Acquiring 3D models of intricate objects (like tree branches, bicycles and insects) is a hard problem due to severe self-occlusions, repeated thin structures and surface discontinuities. In theory, a shape-from-silhouettes (SFS) approach can overcome these difficulties and use many views to reconstruct visual hulls that are close to the actual shapes. In practice, however, SFS is highly sensitive to errors in silhouette contours and the calibration of the imaging system, and therefore not suitable for obtaining reliable shapes with a large number of views. We present a practical approach to SFS using a novel technique called coplanar shadowgram imaging, that allows us to use dozens to even hundreds of views for visual hull reconstruction. Here, a point light source is moved around an object and the shadows (silhouettes) cast onto a single background plane are observed. We characterize this imaging system in terms of image projection, reconstruction ambiguity, epipolar geometry, and shape and source recovery. The coplanarity of the shadowgrams yields novel geometric properties that are not possible in traditional multi-view camera-based imaging systems. These properties allow us to derive a robust and automatic algorithm to recover the visual hull of an object and the 3D positions of light source simultaneously, regardless of the complexity of the object. We demonstrate the acquisition of several intricate shapes with severe occlusions and thin structures, using 50 to 120 views.