Shape representation is a fundamental problem in Computer Graphics. Among known representations for three-dimensional objects, adaptively sampled distance fields (ADFs) are noted for their versatility. ADFs combine the concepts of geometry with volume data, allow objects to be represented with arbitrary precision, and consolidate several operations - such as visualization, level-of-detail modeling, collision detection, proximity tests, morphing and boolean operations | into a single representation. This work proposes methods to accelerate the reconstruction of static ADFs, to improve the quality of reconstructed fields, and to visualize ADF isosurfaces, making use of the massive computational power found in modern graphics hardware (GPUs). In order to effciently represent ADFs on graphics cards, a hierarchical structure based on perfect spatial hashing is proposed. Rendering of ADFs is done completely on GPUs, using a ray casting technique based on sphere tracing. Means to overcome the C0 and C1 discontinuities inherent to ADFs are suggested in order to attain smoothly shaded iso-surfaces. Finally, a new reconstruction method for ADFs, which can better represent curved surfaces, is proposed. Results are presented through simple interactive visualization applications, with ADFs generated from both triangle meshes and primitive solids.