Bijective Composite Mean Value Mappings
Article first published online: 19 AUG 2013
© 2013 The Author(s) Computer Graphics Forum © 2013 The Eurographics Association and John Wiley & Sons Ltd.
Computer Graphics Forum
Volume 32, Issue 5, pages 137–146, August 2013
How to Cite
Schneider, T., Hormann, K. and Floater, M.S. (2013), Bijective Composite Mean Value Mappings. Computer Graphics Forum, 32: 137–146. doi: 10.1111/cgf.12180
- Issue published online: 19 AUG 2013
- Article first published online: 19 AUG 2013
- I.3.3 [Computer Graphics]: Picture/Image Generation—Line and curve generation;
- G.1.1 [Numerical Analysis]: Interpolation—Interpolation formulas
We introduce the novel concept of composite barycentric mappings and give theoretical conditions under which they are guaranteed to be bijective. We then focus on mean value mappings and derive a simple procedure for computing their Jacobians, leading to an efficient GPU-assisted implementation for interactively designing composite mean value mappings which are bijective up to pixel resolution. We provide a number of examples of 2D image deformation and an example of 3D shape deformation based on a natural extension of the concept to spatial mappings.