“Fair Curve Networks in Nonlinear Geometries”

Fair curve networks in nonlinear geometries are an extension of our work [Hofer and Pottmann 2004] on energy-minimizing spline curves in manifolds. Instead of designing with one single curve, we here present a variational approach for the design with an entire network of curves. After a geometric characterization of fair, i.e., energy-minimizing curve networks, we discuss their discretization and computation. Fair curve networks in nonlinear geometries have a variety of applications including surface parameterization, aesthetic remeshing and design of fair surfaces in the presence of obstacles.

Hofer, M., and Pottmann, H. 2004. Energy-minimizing splines in manifolds. ACM Trans. Graphics 23, 3, 284–293.