3D散乱数据点分段二次逼近的曲面拟合

Fitting surface to 3D scattered point set based on piecewise quadratic approximation

为进一步提高曲面重构的保形性及高效性,提出了一种自动构建光顺三角曲面的方法.该法首先通过构建三角形元覆盖边界域来构建一张曲面近似粗网,然后从点集中不断添加新点直至达到指定的容差,在每个插入数据点处构造C1连续的分片二次逼近面片,最终整体的C1曲面由各三角形上的曲面片拼合而成.最后给出了该方法在真实点集上的运用结果并与其他方法所构造的逼近曲面形状进行了比较,结果表明,该方法对密集3D散乱数据点建模有效,生成的曲面质量高,误差小.该方法也适用于数据精简.

In order to improve the shape-preserving and efficiency of surface reconstruction, an automatic method for constructing smooth surfaces defined as curved triangular patches is proposed. The method started with a coarse mesh approximating the surface through triangular elements covering the boundary of the domain, then, iteratively added new points from the data set until a specified error tolerance attained, and at the adjacent region of each point a C1 piecewise quadratic approximation patch was constructed, all the triangle patches were combined together to form the whole surface with C1 continuities. Finally, the method has been implemented on real data set and compared with other methods. The results show that the method is effective for 3D scattered data points with high surface quality and low error. The method is also suitable for data reduction.