Interpolating sampled contours in 3D: perturbation analyses

In four experiments, observers interpolated parabolic sampled contours confined to planes in three-dimensional space. Each sampled contour consisted of eight visible points, placed irregularly along the otherwise invisible parabolic contour. Observers adjusted an additional point until it fell on the contour. We sought to determine how each visible point influenced interpolation by measuring the effect of slightly perturbing its location. Influence fell rapidly to zero as distance from the interpolated point increased, indicating that human visual interpolation of parabolic contours is local. We compare the measured influence for human observers to that predicted by three standard interpolation algorithms. The results were inconsistent with a fit of a quadratic to the points, but were reasonably consistent with a cubic spline and most consistent with an algorithm that minimizes the variance of angles between neighboring line segments defined by the sampled points.