CAGD에서 유리 곡선의 미분과 그 상한에 관한 연구의 흐름
A Brief History of Study on the Bound for Derivative of Rational Curves in CAGD
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초록
CAGD(Computer Aided Geometric Design) 는 곡선, 곡면, 입체를 컴퓨터를 이용하여 수학적으로표현하고 구성하는 알고리즘에 대하여 연구하는 응용수학의 한 분야이다. CAGD에서는 곡선과곡면을 매개변수를 이용하여 표현하는 방식을 주로 사용하는데 CAGD에 이용되는 곡선은 다항식을근간으로 하는 Bézier 곡선과 구간별로 다항식으로 표현되는 B-spline, 또 이들 다항 곡선의 식을 분자와 분모로 하여 나타낸 유리 Bézier 곡선과 NURBS(Non-Uniform Rational B-Spline)가 있다. 이논문에서는 CAGD의 근간이 되는 Bézier 곡선, B-spline, 유리 Bézier 곡선과 NURBS의 매개변수를사용한 정의와 특성을 알아보고 유리 곡선의 미분과 그 상한 계산의 연구 흐름에 대하여 살펴본다.
Abstract
CAGD(Computer Aided Geometric Design) is a branch of applied mathematicsconcerned with algorithms for the design of smooth curves and surfaces and fortheir efficient mathematical representation. The representation is used for the computationof the curves and surfaces, as well as geometrical quantities of importancesuch as curvatures, intersection curves between two surfaces and offset surfaces. The Bézier curves, B-spline, rational Bézier curves and NURBS(Non-Uniform RationalB-Spline) are basically and widely used in CAGD. The definitions and propertiesof these curves are presented in this paper. And a brief history of study onthe bound for derivative of rational curves in CAGD is also presented.
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