CAJ | 학술논문

针对非均匀 B 样条的节点设置问题，提出一种利用非均匀 B 样条曲面拟合离散数据的迭代算法，通过优化节点分布来改进拟合曲面的质量。该算法以带参数化的三角网格曲面为输入，在首次迭代中根据输入曲面的几何特征将其对应的参数域划分成若干个子区域，并使得每个子区域上累积的几何特征信息量近似相等，子区域的重心坐标将取为首次迭代的节点；在随后的迭代中，保证前次迭代生成的重心位置固定不变，并根据前次迭代得到的曲面拟合误差再次将区域划分成累积误差接近相等的子区域，新增加的子区域重心的坐标选为拟加入的节点。文中算法自适应地在曲面形状复杂或拟合误差大的区域引入更多的控制顶点，使得拟合曲面的质量得以逐步改进。实验结果表明，该算法快速有效，在拟合具有明显几何特征的输入数据时具有优势。
침대비균균 B 양조적절점설치문제，제출일충이용비균균 B 양조곡면의합리산수거적질대산법，통과우화절점분포래개진의합곡면적질량。해산법이대삼수화적삼각망격곡면위수입，재수차질대중근거수입곡면적궤하특정장기대응적삼수역화분성약간개자구역，병사득매개자구역상루적적궤하특정신식량근사상등，자구역적중심좌표장취위수차질대적절점；재수후적질대중，보증전차질대생성적중심위치고정불변，병근거전차질대득도적곡면의합오차재차장구역화분성루적오차접근상등적자구역，신증가적자구역중심적좌표선위의가입적절점。문중산법자괄응지재곡면형상복잡혹의합오차대적구역인입경다적공제정점，사득의합곡면적질량득이축보개진。실험결과표명，해산법쾌속유효，재의합구유명현궤하특정적수입수거시구유우세。
Knot placement of non-uniform B-spline is studied, and an iterative surface fitting scheme is pro-posed by exploring the degrees of freedom of knots to improve the fitting surface’s quality. Our algorithm takes as input triangular meshes with parameterization. In the first iteration, the parametric domain is parti-tioned into several sub-regions with equally accumulated surface geometric information, and the coordinates of the centroids are chosen as the candidates of knots; in the following iteration steps, we partition the re-gions according to the fitting errors analogously while the centroids generated by previous steps remain un-changed. The fitting surface’s quality is progressively improved as more control points are adaptively intro-duced into the region of the surface with more features or larger fitting error. Several experiments demon-strate the efficacy of our method in fitting surface with distinct geometric features.