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
Setting the boundary free: a composite approach to surface parameterization
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Mesh parameterization methods and their applications
Foundations and Trends® in Computer Graphics and Vision
Computing Length-Preserved Free Boundary for Quasi-Developable Mesh Segmentation
IEEE Transactions on Visualization and Computer Graphics
Towards flattenable mesh surfaces
Computer-Aided Design
WireWarping: A fast surface flattening approach with length-preserved feature curves
Computer-Aided Design
Pattern computation for compression garment
Proceedings of the 2008 ACM symposium on Solid and physical modeling
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
Pattern computation for compression garment by a physical/geometric approach
Computer-Aided Design
A local/global approach to mesh parameterization
SGP '08 Proceedings of the Symposium on Geometry Processing
Slit map: conformal parameterization for multiply connected surfaces
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Computing Extremal Quasiconformal Maps
Computer Graphics Forum
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Linear parameterization of 3D meshes with disk to-pology is usually performed using the method of barycen-tric coordinates pioneered by Tutte and Floater. This im-poses a convex boundary on the parameterization which can significantly distort the result. Recently, several methods showed how to relax the convex boundary re-quirement while still using the barycentric coordinates formulation. However, this relaxation can result in other artifacts in the parameterization. In this paper we explore these methods and give a general recipe for "natural" boundary conditions for the family of so-called "three point" barycentric coordinates. We discuss the shortcom-ings of these methods and show how they may be rectified using an iterative scheme or a carefully crafted "virtual boundary". Finally, we show how these methods adapt easily to solve the problem of constrained parameterization.