Global Topological Changes of Offset Domains

Offsetting is used in a range of CAD/CAM applications, such as tool path generation for pocket machining. In many applications, topological changes caused by offsetting are undesirable, and should be prevented, or detected. We present methods based on the medial axis transform to determine when a topological change may occur under an inward offset, an outward offset, or a combination of both, for a domain bounded by Jordan curves. In other applications, such as morphological image processing, a combination of outward and inward offsets are used to deliberately change the topology of a domain, e.g. to close small gaps in a region. Such an operation may fail to change the topology if certain conditions are not satisfied. We show how to detect such cases, and how to modify the domain's medial axis transform to achieve the intended topological change.