Two completely local methods for interpolating point-normal data based on rational quadratic curves are presented. The first method can be applied to arbitrary convex data and is capable of reproducing spheres and cylinders. The second method is specialized to cones. The curve methods are used to construct a side-vertex patch that preserves their accuracy. To handle more general configurations, a composite side-side patch involving rational cubic curves is proposed. The composite patch is visually smooth and attains a cubic rate of convergence.