自适应插值曲线细分与学习局部角度

中文摘要 AI 辅助

曲线细分在计算机图形学中至关重要，用于从控制多边形生成光滑的几何对象。插值细分尤其具有吸引力，因为细化后的曲线保证通过设计者的控制点。经典的四点和六点方案保留了这一性质，但其行为由单一的全局张力参数控制，限制了其在平坦区域、急转弯和变化局部几何形状中的适应能力。我们提出了一种自适应局部角度公式，在保持插值结构完整的同时，学习每个新顶点应如何插入。一个紧凑的边级预测器为每条边分配一个插入角度，而原始顶点在每个细化级别上被精确复制。因此，插值是算子的结构性质，不依赖于训练权重。同一预测器与几何特定的测地线基元一起使用，适用于欧几里得平面、二维球面和庞加莱圆盘。在匹配密度评估协议下，该方法相对于最佳验证调优的固定张力基线，将最近邻误差降低了五到十七倍，在欧几里得情况下相对于向心Catmull-Rom降低了约1.8倍。它还显著降低了弯曲能量和切线粗糙度，同时与单独训练的每几何模型保持竞争力。

英文摘要

Curve subdivision is pivotal in computer graphics for generating smooth geometric objects from control polygons. Interpolatory subdivision is especially attractive because the refined curve is guaranteed to pass through the designer's control points. Classical four-point and six-point schemes preserve this property, but their behaviour is governed by a single global tension parameter, limiting their ability to adapt across flat regions, sharp turns and varying local geometries. We introduce an adaptive local-angle formulation that keeps the interpolatory structure intact while learning how each new vertex should be inserted. A compact edge-wise predictor assigns one insertion angle per edge, while the original vertices are copied exactly at every refinement level. Interpolation is therefore a structural property of the operator and does not depend on the trained weights. The same predictor is used with geometry-specific geodesic primitives on the Euclidean plane, the two-sphere and the Poincaré disk. Under a matched-density evaluation protocol, the method reduces nearest-neighbour error by factors of five to seventeen over the best validation-tuned fixed-tension baseline, and by about 1.8 over centripetal Catmull-Rom in the Euclidean case. It also substantially reduces bending energy and tangent roughness, while remaining competitive with separately trained per-geometry models.

发表机构

• University of Bradford（布拉德福德大学）
• Rochester Institute of Technology（罗切斯特理工学院）

机构由 AI 辅助整理，请以论文原文为准。