| Summary: | 碩士 === 國立臺灣科技大學 === 資訊工程系 === 94 === Given a closed polygonal curve C with n points, the closed
polygonal approximation (CPA) problem is defined to find a closed
polygon P to approximate C under some error tolerance criteria.
Based on the local integral square error (LISE) and the curvature
constraint criteria, this paper presents a novel two-pass
O(Fn+mn^2)-time algorithm for solving the CPA problem where m
(<<n) denotes the minimal number of covering feasible segments for
one vertex and empirically the value of $m$ is rather small; F
(<<n^2) denotes the number of feasible approximate segments. The
first pass of our proposed algorithm can be performed in O(Fn+mn^2)
time under the given LISE; the second pass of our proposed algorithm
can be performed in O(n) time under the given curvature constraint
and the longest vertical distance consideration. Note that under the
same LISE criterion, the set of polygonal segments determined by the
first pass of our proposed CPA algorithm is minimal and is the same
as that obtained by the currently published CPA algorithm by {\sl
Chung et al.} whose algorithm takes O(n^3) time. Based on two real
closed curves for representing French and Italy, experimental results
demonstrate that our proposed two-pass CPA algorithm is faster and
more robust than the previous algorithm by Chung {\sl et al.} Based
on two real closed curves for representing a semicircle and a
chromosome, experimental results demonstrate that under the same
number of segments used, our proposed two-pass algorithm has a
better quality, but has a little execution-time degradation when
compared to the currently published CPA algorithm by {\sl Wu}.
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