DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Kim, Hong-Oh | - |
dc.contributor.advisor | 김홍오 | - |
dc.contributor.author | Ahn, Young-Joon | - |
dc.contributor.author | 안영준 | - |
dc.date.accessioned | 2011-12-14T04:38:44Z | - |
dc.date.available | 2011-12-14T04:38:44Z | - |
dc.date.issued | 1998 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=135103&flag=dissertation | - |
dc.identifier.uri | http://hdl.handle.net/10203/41802 | - |
dc.description | 학위논문(박사) - 한국과학기술원 : 수학과, 1998.2, [ 70 p. ] | - |
dc.description.abstract | We study on the geometric properties of the quadratic rational $Bézier$ curves and approximations using them. We find necessary and sufficient conditions for the curvature of a quadratic rational $Bézier$ curve to be monotone, to have a unique local minimum, to have a unique local maximum and to have both extrema, and we also visualize them in figures. We characterize the best approximation of a regular plane curve by a quadratic rational $Bézier$ curve with possible contact order at both end points and prove its uniqueness. We also present a Remes type algorithm to obtain the best approximation. We apply our characterization to the degree reduction of cubic rational $Bézier$ curve to quadratic one and also to the cubic offset approximation, and present the numerical results. For the circular arc of angle 0<α<π we present the explicit form of the best $GC^3$ quartic approximation and the best $GC^2$ quartic approximations of various types, and give the explicit form of the Hausdorff distance between the circular arc and the approximate $Bézier$ curves for each case. We also show the existence of the $GC^4$ quintic approximations to the arc, and find the explicit form of the best $GC^3$ quintic approximation in certain constraints and their distances from the arc. All approximations we construct in this thesis have the optimal order of approximation, twice of the degree of approximate $Bézier$ curves. | eng |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | Curvatures | - |
dc.subject | Geometric approximation | - |
dc.subject | B{\``e}zier curves | - |
dc.subject | Quadratic rational B-splines | - |
dc.subject | Arc approximation | - |
dc.subject | 원호 근사 | - |
dc.subject | 곡률 | - |
dc.subject | 기하적인 근사 | - |
dc.subject | 베지어 곡선 | - |
dc.subject | 이차 유리 비-스플라인 | - |
dc.title | Approximations of planar curves by quadratic rational B-splines | - |
dc.title.alternative | 평면곡선의 이차 유리 B-spline에 의한 근사 | - |
dc.type | Thesis(Ph.D) | - |
dc.identifier.CNRN | 135103/325007 | - |
dc.description.department | 한국과학기술원 : 수학과, | - |
dc.identifier.uid | 000955209 | - |
dc.contributor.localauthor | Kim, Hong-Oh | - |
dc.contributor.localauthor | 김홍오 | - |
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