The potential of cylindrical co-ordinate three-dimensional surface models
D. J. Mott · British Journal of Radiology · 1988
In the rapidly expanding field of the creation of three-dimensional (3D) surface models from stacks of contiguous computed tomography (CT) or nuclear magnetic resonance (NMR) cross-sectional scans, the views generated are usually orthogonal projections. This results in images of internal or external anatomy being produced as if those objects were being observed by the viewer. The problem of displaying 3D surfaces on a two-dimensional plane is one that has long been studied by cartographers and the use of cylindrical co-ordinates offers one solution. In this the locations of structures on a surface are found in r, θ, z, cylindrical co-ordinates where r is the radius from an axis through the body, θ is the angular location around the axis and z is the distance along the axis. If the z axis is taken as the axis of rotation of the CT scanner then Fig. 1 illustrates this co-ordinate system on a stack of CT slices and its relationship to the x i, y i co-ordinate system of each image.