Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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max edge distance
Simplification
key
Figure 4-1: A sample process for the Douglas-Peucker algorithm
The Douglas-Peucker algorithm is for the selection of representative points to simplify a curve
composed of line segments. It uses a point-to-edge distance tolerance. The algorithm starts with a crude
simplification that is the single edge joining the first and last vertices of the original polyline. It then
computes the perpendicular distance of all intermediate vertices to that edge. The vertex that is furthest
away from that edge, and that has a computed distance that is larger than a specified tolerance, will be
marked as a key and added to the simplification. This process will recurse for each edge in the current
simplification until all vertices of the original polyline are within tolerance of the simplification results.
This process is illustrated in Figure 4-1.
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Transcribed Image Text:max edge distance Simplification key Figure 4-1: A sample process for the Douglas-Peucker algorithm The Douglas-Peucker algorithm is for the selection of representative points to simplify a curve composed of line segments. It uses a point-to-edge distance tolerance. The algorithm starts with a crude simplification that is the single edge joining the first and last vertices of the original polyline. It then computes the perpendicular distance of all intermediate vertices to that edge. The vertex that is furthest away from that edge, and that has a computed distance that is larger than a specified tolerance, will be marked as a key and added to the simplification. This process will recurse for each edge in the current simplification until all vertices of the original polyline are within tolerance of the simplification results. This process is illustrated in Figure 4-1.
(4) The following program is a non-recursive solution. Fill out the numbered blanks in the program
and highlight your answers with the corresponding numbers.
# Assume all points are not selected at the beginning
def DouglasPeuker_NR(points, threshold):
stack = Stack () # initialize a stack
# push a tuple indicating the index of the starting and ending point
stack.push((0, _®_))
while not
e = stack.pop()
if
O_:
points[e[0]].selected
= True
points[e[1]]. selected = True
else:
maxIdx, maxDist = farthestPoint (points[_@_:,
6_])
maxIdx += e[0]
if maxDist >= threshold:
stack.push((_®_, maxIdx))
stack.push((_O_, e[1]))
else:
points[e[0]].selected = True
points[e[1]].selected
= True
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Transcribed Image Text:(4) The following program is a non-recursive solution. Fill out the numbered blanks in the program and highlight your answers with the corresponding numbers. # Assume all points are not selected at the beginning def DouglasPeuker_NR(points, threshold): stack = Stack () # initialize a stack # push a tuple indicating the index of the starting and ending point stack.push((0, _®_)) while not e = stack.pop() if O_: points[e[0]].selected = True points[e[1]]. selected = True else: maxIdx, maxDist = farthestPoint (points[_@_:, 6_]) maxIdx += e[0] if maxDist >= threshold: stack.push((_®_, maxIdx)) stack.push((_O_, e[1])) else: points[e[0]].selected = True points[e[1]].selected = True
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