Quadrangular remeshing of triangulated surfaces has received an increasing attention in recent years. A particularly elegant approach is the extraction of quads from the streamlines of a harmonic field. While the construction of such fields is by now a standard technique in geometry processing, enforcing design constraints is still not fully investigated. This work presents a technique for handling directional constraints by directly controlling the gradient of the field. In this way, line constraints sketched by the user or automatically obtained as feature lines can be fulfilled efficiently. Furthermore, we show the potential of quasi-harmonic fields as a flexible tool for controlling the behavior of the field over the surface. Treating the surface as an inhomogeneous domain we can endow specific surface regions with field attraction/repulsion properties.

We present a new method for noise removal on static and time-varying range data. Our approach predicts the restored position of a perturbed vertex using similar vertices in its neighborhood. It defines the required similarity measure in a new non-local fashion which compares regions of the surface instead of point pairs. This allows our algorithm to obtain a more accurate denoising result than previous state-of-the-art approaches and, at the same time, to better preserve fine features of the surface. Furthermore, our approach is easy to implement, effective, and flexibly applicable to different types of scanned data. We demonstrate this on several static and interesting new time-varying datasets obtained using laser and structured light scanners.