We consider the problem of Bézier curves/surfaces subdivision using blossoms. We propose closed-form formulae for blossoms evaluation, as needed for the calculation of control points. This approach leads to direct and efficient way to obtain subdivisions for Bézier curves and both tensor product and triangular Bézier surfaces. It simplifies considerably the computation of control points of subdivisions which is crucial in applications where curves/surfaces need to be refined or adapted dynamically. For instance, in CAD/CAM systems, architectural design, or animation, the ability to quickly and accurately determine new control points is essential for manipulation and rendering complex shapes. More efficient subdivision can facilitate complex operations like finding intersections between surfaces or smoothly blending multiple surfaces.

翻译：本文研究利用开花原理进行贝塞尔曲线/曲面细分的问题。我们提出了计算控制点所需的开花值闭式计算公式。该方法为贝塞尔曲线、张量积贝塞尔曲面及三角贝塞尔曲面提供了直接高效的细分途径，显著简化了细分控制点的计算过程——这在需要动态优化或调整曲线/曲面的应用场景中至关重要。例如在CAD/CAM系统、建筑设计与动画制作中，快速精确地确定新控制点对于复杂几何形状的操控与渲染具有决定性意义。更高效的细分算法能够促进曲面求交、多曲面平滑融合等复杂操作的实现。