CAJ | 학술논문

为了避免用逼近型√3细分方法构造插值曲面过程中出现的烦琐运算,利用√3细分方法极限点计算公式,提出一种用逼近型√3细分方法构造闭三角网格插值曲面的方法. 给定待插值的闭三角网格,先用一个新的几何规则与原√3细分方法的拓扑规则细分一次得到一个初始网格,用√3细分方法细分该初始网格得到插值曲面; 新几何规则根据极限点公式确定,保证了初始网格的极限曲面插值待插值的三角网格. 由于初始网格的顶点仅与待插值顶点2邻域内的点相关,所以插值曲面具有良好的局部性,即改变一个待插值点的位置时,只影响插值曲面在其附近的形状. 该方法中只有确定初始网格顶点的几何规则与原√3细分方法不同,故易于整合到原有的细分系统中. 实验结果表明,该方法具有计算简单、有充分的自由度调整插值曲面的形状等特点,使得利用√3细分方法构造三角网格的插值曲面变得极其简单.
위료피면용핍근형√3세분방법구조삽치곡면과정중출현적번쇄운산,이용√3세분방법겁한점계산공식,제출일충용핍근형√3세분방법구조폐삼각망격삽치곡면적방법. 급정대삽치적폐삼각망격,선용일개신적궤하규칙여원√3세분방법적탁복규칙세분일차득도일개초시망격,용√3세분방법세분해초시망격득도삽치곡면; 신궤하규칙근거겁한점공식학정,보증료초시망격적겁한곡면삽치대삽치적삼각망격. 유우초시망격적정점부여대삽치정점2린역내적점상관,소이삽치곡면구유량호적국부성,즉개변일개대삽치점적위치시,지영향삽치곡면재기부근적형상. 해방법중지유학정초시망격정점적궤하규칙여원√3세분방법불동,고역우정합도원유적세분계통중. 실험결과표명,해방법구유계산간단、유충분적자유도조정삽치곡면적형상등특점,사득이용√3세분방법구조삼각망격적삽치곡면변득겁기간단.
To avoid the complex computation in the process of interpolating triangular mesh by √3 subdivision scheme, we propose a simple and efficient algorithm for interpolating closed triangular meshes by √3 subdivision scheme using the limit point formula of √3 subdivision scheme. Given the interpolated triangular mesh, by subdividing it with a new geometric rule and the topology rules of √3 subdivision scheme we obtain an initial mesh, whose limit surface of √3 subdivision scheme is the interpolation surface; the new geometric rule is determined by the limit point formula of √3 subdivision scheme, and assure that the limit surface of initial mesh interpolate the given triangular mesh. The new points of initial mesh are defined by the interpolated vertices and their 2-neighborhood vertices, so the interpolation method is local, i.e. the perturbation of a given vertex only influences the surface shape near this vertex. The geometric and topology rules of our interpolation method are the same as those of the √3 subdivision scheme except the first geometric rule of obtaining the initial mesh, so it is very easy to incorporate our method to the origin subdivision system. Numerical examples show that the new interpolation method has many advantageous properties, such as simplification, having enough freedoms to adjust the shape of the interpolation surfaces, and so on. These features make surface interpolation using √3 subdivision scheme very simple.