Automatic reconstruction of B-spline surfaces of arbitrary topological type
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Parametrization and smooth approximation of surface triangulations
Computer Aided Geometric Design
Computing a canonical polygonal schema of an orientable triangulated surface
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Optimally cutting a surface into a disk
Proceedings of the eighteenth annual symposium on Computational geometry
Edgebreaker: a simple compression for surfaces with handles
Proceedings of the seventh ACM symposium on Solid modeling and applications
Cutting 3D freeform objects with genus-n into single boundary surfaces using topological graphs
Proceedings of the seventh ACM symposium on Solid modeling and applications
Bounded-distortion piecewise mesh parameterization
Proceedings of the conference on Visualization '02
Computer Aided Geometric Design
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Discrete one-forms on meshes and applications to 3D mesh parameterization
Computer Aided Geometric Design
Families of cut-graphs for bordered meshes with arbitrary genus
Graphical Models
Discrete one-forms on meshes and applications to 3D mesh parameterization
Computer Aided Geometric Design
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Parameterization of 3D meshes is important for many graphics and CAD applications, in particular for texture mapping, re-meshing and morphing. Current parameterization methods for closed manifold genus-n meshes usually involve cutting the mesh according to the object generators, fixing the resulting boundary and then applying the 2D position for each of the mesh vertices on a plane, such that the flattened triangles are not too distorted and do not overlap. Unfortunately, fixing the boundary distorts the resulting parameterization, especially near the boundary. A special case is that of closed manifold genus-1 meshes that have two generators. They can therefore be flattened naturally to a plane without the use of a fixed boundary while still maintaining the continuity of the parameterization. Therefore, in treating genus-1 objects, this attribute must be exploited. This paper introduces a generalized method for planar parameterization of closed manifold genus-1 meshes. As in any planar parameterization with a fixed boundary, weights are assigned over the mesh edges. The type of weights defined depends on the type of mesh characteristics to be preserved. The paper proves that the method satisfies the non-overlapping requirement for any type of positive barycentric weights, including nonsymmetrical weights. Moreover, convergence is guaranteed according to the Gauss-Seidel method. The proposed method is simple to implement, fast and robust. The feasibility of the method will be demonstrated on several complex objects.