• Title/Summary/Keyword: degree reduction

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APPLICATION OF DEGREE REDUCTION OF POLYNOMIAL BEZIER CURVES TO RATIONAL CASE

  • PARK YUNBEOM;LEE NAMYONG
    • Journal of applied mathematics & informatics
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    • v.18 no.1_2
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    • pp.159-169
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    • 2005
  • An algorithmic approach to degree reduction of rational Bezier curves is presented. The algorithms are based on the degree reduction of polynomial Bezier curves. The method is introduced with the following steps: (a) convert the rational Bezier curve to polynomial Bezier curve by using homogenous coordinates, (b) reduce the degree of polynomial Bezier curve, (c) determine weights of degree reduced curve, (d) convert the Bezier curve obtained through step (b) to rational Bezier curve with weights in step (c).

MULTI-DEGREE REDUCTION OF BÉZIER CURVES WITH CONSTRAINTS OF ENDPOINTS USING LAGRANGE MULTIPLIERS

  • Sunwoo, Hasik
    • Journal of the Chungcheong Mathematical Society
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    • v.29 no.2
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    • pp.267-281
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    • 2016
  • In this paper, we consider multi-degree reduction of $B{\acute{e}}zier$ curves with continuity of any (r, s) order with respect to $L_2$ norm. With help of matrix theory about generalized inverses we can use Lagrange multipliers to obtain the degree reduction matrix in a very simple form as well as the degree reduced control points. Also error analysis comparing with the least squares degree reduction without constraints is given. The advantage of our method is that the relationship between the optimal multi-degree reductions with and without constraints of continuity can be derived explicitly.

Individual differences in the reduction degree of the Korean suffix 'nɨn'

  • Kim, Jungsun
    • Phonetics and Speech Sciences
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    • v.12 no.2
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    • pp.9-16
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    • 2020
  • The present study examines the degree of suffix reduction that occurs when the Korean suffix [-nɨn] was attached to the root in spontaneous Seoul Korean speech. Specifically, it focuses on the degrees of reduction produced by individual speakers. The degree of reduction was assessed as the duration of the suffix [-nɨn] to clarify the continuum between the full and reduced forms. The results revealed that, first, the reduced forms of the suffix [-nɨn] were significantly distinguished from the full forms in the suffixation processes. Second, regarding parts of speech, the differences among individual speakers on the degrees of reduction were clearer when the suffix [-nɨn] was attached to verbs, rather than nouns and pronouns. Finally, the length of a root played a critical role in determining the degree of reduction of the suffix [-nɨn]. The degrees of reduction for individual speakers significantly differed when the suffix [-nɨn] was attached to two-syllable roots than three- and four-syllable roots. In conclusion, individual differences in the degrees of reduction were likely to occur when the roots are verbs and when two-syllable roots.

The Degree Reduction of B-splines using Bzier Methods (Bzier 방법을 이용한 B-spline의 차수 감소)

  • Kim, Hyeok-Jin;Kim, Tae-Wan;Wi, Yeong-Cheol;Kim, Ha-Jin
    • Journal of KIISE:Computer Systems and Theory
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    • v.26 no.8
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    • pp.875-883
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    • 1999
  • 서로 다른 기하학적 모델링 시스템에 사용되는 곡선 및 곡면의 자료 교환에서, 시스템이 지원하는 그 곡선 및 곡면의 최대 차수에 제한이 있을 때, 낮은 차수로의 차수 감소가 필요하다. 본 논문에서는 근사 변환에 의한 B-spline 곡선의 차수 감소 방법을 제시한다. 기존의 Bzier 곡선의 차수감소 방법들을 적용하고, 그 방법들을 비교 분석한다. B-spline 곡선의 knot 제거 알고리즘이 자료 감소를 위해 차수 감소 과정에 적용된다.Abstract The degree reduction of B-splines is required in exchanging parametric curves and surfaces of the different geometric modeling systems because some systems limit the supported maximal degree. We propose an approximate degree reduction method of B-spline curves using the existing Bzier degree reduction methods. Knot removal algorithm is used to reduce data in the degree reduction process.

