Thin surfaces, such as the leaves of a plant, pose a significant challenge
for implicit surface reconstruction techniques, which typically assume a
closed, orientable surface. We show that by approximately interpolating a point
cloud of the surface (augmented with off-surface points) and restricting the
evaluation of the interpolant to a tight domain around the point cloud, we need
only require an orientable surface for the reconstruction. We use polyharmonic
smoothing splines to fit approximate interpolants to noisy data, and a
partition of unity method with an octree-like strategy for choosing subdomains.
This method enables us to interpolate an N-point dataset in O(N) operations. We
present results for point clouds of capsicum and tomato plants, scanned with a
handheld device. An important outcome of the work is that sufficiently smooth
leaf surfaces are generated that are amenable for droplet spreading
simulations
