This dissertation focuses on the varied and interesting field of surface reconstruction. For example, in geometric modeling an implicit surface is defined by specifying for each point in space whether it is inside or outside an object, from which an explicit surface can then be constructed. In various medical applications a laser range scanner can be used to obtain a set of data from the surface of a patient's body part, from which an accurate reconstruction of the original surface is then created.

This dissertation provides a broad overview of such surface reconstruction techniques, highlighting the data conversions commonly used. This dissertation then advances the field in a number of ways. In particular, traditional implicit surfaces and their polygonizers are generally limited to manifolds. To allow a wider range of surfaces, including manifolds-with-boundary and certain non-manifolds, implicit surfaces are extended in multiple region implicit surfaces (MRISs). A detailed study of the reconstruction of MRISs is described, and two different approaches are examined. The first is an all-at-once approach that reconstructs an entire MRIS as a unit, whereas the second considers each of the component manifolds-with-boundary that make up an MRIS separately, thus reconstructing them one at a time. A number of examples are presented showing the types of surfaces possible with this new approach.

These MRISs and associated polygonizers are then applied to surface reconstruction from structured range data, as might be obtained by plane-of-light laser range scanners. After describing laser scanning systems and previous reconstruction algorithms, a new method of reconstruction is presented that directly defines an MRIS from structured range data, making use of both the structure and volumetric information available. This method has been developed to be simple, efficient and general purpose, being suitable for any number of scanners each moved with any type of motion. A number of possible medical applications of this work are discussed, such as its use in the fabrication of prosthetics and orthotics, for masks used in cancer radiation treatment, and for the study of scoliosis.