Approximate conversion using the degree reduction of NURBS (NURBS의 차수 감소 방법을 이용한 근사변환)

  • 김혁진
    • Journal of the Korea Society of Computer and Information
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    • v.8 no.1
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    • pp.7-12
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    • 2003
  • Because some systems limit the supported maximal degree, the degree reduction of NURBS is necessary in Parametric curves and surfaces of the different geometric modeling systems. Therefore an approximate degree reduction method of NURBS curves was introduced in this research. Also the existing Eck's B$\'{e}$zier degree reduction method and knot removal algorithm were used to reduce data in the degree reduction process. Finally we found that this method was stable, efficient for implementations, and easy to use algorithms.

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MATRIX REPRESENTATION FOR MULTI-DEGREE REDUCTION OF $B{\acute{E}}GREE$ CURVES USING CHEBYSHEV POLYNOMIALS

  • SunWoo, Ha-Sik
    • Journal of applied mathematics & informatics
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    • v.26 no.3_4
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    • pp.605-614
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    • 2008
  • In this paper, we find the matrix representation of multi-degree reduction by $L_{\infty}$ of $B{\acute{e}}zier$ curves with constraints of endpoints continuity. Using the basis transformation between Chebyshev polynomials and Bernstein polynomials we can derive the matrix representation of multi-degree reduction of $B{\acute{e}}zier$ with respect to $L_{\infty}$ norm.

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A DEGREE REDUCTION METHOD FOR AN EFFICIENT QUBO FORMULATION FOR THE GRAPH COLORING PROBLEM

  • Hyosang Kang;Hyunwoo Jung;Chaehwan Seol;Namho Hong;Hyunjin Lim;Seokhyun Um
    • The Pure and Applied Mathematics
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    • v.31 no.1
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    • pp.57-81
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    • 2024
  • We introduce a new degree reduction method for homogeneous symmetric polynomials on binary variables that generalizes the conventional degree reduction methods on monomials introduced by Freedman and Ishikawa. We also design an degree reduction algorithm for general polynomials on binary variables, simulated on the graph coloring problem for random graphs, and compared the results with the conventional methods. The simulated results show that our new method produces reduced quadratic polynomials that contains less variables than the reduced quadratic polynomials produced by the conventional methods.

An Experimental Analysis of Approximate Conversions for B-splines (B-spline에 대한 근사변환의 실험적 분석)

  • Kim Hyeock Jin
    • Journal of the Korea Society of Computer and Information
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    • v.10 no.1 s.33
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    • pp.35-44
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    • 2005
  • The degree reduction of B-splines is necessary in exchanging parametric curves and surfaces of the different geometric modeling systems because some systems limit the supported maximal degree. In this paper, We provide an our experimental results in approximate conversion for B-splines apply to degree reduction. We utilize the existing Bezier degree reduction methods, and analyze the methods. Also, knot removal algorithm is used to reduce data in the degree reduction Process.

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DEGREE REDUCTION OF B-SPLINE CURVES

  • Lee, Byung-Gook;Park, Yun-Beom
    • Journal of applied mathematics & informatics
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    • v.8 no.3
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    • pp.819-827
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    • 2001
  • An algorithmic approach to degree reduction of B-spline curves is presented. The new algorithms are based on the blossoming spline curves are obtained by the generalized least square method. The computations are carried out by minimizing the $L_2$ distamce between the two curves.

A Study on Reduction of Food Waste (음식물 쓰레기 소멸화에 관한 연구)

  • 서명교;이상봉;이국의;이상훈
    • Journal of Environmental Health Sciences
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    • v.27 no.1
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    • pp.14-19
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    • 2001
  • The physical and chemical transformation and reduction degree of food waste were investigated in a food waste reduction machine using thermophilic bacteria. The first operation of the reduction machine for grain, vegetables, fishes and flesh wastes proceeded during three weeks. The first and second reduction percentages of the wastes were 98.3% and 93.2%, respectively. The residue of food waste was composed of fruits, fish, and vegetables. The temperature distribution of the reduction machine ranged between 30 and 6$0^{\circ}C$ appropriate for growth of thermophilic bacteria. At initial stage the pH in the reduction machine decreased with organic acids produced, but increased as the organic acids decomposed by different thermophilic bacteria. In the reduction machine, the moisture content of the food waste was reduced from 80-90% to 10-20% after 24 hours, and the salinity of residue was 0.29% after the second operation. The degree of odor was most high between 2 and 4 hours.

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