Surface patch reconstruction via curve sampling

This paper introduces a method that reconstructs a surface patch by sampling along three concurrent curves on the surface with a touch sensor. These data curves, each lying in a different plane, form a "skeleton" from which the patch is built in two phases. First, the Darboux frame at the curve intersection is estimated to reflect the local geometry. Second, polynomial fitting is carried out in the Darboux frame. The use of total (absolute) Gaussian curvature effectively prevents unnecessary folding of the surface normally expected to result from fitting over one-dimensional data. The reconstructed patch attains remarkable accuracy as demonstrated through experiments. This work carries a promise for in-hand manipulation. It also has potential application in building accurate models for complex curved objects which can cause occlusion to a camera or a range sensor