The purpose of this paper is to present a fast algorithm for the adaptive discretization of three-dimensional parametric curves.
The proposed algorithm computes the parametric increments of all segments to obtain the parametric coordinates of all discrete nodes. This process is recursively applied until the optimal discretization of curves is obtained. The parametric increment of a segment is inversely proportional to the number of sub-segments, which can be subdivided, and the sum of parametric increments of all segments is constant. Thus, a new expression for parametric increment of a segment can be obtained. In addition, the number of sub-segments, which a segment can be subdivided is calculated approximately, thus avoiding Gaussian integration.
The proposed method can use less CPU time to perform the optimal discretization of three-dimensional curves. The results of curves discretization can also meet requirements for mesh generation used in the preprocessing of numerical simulation.
Several numerical examples presented have verified the robustness and efficiency of the proposed algorithm. Compared with the conventional algorithm, the more complex the model, the more time the algorithm saves in the process of curve discretization.
