ACM Transactions on Graphics (TOG)
Piecewise surface flattening for non-distorted texture mapping
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Parametrization and smooth approximation of surface triangulations
Computer Aided Geometric Design
Non-distorted texture mapping for sheared triangulated meshes
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
A Supernodal Approach to Sparse Partial Pivoting
SIAM Journal on Matrix Analysis and Applications
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Multigrid
Texture mapping progressive meshes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Constrained texture mapping for polygonal meshes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Least squares conformal maps for automatic texture atlas generation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Bounded-distortion piecewise mesh parameterization
Proceedings of the conference on Visualization '02
Texture Mapping Using Surface Flattening via Multidimensional Scaling
IEEE Transactions on Visualization and Computer Graphics
Quasi-Conformally Flat Mapping the Human Cerebellum
MICCAI '99 Proceedings of the Second International Conference on Medical Image Computing and Computer-Assisted Intervention
Spanning Tree Seams for Reducing Parameterization Distortion of Triangulated Surfaces
SMI '02 Proceedings of the Shape Modeling International 2002 (SMI'02)
Seamster: inconspicuous low-distortion texture seam layout
Proceedings of the conference on Visualization '02
Graphical Models - Special issue on SMI 2002
Fair morse functions for extracting the topological structure of a surface mesh
ACM SIGGRAPH 2004 Papers
Feature-based surface parameterization and texture mapping
ACM Transactions on Graphics (TOG)
IEEE Transactions on Visualization and Computer Graphics
Creating entirely textured 3D models of real objects using surface flattening
Machine Graphics & Vision International Journal
Woven model based geometric design of elastic medical braces
Computer-Aided Design
Setting the boundary free: a composite approach to surface parameterization
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Linear angle based parameterization
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Mesh parameterization methods and their applications
Foundations and Trends® in Computer Graphics and Vision
Texture mapping on 3D surfaces using clustering-based cutting paths
International Journal of Computational Science and Engineering
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
Freeform surface flattening based on fitting a woven mesh model
Computer-Aided Design
Pattern flattening for orthotropic materials
Computer-Aided Design
Data fusion for photorealistic 3d models
CAIP'05 Proceedings of the 11th international conference on Computer Analysis of Images and Patterns
Feature-Constrained texturing system for 3d models
KES'05 Proceedings of the 9th international conference on Knowledge-Based Intelligent Information and Engineering Systems - Volume Part III
A new smoothing algorithm for quadrilateral and hexahedral meshes
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
Real-time content-aware texturing for deformable surfaces
Proceedings of the 10th European Conference on Visual Media Production
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Texture is an essential component of computer generated models. For a texture mapping procedure to be effective it has to generate continuous textures and cause only small mapping distortion. The Angle Based Flattening (ABF) parameterization method is guaranteed to provide a continuous (no foldovers) mapping. It also minimizes the angular distortion of the parameterization, including locating the optimal planar domain boundary. However, since it concentrates on minimizing the angular distortion of the mapping, it can introduce relatively large linear distortion.In this paper we introduce a new procedure for reducing length distortion of an existing parameterization and apply it to ABF results. The linear distortion reduction is added as a second step in a texture mapping computation. The new method is based on computing a mapping from the plane to itself which has length distortion very similar to that of the ABF parameterization. By applying the inverse mapping to the result of the initial parameterization, we obtain a new parameterization with low length distortion. We notice that the procedure for computing the inverse mapping can be applied to any other (convenient) mapping from the three-dimensional surface to the plane in order to improve it.The mapping in the plane is computed by applying weighted Laplacian smoothing to a Cartesian grid covering the planar domain of the initial mapping. Both the mapping and its inverse are provably continuous. Since angle preserving (conformal) mappings, such as ABF, locally preserve distances as well, the planar mapping has small local deformation. As a result, the inverse mapping does not significantly increase the angular distortion.The combined texture mapping procedure provides a mapping with low distance and angular distortion, which is guaranteed to be continuous.