| Planes are fundamental geometric primitives. Evidence in art and science shows that planar sections are useful -- structures composed purely of planar primitives are employed in architecture, design and manufacturing, where one can with relative ease physically create a model from planar parts. In medical visualization, patient-aligned planes may suffice to represent important features within a volumetric dataset. Many different applications involving 3D shape can geometrically benefit from a contextually-appropriate piecewise planar representation. This thesis systematically studies planar section representations of 3D shape.;We show that humans are consistent in abstracting existing 3D shapes using a minimal number of planar 3D sections. We provide geometric insights that allow us to replicate human planar abstraction of 3D shapes algorithmically, and evaluate the algorithm's performance with a shape recognition study.;We study how humans create planar shape representations interactively from scratch. Observations of their interaction patterns are used to develop a streamlined interactive drawing system. The system is further augmented to facilitate procedural creation, incorporate existing geometry and aid fabrication. A physical simulation approach identifies structurally weak models before they are fabricated, and allows interactive refinement.;We then study the perceptual efficacy of a range of planar representations of 3D shape in a large-scale user study. The analysis of results reveals geometric sources responsible for error, and we use these sources to create predictive linear models of error. With this knowledge, we demonstrate we are able to improve the quality of algorithmically-created representations.;Finally we present a number of applications of planar section representations. Some applications are artistic in nature, such as paper statues, puppets, detailed compositions and scanimations. Other applications are more scientific, including surface reconstruction and compression, 3D annotation, volumetric data visualization, 3D navigation, and poly-postors.;Overall, the dissertation provides a comprehensive treatment of various aspects of planar section representations of 3D shape and their applications. We provide both qualitative and quantitative perceptual validation that planar section representations are indeed effective proxies of 3D shape, useful in both artistic and scientific settings. |
