Texture mapping progressive 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
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Mesh editing with poisson-based gradient field manipulation
ACM SIGGRAPH 2004 Papers
Linear rotation-invariant coordinates for meshes
ACM SIGGRAPH 2005 Papers
Volume and shape preservation via moving frame manipulation
ACM Transactions on Graphics (TOG)
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
On Linear Variational Surface Deformation Methods
IEEE Transactions on Visualization and Computer Graphics
Simple and Efficient Mesh Editing with Consistent Local Frames
PG '07 Proceedings of the 15th Pacific Conference on Computer Graphics and Applications
Conformal equivalence of triangle meshes
ACM SIGGRAPH 2008 papers
ACM SIGGRAPH 2008 papers
Optimal Surface Parameterization Using Inverse Curvature Map
IEEE Transactions on Visualization and Computer Graphics
Variational harmonic maps for space deformation
ACM SIGGRAPH 2009 papers
Spectral conformal parameterization
SGP '08 Proceedings of the Symposium on Geometry Processing
SMI 2012: Full Spectral computations on nontrivial line bundles
Computers and Graphics
Shape-Up: Shaping Discrete Geometry with Projections
Computer Graphics Forum
Can Mean-Curvature Flow be Modified to be Non-singular?
Computer Graphics Forum
Linear Surface Reconstruction from Discrete Fundamental Forms on Triangle Meshes
Computer Graphics Forum
Planar shape interpolation with bounded distortion
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Robust fairing via conformal curvature flow
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Geometry curves: A compact representation for 3D shapes
Graphical Models
SMI 2013: Laplacians on flat line bundles over 3-manifolds
Computers and Graphics
Differential-Based Geometry and Texture Editing with Brushes
Journal of Mathematical Imaging and Vision
| Hi-index | 0.00 |
We introduce a new method for computing conformal transformations of triangle meshes in R3. Conformal maps are desirable in digital geometry processing because they do not exhibit shear, and therefore preserve texture fidelity as well as the quality of the mesh itself. Traditional discretizations consider maps into the complex plane, which are useful only for problems such as surface parameterization and planar shape deformation where the target surface is flat. We instead consider maps into the quaternions H, which allows us to work directly with surfaces sitting in R3. In particular, we introduce a quaternionic Dirac operator and use it to develop a novel integrability condition on conformal deformations. Our discretization of this condition results in a sparse linear system that is simple to build and can be used to efficiently edit surfaces by manipulating curvature and boundary data, as demonstrated via several mesh processing applications.