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몬테카를로 방법 기반의이동최소제곱을이용한 밀도데이터의 벡터장 시각화

Visualization of Vector Fields from Density Data Using Moving Least Squares Based on Monte Carlo Method

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(사)한국컴퓨터그래픽스학회 (Korea Computer Graphics Society)|2024.06|한국컴퓨터그래픽스학회논문지 (Journal of the Korea Computer Graphics Society)|제30권 제2호|pp. 1-9

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참고문헌

키워드

시각화VisualizationMonte Carlo Method몬테카를로법이동최소제곱벡터장물리 기반 시뮬레이션Moving least squaresVector fieldPhysically based simulations

초록

본 논문에서는 밀도데이터로부터 다양한 벡터장 패턴을 시각화하는 새로운 방법을 제안한다. 이를 위해 물리 기반 시뮬레이션과 기하학적 처리에서 사용되는 이동최소제곱(Moving least squares, MLS)을이용한다. 하지만 일반적인 MLS는 벡터기반의 제약조건을 통해 고차 보간되기 때문에 밀도의 특성을 고려하지 못한다. 본 논문에서는 입력 데이터에 내포되어 있는밀도의 특성을 효율적으로 고려하기 위해 몬테카를로 기반의 가중치를 MLS에 통합하여 다양한 형태의 백터장을 표현할수 있도록 알고리즘을 설계한다. 결과적으로 일반적인 MLS와 발산제약 기반의 MLS 같은 기존 기법으로는 표현하기 힘든디테일한 벡터장을 실험을 통해 보여준다.

Abstract

In this paper, we propose a new method to visualize different vector field patterns from density data. We use moving least squares (MLS), which is used in physics-based simulations and geometric processing. However, typical MLS does not take into account the nature of density, as it is interpolated to a higher order through vector-based constraints. In this paper, we design an algorithm that incorporates Monte Carlo-based weights into the MLS to efficiently account for the density characteristics implicit in the input data, allowing the algorithm to represent different forms of white noise. As a result, we experimentally demonstrate detailed vector fields that are difficult to represent using existing techniques such as naive MLS and divergence-constrained MLS.

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