This paper presents a learning-based method to solve the traditional parameterization and knot placement problems in B-spline approximation. Different from conventional heuristic methods or recent AI-based methods, the proposed method does not assume ordered or fixed-size data points as input. There is also no need for manually setting the number of knots. It casts the parameterization and knot placement problems as a sequence-to-sequence translation problem, a generative process automatically determining the number of knots, their placement, parameter values, and their ordering. Once trained, SplineGen demonstrates a notable improvement over existing methods, with a one to two orders of magnitude increase in approximation accuracy on test data.

翻译：本文提出一种基于学习的方法，以解决B样条逼近中传统的参数化与节点配置问题。与传统的启发式方法或近期基于人工智能的方法不同，所提方法不要求输入数据点有序或具有固定尺寸，也无需手动设置节点数量。该方法将参数化与节点配置问题构建为序列到序列的翻译问题，通过生成过程自动确定节点数量、节点位置、参数值及其排序顺序。训练完成后，SplineGen在测试数据上展现出相较于现有方法的显著改进，逼近精度提升了一到两个数量级。