Abstract
We present a theoretical overview of signed distance functions and analyze how this representation changes when applying an offset transformation. First, we analyze the properties of signed distance and the sets they describe.
Second, we introduce our main theorem regarding the distance to an offset set in (X,||.||) strictly normed Banach spaces. An offset set of D in X is the set of points equidistant to D. We show when such a set can be represented by f(x)-c=0, where c denotes the radius of the offset. Finally, we explain these results for applications that offset signed distance functions.
Subject
Computer Vision and Pattern Recognition,Software,Computer Science (miscellaneous),Electrical and Electronic Engineering,Information Systems and Management,Management Science and Operations Research,Theoretical Computer Science
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