کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
441108 | 691368 | 2016 | 9 صفحه PDF | دانلود رایگان |
• A method is proposed for creating a planar free-form deformation of degree 1×n1×n that has a rational inverse.
• The control points can be freely positioned, and weights are computed that produce a birational map.
• Weight computation is simple, and can be performed in real-time as the control points are moved.
This paper shows that generic 2D-Free-Form Deformations of degree 1×n1×n can be made birational by a suitable assignment of weights to the Bézier or B-spline control points. An FFD that is birational facilitates operations such as backward mapping for image warping, and Extended Free-Form Deformation. While birational maps have been studied extensively in the classical algebraic geometry literature, this paper is the first to present a family of non-linear birational maps that are flexible enough to be of practical use in geometric modeling.
Journal: Computer Aided Geometric Design - Volume 44, May 2016, Pages 1–9