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In this paper, we employ Delaunay triangulation techniques to reconstruct high quality visual hulls. From a set of calibrated images, the algorithm first computes a sparse set of initial points with a dandelion model and builds a Delaunay triangulation restricted to the visual hull surface. It then iteratively refines the triangulation by inserting new sampling points, which are the intersections between the visual hull surface and the Voronoi edges dual to the triangulation's facets, until certain criteria are satisfied. The intersections are computed by cutting line segments with the visual hull, which is then converted to the problem of intersecting a line segment with polygonal contours in 2D. A barrel-grid structure is developed to quickly pick out possibly intersecting contour segments and thus accelerate the process of intersecting in 2D. Our algorithm is robust, fast, fully adaptive, and it produces precise and smooth mesh models composed of well-shaped tri-angles.