Abstract: Synthetic point clouds are widely used in science research, machine learning, animation making, and pedagogue. In this article a 3D point cloud generation algorithm for parametric surfaces is introduced. The algorithm can generate qualified point clouds distributed along a surface with specified parameter equations, paramenter ranges, and noise strengths. The generated results have a uniform volume density along the surface, blue noises in normal directions with an identical standard deviation, thus they artificially simulate scanned data obtained with ideal 3D acquisition equipments. The algorithm is based on a parameter velocity adjustment method, a curvature compensation technique and a blue noise sampling technique, which can eliminate the density differences arised from paramenter velocity changes and make the noises at high curvature parts be pattern-wise distributed with an identical standard deviation. The experimental results show that the density, thickness and noise magnitude of the generated point clouds are uniform in visual effects as well as in quantitative metrics, and that the point clouds are isotropic. As the algorithm is perceived as a low-cost virtual 3D equipment, it will be applied in surface reconstruction testing or machine learning.

Key words: synthetic point cloud, parametric surface, parametric curve, iso-distribution

摘要： 人造点云广泛用于科学研究、机器学习、动画制作和教学等领域。介绍一种参数曲面人造3D点云生成算法，该算法能根据曲面参数方程及指定的参数范围和噪音强度生成点云，使之沿曲面方向服从同等密度分布，曲面法向服从同一标准差的蓝噪音模式化分布（如正态分布），从而模拟理想3D数字化设备的拍摄结果。算法设计基于参数速度调节、曲率补偿、蓝噪音采样等技术，参数速度调节使得点云不因参数速度变化造成密度差异，曲率补偿技术使得生成的点云在曲面尖锐部位也能获得比较均匀的法向噪音效果。实验结果显示生成的点云呈现密度、厚度、噪音均无明显差别的“均匀”视觉效果和量化指标，并且各向同性。该算法作为3D数字化设备的低成本虚拟替代物，可应用于曲面重建测试和机器学习等领域。

关键词: 人造点云, 参数曲面, 参数曲线, 等分布