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We present an algorithm that allows stream surfaces to recognize and adapt to vector field topology. Standard stream surface algorithms either refine the surface uncontrolled near critical points which slows down the computation considerably and may lead to a poor surface approximation. Alternatively, the concerned region is omitted from the stream surface by severing it into two parts thus generating an incomplete stream surface. Our algorithm utilizes topological information to provide adoi:10.1111/j.1467-8659.2009.01672.x fatcat:3yqi2mmhcnevngqs2y7mui54zu