Computational geometry: an introduction
Computational geometry: an introduction
Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
A first course in the numerical analysis of differential equations
A first course in the numerical analysis of differential equations
Parametrization and smooth approximation of surface triangulations
Computer Aided Geometric Design
MAPS: multiresolution adaptive parameterization of surfaces
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
How to morph tilings injectively
Journal of Computational and Applied Mathematics
Consistent mesh parameterizations
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Computer Aided Geometric Design
Fundamentals of spherical parameterization for 3D meshes
ACM SIGGRAPH 2003 Papers
Discrete one-forms on meshes and applications to 3D mesh parameterization
Computer Aided Geometric Design
Geometric modeling based on triangle meshes
ACM SIGGRAPH 2006 Courses
Parameterizations of digital surfaces homeomorphic to a sphere using discrete harmonic functions
Pattern Recognition Letters
Parameterizations of digital surfaces homeomorphic to a sphere using discrete harmonic functions
Pattern Recognition Letters
Asymptotic properties of some triangulations of the sphere
Journal of Computational and Applied Mathematics
A Simple Criterion for Nodal 3-connectivity in Planar Graphs
Electronic Notes in Theoretical Computer Science (ENTCS)
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
Discrete one-forms on meshes and applications to 3D mesh parameterization
Computer Aided Geometric Design
Bounded distortion mapping spaces for triangular meshes
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Injective and bounded distortion mappings in 3D
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
| Hi-index | 0.00 |
We call a piecewise linear mapping from a planar triangulation to the plane a convex combination mapping if the image of every interior vertex is a convex combination of the images of its neighbouring vertices. Such mappings satisfy a discrete maximum principle and we show that they are one-to-one if they map the boundary of the triangulation homeomorphically to a convex polygon. This result can be viewed as a discrete version of the Radó-Kneser-Choquet theorem for harmonic mappings, but is also closely related to Tutte's theorem on barycentric mappings of planar graphs.