구면좌표계 기반 옥트리의 안정적인 구성과 극홀 필링 방식
Stable Construction of Spherical Coordinate-based Octree and Polar Hole-Filling
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초록
본 논문에서는 구면 좌표계 기반 적응형(Adaptive) 자료구조인 구면 옥트리(Spherical octree)를안정적으로 구성할 수 있는 방법을 제안한다. 내부 원의 중점을 계산할 때 오차로 인해 안정성이감소되는 부분을 레벨셋(Level-set)를 통해 보정하고, 구면 옥트리와 듀얼 컨투어링(Dual contouring) 을 기반으로 표면을 복원할 때 극좌에 부근에서 발생하는 홀(Hole)을 표면의 법선벡터(Normal vector) 활용하여 정확하게 필링(Filling)하는 방법을 제안한다. 본 논문에서 새롭게 제안하는 방법은 이전 기법에 비해 계산양이 거의 증가되지 않지만 안정성 측면에서 크게 개선된 결과를 보여준다. 본 논문에서는 1) 구의 중심을 발산하지 않도록 수렴 방향을 보정함으로써 안정적으로 계산하는 방법을 제안하고, 특정 모델에만 적용됐던 이전 구면 옥트리 한계를 다양한 모델에서 적용되도록 했다. 2) 듀얼 컨투어링에서 발생하는 홀 필링(Hole filling)의 정확도를 방향까지 고려함으로써 구면 옥트리를 좀 더 정확하게 근사했다. 결과적으로 이전 구면 옥트리 구조에서 발생하는문제를 해결함으로써 표면에서 발생하는 발산문제를 완화시켰다.
Abstract
In this paper, we propose a method to stably construct a spherical octree, an adaptive data structure based on a spherical coordinate system. In this paper, we propose a method to compensate for the stability degradation caused by the error in calculating the center of the inner circle through levelsets, and to accurately fill the hole that occurs near the extreme left when reconstructing a surface based on spherical octree and double contouring by utilizing the normal vector of the surface. Compared with the existing techniques, the new method proposed in this paper shows a significant improvement in stability with little increase in computation. As a result, it solves the instability problem arising from the existing spherical octree structure and alleviates the divergence problem arising from the surface.
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