Stripe Parameterization of Tubular Surfaces

We present a novel algorithm for automatic parameterization oftube-like surfaces of arbitrarygenus such as the surfaces of knots, trees, blood vessels, neurons, or any tubular graph with a globally consistentstripe texture. Mathematically these surfaces can be described as thickened graphs, and the calculatedparameterizationstripe will follow either around thetube, along the underlying graph, a spiraling combination of both, or obey an arbitrary texture map whosecharts have a 180 degree symmetry.We use the principalcurvature frame field of the underlyingtube-like surface to guide the creation of a global, topologically consistentstripeparameterization of the surface. Our algorithm extends the QuadCover algorithm and is based, first, on the use of so-called projectivevector fields instead of frame fields, and second, on different types ofbranch points. That does not only simplify the mathematical theory, but also reduces computation time by the decomposition of the underlying stiffness matrices.