Parameterizations that use mesh simplification to build the base domain always adopt the vertex removal scheme. This paper applies edge collapse to constructing the base domain instead. After inducing the parameterization of the original mesh over the base domain, new algorithms map the new vertices in the simplified mesh back to the original one according to the edge transition sequence to integrate the parameterization. We present a direct way, namely edge classification, to deduce the sequence. Experimental results show that the new parameterization features considerable saving in computing complexity and maintains smoothness.
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