Direct Manipulation of FFD: Efficient Explicit Solutions and Decomposible Multiple Point Constraints

Shi-Min Hu Tsinghua University Hui Zhang Tsinghua University Chiew-Lan Tai Hong Kong University of Science & Technology Jia-Guang Sun Tsinghua University

Geometric Modeling and Processing mathscidoc:1608.16080

The Visual Computers, 17, (6), 370-379, 2001
The ability to directly manipulate an embedded object in the free-form deformation (FFD) method improves controllability. However, the existing solution to this problem involves a pseudo-inverse matrix that requires complicated calculations. This paper solves the problem using a constrained optimization method. We derive the explicit solutions for deforming an object which is to pass through a given target point. For constraints with multiple target points, the proposed solution also involves simple calculations, only requiring solving a system of linear equations.We show that the direct manipulations exhibit the commutative group property, namely commutative, associative, and invertible properties, which further enhance the controllability of FFD. In addition, we show that multiple point constraints can be decomposed into separate manipulations of single point constraints, thus providing the user the freedom of specifying the constraints in any appropriate order.
Direct Manipulation, FFD, Deformation, Multiple Point Constraints
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@inproceedings{shi-min2001direct,
  title={Direct Manipulation of FFD: Efficient Explicit Solutions and Decomposible Multiple Point Constraints},
  author={Shi-Min Hu, Hui Zhang, Chiew-Lan Tai, and Jia-Guang Sun},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160826223802049679463},
  booktitle={The Visual Computers},
  volume={17},
  number={6},
  pages={370-379},
  year={2001},
}
Shi-Min Hu, Hui Zhang, Chiew-Lan Tai, and Jia-Guang Sun. Direct Manipulation of FFD: Efficient Explicit Solutions and Decomposible Multiple Point Constraints. 2001. Vol. 17. In The Visual Computers. pp.370-379. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160826223802049679463.
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