Iterative Methods for Improving Mesh Parameterizations

13 years 10 months ago

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We present two complementary methods for automatically improving mesh parameterizations and demonstrate that they provide a very desirable combination of efﬁciency and quality. First, we describe a new iterative method for constructing quasi-conformal parameterizations with free boundaries. We formulate the problem as ﬁtting the coordinate gradients to two guidance vector ﬁelds of equal magnitude that are everywhere orthogonal. In only one linear step, our method efﬁciently generates parameterizations with natural boundaries from those with convex boundaries. If repeated until convergence, it produces the unique global minimizer of the Dirichlet energy. Next, we introduce a new non-linear optimization framework that can rapidly reduce interior distortion under a variety of metrics. By iteratively solving linear systems, our algorithm converges to a high quality, low distortion parameterization in very few iterations. The two components of our system are effective both in combi...

Shen Dong, Michael Garland

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