An approach to visual sampling and reconstruction motivated by concepts from numerical grid generation is presented. Adaptive meshes that can nonuniformly sample and reconstruct intensity and range data are presented. These meshes are dynamic models which are assembled by interconnecting nodal masses with adjustable springs. Acting as mobile sampling sites, the nodes observe properties of the input data, such as intensities, depths, gradients, and curvatures. Based on these nodal observations, the springs automatically adjust their stiffnesses so as to distribute the available degrees of freedom of the reconstructed model in accordance with the local complexity of the input data. The adaptive mesh algorithm runs at interactive rates with continuous 3-D display on a graphics workstation It is applied to the adaptive sampling and reconstruction of images and surfaces.>