Abstract
Planar shape interpolation is a classic problem in computer graphics. We present a novel shape interpolation method that blends C∞ planar harmonic mappings represented in closed-form. The intermediate mappings in the blending are guaranteed to be locally injective C∞ harmonic mappings, with conformal and isometric distortion bounded by that of the input mappings. The key to the success of our method is the fact that the blended differentials of our interpolated mapping have a simple closed-form expression, so they can be evaluated with unprecedented efficiency and accuracy. Moreover, in contrast to previous approaches, these differentials are integrable, and result in an actual mapping without further modification. Our algorithm is embarrassingly parallel and is orders of magnitude faster than state-of-the-art methods due to its simplicity, yet it still produces mappings that are superior to those of existing techniques due to its guaranteed bounds on geometric distortion.
| Original language | English |
|---|---|
| Article number | a105 |
| Journal | ACM Transactions on Graphics |
| Volume | 35 |
| Issue number | 4 |
| DOIs | |
| State | Published - 11 Jul 2016 |
| Event | ACM SIGGRAPH 2016 - Anaheim, United States Duration: 24 Jul 2016 → 28 Jul 2016 |
Bibliographical note
Funding Information:This research was partially funded by the Israel Science Foundation (grants No. 1869/15 and 2102/15) and by the Max Planck Center for Visual Computing and Communication. We gratefully acknowledge the support of NVIDIA Corporation with the donation of the GPU. Finally we thank the anonymous reviewers for their valuable comments and suggestions.
Publisher Copyright:
© 2016 ACM.
Keywords
- Animation
- Bounded distortion
- Harmonic mappings
- Injective mappings
- Shape deformation
- Shape interpolation