local progressive iterative approximation (LPIA) has also been proposed. But to this day, there are two problems about PIA and LPIA: (1) Only an approximation process is discussed, but the accurate convergence curves (surfaces) are not given. (2) In order to obtain an interpolating curve (surface) with high accuracy, recursion computations are needed time after time, which result in a large workload. To overcome these limitations, this paper gives an explicit matrix expression of the control points of the limit curve (surface) by the PIA or LPIA method, and proves that the column vector consisting of the control points of the PIA's limit curve (or surface) can be obtained by multiplying the column vector consisting of the original data points on the left by the inverse matrix of the collocation matrix (or the Kronecker product of the collocation matrices in two direction) of the blending basis at the parametric values chosen by the original data points. Analogously, the control points of the LPIA's limit curve (or surface) can also be calculated by one-step. Furthermore, the $G^1$ joining conditions between two adjacent limit curves obtained from two neighboring data points sets are derived. Finally, a simple LPIA method is given to make the given tangential conditions at the endpoints can be satisfied by the limit curve.

• Journal of Korean Ophthalmic Optics Society
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• v.8 no.1
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• pp.35-39
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• 2003

The display technology on the retina is the key role in inspecting the condition of the patients. 2-dimensional retina image is widely used in the eye examination as of today. Recently, 3-dimensional retina image ones have been introduced to this area, but the quality of the image is not fully satisfied to the operator. For the purpose of developing 3-D retina imaging instrument, the optimization of a 3-D retina imaging system using Code-V tool was investigated in this thesis. He-Ne laser having the wavelength 632.8 nm was used to make a power source to detect the retina. Several lenses and mirrors installed on sledge which were developed to perform focus control on 3-D device were designed to make a beam focusing and direct line. Polygon scanner having 24 mirror facets and galvanometer making tilting movement were utilized to make a 2-D laser plane. Also, design of eye ball had been fulfilled to see the focus of the 2-D plane. Reflected ray from retina detected on the sensor array with the same path. All cognitive components were optimized for aberration correction in order to focus on retina. Results of optimization were compared to those of initial designed optics system. On the basis of above results, the result of third aberration has been corrected to stable values to the optical system. MTF evaluating the resolution of an image has been closely correlated to the diffraction limit and PSF indicating the strength distribution of an image has shown the SR value as 0.9998 having high performance. The possibility of new and powerful 3-D retina image instrument was verified by simulating each component of the instrument by Code-V.