Abstract:
The orientation of a closed-curve is determined by first constructing a new convex polygon. By using the orientation of the closed curve the convexity-concavity of vertices and arcs are identified. Finally,the convexity-concavity of the closed curve is detected.The presented algorithm is robust and highly efficient.The complexity of its computing time reaches
O(n) and it needs only 15
n+33
k+25 comparisons,12
n-6
k+14 multiplications or divisions,10
n+16
k+21additions and subtractions,2 sine and cosine,
k square roots at most,where
n is the number of vertices of the closed curve including the centers of arcs and
k is the number of arcs.
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