ABF++ : Fast and Robust Angle Based
Flattening
Alla
Sheffer Bruno Levy
Maxim Mogilnitsky Alexander Bogomyakov
Parameterizations
generated with ABF++ (The seams were cut with Seamster)
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Abstract Conformal parameterization of
mesh models has numerous applications in geometry processing. Conformality is desirable for remeshing,
surface reconstruction, and many other mesh processing applications. Subject
to the conformality requirement, those applications
typically benefit from parameterizations with smaller stretch. The Angle
Based Flattening (ABF) method, presented a few years ago, generates provably
valid conformal parameterizations with low stretch. However it is quite time
consuming and becomes error prone for large meshes due to numerical error
accumulation. This work presents ABF++, a highly efficient extension of the
ABF method that overcomes those drawbacks, while maintaining all the
advantages of ABF. ABF++ robustly parameterizes meshes of hundreds of
thousands and millions of triangles within minutes. It is based on three main
components : (1) a new numerical solution technique that dramatically reduces
the dimension of the linear systems solved at each iteration, speeding up the
solution ; (2) a new robust scheme for reconstructing the u,v's
from the angle space solution that avoids the numerical instabilities which
hindered the ABF reconstruction scheme ; and (3) an efficient hierarchical
solution technique. The speedup at (1) does not come at the expense of
greater distortion and the resulting parameterizations remain provably valid.
The hierarchical technique (3) enables parameterization of models with
millions of faces in seconds, at the expense of a minor increase in
parametric distortion. As a result of those extensions the ABF++ method is
extremely suitable for robustly and efficiently parameterizing
models for geometry processing applications. |
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Paper PDF, 5.8 MB
ACM Transactions on Graphics, 2005, |
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Link to Inria Page |