Decorating arbitrary meshes with Celtic knots requires polygonal meshes with regular connectivity and close to regular face geometry. Because these properties are often irregular, especially in scanned or reconstructed models, the Celtic knots produced may be erratic and undesireable. In this paper we remesh models based on planar tilings defined by the user. Such pattern-oriented surfaces allow us to decorate models with attractive Celtic knots in a consistent fashion and may be applicable to a large number of algorithms that are sensitive to mesh structure.