Journal of Korea Multimedia Society (한국멀티미디어학회논문지)

Korea Multimedia Society (한국멀티미디어학회)
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A New Tree Modeling based on Convolution Sums of Restricted Divisor Functions

약수 함수의 합성 곱 기반의 새로운 나무 모델링

  • 김진모 (동국대학교 영상문화콘텐츠연구원) ;
  • 김대열 (국가수리과학연구소)
  • Received : 2012.12.19
  • Accepted : 2013.03.07
  • Published : 2013.05.31
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Abstract

In order to model a variety of natural trees that are appropriate to outdoor terrains consisting of multiple trees, this study proposes a modeling method of new growth rules(based on the convolution sums of divisor functions). Basically, this method uses an existing growth-volume based algorithm for efficient management of the branches and leaves that constitute a tree, as well as natural propagation of branches. The main features of this paper is to introduce the theory of convolution sums of divisor functions that is naturally expressed the growth or fate of branches and leaves at each growth step. Based on this, a method of modeling various tree is proposed to minimize user control through a number of divisor functions having generalized generation functions and modification of the growth rule. This modeling method is characterized by its consideration of both branches and leaves as well as its advantage of having a greater effect on the construction of an outdoor terrain composed of multiple trees. Natural and varied tree model creation through the proposed method was conducted, and using this, the possibility of constructing a wide nature terrain and the efficiency of the process for configuring multiple trees were evaluated experimentally.

본 연구는 다수의 나무로 구성된 실외 지형에 적합하고 다양하고 자연스러운 나무를 모델링하기 위하여 새로운 성장 규칙(약수 함수의 합성 곱 기반)의 모델링 방법을 제안한다. 기본적으로 나무를 구성하는 가지와 잎의 효율적 관리와 자연스러운 가지 증식을 위하여 기존의 성장 볼륨기반 알고리즘을 활용한다. 이 논문의 주요 특징은 각 성장 단계에서 가지와 잎의 성장과 운명을 자연스럽게 표현하는 약수 함수 합성 곱 이론을 도입하는 것이다. 이를 기반으로 일반화된 생성 함수를 갖는 여러 약수 함수와 성장 규칙의 변형을 통해 사용자의 제어를 최소화하여 다양한 나무를 모델링하는 방법을 제안한다. 이 모델링 방법은 가지와 잎을 동시에 고려하는 특징이 있으며, 다수의 나무들로 구성된 실외 지형 구축에 보다 효과적이라는 이점이 있다. 제안한 방법을 통해 자연스럽고 다양한 나무 모델 생성과 이를 활용하여 넓은 자연 지형 구축 가능성과 다수의 나무를 구성하는 과정에서의 효율성을 실험을 통해 증명한다.

Keywords

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