RMF를 이용한 계층적 B-spline 곡선의 다단계편집기법
Multilevel Editing for Hierarchical B-spline Curves using Rotation Minimizing Frames
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초록
본 논문에서는 계층적 B-spline 곡선 (hierarchical B-spline curve)에 대한 효율적이고 안정적인 새로운 다단계 편집 (multilevel editing)기법을 제안한다. 각 단계 변위함수 (displacement function)의 제어점 (control point)에 대하여 이전 단계 곡선상의 노드점 (nodal point)에서 정의되는 Rotation Minimizing Frame (RMF)을 해당 제어점의 참조좌표계 (reference coordinate system)로 설정한다. 다단계 편집과정에서 편집된 제어점의 변위는 설정된 참조좌표계를 기준으로 표현된다. 이전 단계에서 곡선의 형상이 편집되면 새로운 참조좌표계가 정의되고, 현재 단계에서 변위함수의 제어점들은 새로운 참조좌표계를 기준으로 적용되어 이전단계 곡선의 변형에 대한 상대적인 편집결과를 유지하게 된다. 본 논문에서는 다양한 형태의 곡선에 대한 다단계 편집실험을 통해 제안된 기법의 효율성과 안정성을 입증한다.
Abstract
We present an efficient and robust technique for multilevel editing of hierarchical B-spline curves. For each control point of displacement functions a rotation minimizing frame (RMF) is defined as reference coordinate system where its edited offset is represented. When the curve is edited in lower level, the reference coordinate systems are updated and the displacement functions in current level are applied to the new ones, which maintains relative changes to the curve in lower level. We demonstrate the effectiveness and robustness of the proposed technique using several experimental results.
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