📄 中文摘要
插值细分方案通过反复插入新顶点，从分段线性控制多边形生成平滑曲线。传统方案依赖于单一的全局张力参数，通常需要在欧几里得、球面和双曲几何中分别制定不同的公式。研究提出了一种共享的学习张力预测器，用以用每条边的插入角度替代全局参数，这些角度由一个包含14万参数的网络预测。该网络以局部内在特征和可训练的几何嵌入作为输入，预测的角度驱动几何特定的插入算子在三种空间中应用，而无需对网络架构进行修改。受限的sigmoid输出头确保了结构安全界限，保证了插入过程的稳定性。
一种神经张力算子用于恒曲率几何中的曲线细分
📄 English Summary
A Neural Tension Operator for Curve Subdivision across Constant Curvature Geometries
Interpolatory subdivision schemes generate smooth curves from piecewise-linear control polygons by repeatedly inserting new vertices. Classical schemes rely on a single global tension parameter and typically require separate formulations in Euclidean, spherical, and hyperbolic geometries. A shared learned tension predictor is introduced to replace the global parameter with per-edge insertion angles predicted by a single 140K-parameter network. The network takes local intrinsic features and a trainable geometry embedding as input, and the predicted angles drive geometry-specific insertion operators across all three spaces without architectural modification. A constrained sigmoid output head enforces a structural safety bound, ensuring stability during the insertion process.