Abstract This paper presents a flexible free-form deformation (FFD) method that overcomes two limitations of many FFD methods: the cumbersome interface and the fixed topology of the control lattice. The novelty of the method mainly lies in two aspects: (1) a specifically-tailored T-spline volume with its local refinement is introduced to define the deformation space and construct the deformation tool, and (2) a proxy represented as a three-dimensional mesh close to the object to be deformed is constructed from the control lattice of the T-spline volume and is used to manipulate and drive the deformation. While the method inherits all the virtues of FFD such as C2 continuous local and global modifications, the proxy provides a much concise and intuitive interface for the user to edit the deformation in a way similar to cage-based deformations. Moreover, the method allows local topology changes of the proxy after parameterization, which is not available for most FFD methods or even cage-based deformations. These features enable more complicated free-form deformation to be achieved in a flexible and intuitive manner, as demonstrated by many experimental examples.

中文翻译：

---

通过拓扑可调的控制点阵代理驱动的自由形式变形

摘要 本文提出了一种灵活的自由形式变形 (FFD) 方法，它克服了许多 FFD 方法的两个限制：繁琐的界面和控制格的固定拓扑结构。该方法的新颖之处主要在于两个方面：（1）引入了一个专门定制的具有局部细化的 T 样条体积来定义变形空间并构造变形工具，以及（2）一个表示为三元组的代理。靠近要变形对象的三维网格由 T 样条体积的控制点阵构成，用于操纵和驱动变形。虽然该方法继承了 FFD 的所有优点，例如 C2 连续局部和全局修改，但代理为用户提供了一个非常简洁直观的界面，以类似于基于笼的变形的方式编辑变形。此外，该方法允许参数化后代理的局部拓扑变化，这对于大多数 FFD 方法甚至基于笼的变形都是不可用的。正如许多实验示例所证明的那样，这些特征能够以灵活和直观的方式实现更复杂的自由形式变形。