HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

Least Squares Conformal Maps for Automatic Texture Atlas Generation

Bruno Lévy 1 Sylvain Petitjean 1 Nicolas Ray 1 Jérôme Maillot
1 ISA - Models, algorithms and geometry for computer graphics and vision
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : A Texture Atlas is an efficient color representation for 3D Paint Systems. The model to be textured is decomposed into charts homeomorphic to discs, each chart is parameterized, and the unfolded charts are packed in texture space. Existing texture atlas methods for triangulated surfaces suffer from several limitations, requiring them to generate a large number of small charts with simple borders. The discontinuities between the charts cause artifacts, and make it difficult to paint large areas with regular patterns. In this paper, our main contribution is a new quasi-conformal parameterization method, based on a least-squares approximation of the Cauchy-Riemann equations. The so-defined objective function minimizes angle deformations, and we prove the following properties: the minimum is unique, independent of a similarity in texture space, independent of the resolution of the mesh and cannot generate triangle flips. The function is numerically well behaved and can therefore be very efficiently minimized. Our approach is robust, and can parameterize large charts with complex borders. We also introduce segmentation methods to decompose the model into charts with natural shapes, and a new packing algorithm to gather them in texture space. We demonstrate our approach applied to paint both scanned and modeled data sets.
Document type :
Journal articles
Complete list of metadata

Contributor : Publications Loria Connect in order to contact the contributor
Submitted on : Wednesday, July 7, 2021 - 4:55:51 PM
Last modification on : Thursday, February 10, 2022 - 12:19:06 PM
Long-term archiving on: : Friday, October 8, 2021 - 6:54:48 PM


Files produced by the author(s)




Bruno Lévy, Sylvain Petitjean, Nicolas Ray, Jérôme Maillot. Least Squares Conformal Maps for Automatic Texture Atlas Generation. ACM Transactions on Graphics, Association for Computing Machinery, 2002, 21 (3), 10 p. ⟨10.1145/566654.566590⟩. ⟨inria-00100754⟩



Record views


Files downloads