We present a new procedural incompressible velocity field authoring tool, which lets users design a volumetric flow by directly specifying velocity along control curves. Our method combines the Method of Regularized Stokeslets with Galerkin discretization. Based on the highly viscous Stokes flow assumption, we find the force along a given set of curves that satisfies the velocity constraints along them. We can then evaluate the velocity anywhere inside the surrounding infinite 2D or 3D domain. We also show the extension of our method to control the angular velocity along control curves. Compared to a collocation discretization, our method is not very sensitive to the vertex sampling rate along control curves and only requires a small linear system solve.

翻译：我们提出了一种新的程序化不可压缩速度场创作工具，允许用户通过直接指定控制曲线上的速度来设计体积流动。该方法将正则化Stokeslet方法与Galerkin离散化相结合。基于高黏性斯托克斯流动假设，我们求解满足给定曲线集上速度约束的沿曲线分布力场。随后可在周围无限二维或三维域内任意位置计算速度场。我们还展示了该方法在控制曲线角速度调控方面的扩展。与配点离散化方法相比，本方法对控制曲线顶点采样率不敏感，且仅需求解小型线性系统。