Abstract
A method for representing knots by means of a chain code is presented. Knots which are digitalized and represented by the orthogonal direction change chain code are called discrete knots. Discrete knots are composed of constant straight-line segments using only orthogonal directions. The chain elements represent the orthogonal direction changes of the constant straight-line segments of the discrete knot. There are only five possible orthogonal direction changes for representing any discrete knot. Thus, this chain code only considers relatives directions changes, which allows us to have a unique knot descriptor invariant under translation and rotation. Also, this knot descriptor may be starting point normalized. Finally, this unique knot descriptor produces a numerical string of finite length over a finite alphabet, allows us the usage of grammatical techniques for discrete-knot analysis. Thus, we present some prime discrete knot detection examples within composite discrete knots.
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