Computing dense disparity fields from large-baseline stereo is a difficult problem because of long-range correspondences involved. A typical solution to this problem is to use optical flow or block matching methods implemented over a hierarchy of resolutions. However, these approaches cannot easily cope with disparity discontinuities. Recently, we have proposed a novel approach that combines feature matching and Delaunay triangulation. In this approach, first feature points are extracted using intensity corner detector, and then corresponding feature-point pairs are found using cross-correlation. These two steps result in a reliable but sparse map of disparity vectors. In order to compute a dense disparity field, the third step involves Delaunay triangulation followed by disparity interpolation based on an affine (planar) model. The resulting disparity fields are continuous everywhere, and thus are not realistic; typical stereo image pairs exhibit disparity discontinuities at object boundaries. To address this problem, in the past we subdivided some Delaunay triangles into smaller ones. Although this approach has significantly improved the rendition of disparity discontinuities, it did not always work reliably. In this paper, we propose an adaptive interpolation over Delaunay triangles. As before, the interpolation is distance-dependent, i.e., accounts for Euclidian distance between the position of disparity under interpolation and three vertices of a triangle. The distance-dependent weights, however, are now additionally adapted so that the interpolated, pixel-based disparities within each triangle afford discontinuities. The new method has been applied to natural stereoscopic images. The resulting dense disparity fields exhibit clear, although subtle, discontinuities at object boundaries, and are more realistic than disparity fields obtained by the prior approach.