On the optimal layout of planar graphs with fixed boundary
SIAM Journal on Computing
Parametrization and smooth approximation of surface triangulations
Computer Aided Geometric Design
Level set diagrams of polyhedral objects
Proceedings of the fifth ACM symposium on Solid modeling and applications
How to morph tilings injectively
Journal of Computational and Applied Mathematics
Cut-and-paste editing of multiresolution surfaces
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Metamorphosis of Arbitrary Triangular Meshes
IEEE Computer Graphics and Applications
One-to-one piecewise linear mappings over triangulations
Mathematics of Computation
Computer Aided Geometric Design
Tutte's barycenter method applied to isotopies
Computational Geometry: Theory and Applications - Special issue on the thirteenth canadian conference on computational geometry - CCCG'01
Matchmaker: constructing constrained texture maps
ACM SIGGRAPH 2003 Papers
Discrete multiscale vector field decomposition
ACM SIGGRAPH 2003 Papers
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Hodge decompositions and computational electromagnetics
Hodge decompositions and computational electromagnetics
Discrete exterior calculus
Free-Boundary Linear Parameterization of 3D Meshes in the Presence of Constraints
SMI '05 Proceedings of the International Conference on Shape Modeling and Applications 2005
Planar parameterization for closed 2-manifold genus-1 meshes
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Journal of Graph Theory
Recent Advances in Computational Conformal Geometry
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Surface Quasi-Conformal Mapping by Solving Beltrami Equations
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Fast Spherical Mapping for Genus-0 Meshes
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part II
Spectral conformal parameterization
SGP '08 Proceedings of the Symposium on Geometry Processing
Discrete surface Ricci flow: theory and applications
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Slit map: conformal parameterization for multiply connected surfaces
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Drawing 3-polytopes with good vertex resolution
GD'09 Proceedings of the 17th international conference on Graph Drawing
Bounded distortion mapping spaces for triangular meshes
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Duals of orphan-free anisotropic voronoi diagrams are embedded meshes
Proceedings of the twenty-eighth annual symposium on Computational geometry
GD'12 Proceedings of the 20th international conference on Graph Drawing
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We describe how some simple properties of discrete one-forms directly relate to some old and new results concerning the parameterization of 3D mesh data. Our first result is an easy proof of Tutte's celebrated ''spring-embedding'' theorem for planar graphs, which is widely used for parameterizing meshes with the topology of a disk as a planar embedding with a convex boundary. Our second result generalizes the first, dealing with the case where the mesh contains multiple boundaries, which are free to be non-convex in the embedding. We characterize when it is still possible to achieve an embedding, despite these boundaries being non-convex. The third result is an analogous embedding theorem for meshes with genus 1 (topologically equivalent to the torus). Applications of these results to the parameterization of meshes with disk and toroidal topologies are demonstrated. Extensions to higher genus meshes are discussed.