The emerging field of Engineering Oriented Geometry (EOG) comprises new and extended geometric modeling methods that are directly related to the shared inherent engineering attributes of design, analysis, and manufacturing. This paper describes EOG methods that can be applied to scanned data, focusing on two main sub-areas: (a) shape reconstruction from scanned data; and (b) geometric modeling for analysis. The paper describes the main developments in geometric shape reconstruction methods for scanned data and in geometric modeling for analysis. In the field of geometric reconstruction efficient algorithms have been developed to cope with the open engineering problem of reconstruction from large scale, noisy, and incomplete data. Taken together, these solutions provide a comprehensive methodology that is fundamental to advancing the field of shape reconstruction. They constitute a new EOG model philosophy that can be implemented in CAD engineering for further processing, such as design, analysis, and manufacturing. Integrating CAD and multiscale analysis into one module creates a new paradigm that affects both fields and had the potential to lead to new areas of mechanical analysis.