Approximations of planar curves by quadratic rational B-splines평면곡선의 이차 유리 B-spline에 의한 근사

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dc.contributor.advisorKim, Hong-Oh-
dc.contributor.advisor김홍오-
dc.contributor.authorAhn, Young-Joon-
dc.contributor.author안영준-
dc.date.accessioned2011-12-14T04:38:44Z-
dc.date.available2011-12-14T04:38:44Z-
dc.date.issued1998-
dc.identifier.urihttp://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=135103&flag=dissertation-
dc.identifier.urihttp://hdl.handle.net/10203/41802-
dc.description학위논문(박사) - 한국과학기술원 : 수학과, 1998.2, [ 70 p. ]-
dc.description.abstractWe 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.languageeng-
dc.publisher한국과학기술원-
dc.subjectCurvatures-
dc.subjectGeometric approximation-
dc.subjectB{\``e}zier curves-
dc.subjectQuadratic rational B-splines-
dc.subjectArc approximation-
dc.subject원호 근사-
dc.subject곡률-
dc.subject기하적인 근사-
dc.subject베지어 곡선-
dc.subject이차 유리 비-스플라인-
dc.titleApproximations of planar curves by quadratic rational B-splines-
dc.title.alternative평면곡선의 이차 유리 B-spline에 의한 근사-
dc.typeThesis(Ph.D)-
dc.identifier.CNRN135103/325007-
dc.description.department한국과학기술원 : 수학과, -
dc.identifier.uid000955209-
dc.contributor.localauthorKim, Hong-Oh-
dc.contributor.localauthor김홍오-
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MA-Theses_Ph.D.(박사논문)
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