凸包算法作为计算几何的基础和核心问题足以引起重视.
这里给出Jarvis步进算法的Python实现.
测试环境是Ubuntu Python3.4
依赖了numpy(数学运算) matplotlib(绘图) logging(日志) unittest2(测试) 如果没有则需要安装
程序给出了to-left-test lowest-then-leftmost jarvis三个工具的实现
算法的基本思想就是:
- 找到LTL(lowest-then-leftmost)点,这个点一定是一个EP(extreme point)
- 以LTL点为起点,遍历所有点,利用
to-left-test找到连线最靠右的那条线的端点. - 将端点记为EP,并以之为起点重复上步骤.
- 直到端点与最初起点相同,结束算法返回EE(extreme edge)数列.
# coding=utf-8
'''
Created on Jan 13, 2016
@author: yangjie
'''
"""
def logger
"""
import logging
from matplotlib import pyplot
import numpy
import random
import unittest2
formatStr = "%(asctime)s [%(filename)s line %(lineno)d] [%(name)s %(levelname)s] %(message)s"
fmt = logging.Formatter(formatStr)
streamHandler = logging.StreamHandler()
streamHandler.setFormatter(fmt)
CHLogger = logging.getLogger("CHLogger")
CHLogger.setLevel(logging.INFO)
CHLogger.addHandler(streamHandler)
class PointBasket():
"""
container of points and edges
"""
def __init__(self):
self.pointContainer = []
self.edgeContainer = []
def appendPoint(self, point):
"""
add a point to container
"""
try:
self.pointContainer.append(point)
CHLogger.info("append point %f,%f" % (point.posX, point.posY))
except Exception as error:
CHLogger.error(error)
def appendEdge(self, pointStart, pointEnd):
"""
add a edge to container, extreme edge.
"""
try:
self.edgeContainer.append((pointStart, pointEnd))
CHLogger.info("append edge (%f,%f)(%f,%f)" %
(pointStart.posX, pointStart.posY, pointEnd.posX, pointEnd.posY))
except Exception as error:
CHLogger.error(error)
def getPointPos(self):
"""
return a dic of position x and position y of points
"""
try:
pos = {"posX": [], "posY": []}
for point in self.pointContainer:
pos["posX"].append(point.posX)
pos["posY"].append(point.posY)
CHLogger.info("get point pos")
return pos
except Exception as error:
CHLogger.error(error)
return None
def getEdgePos(self):
"""
return a dic of position x and position y of edges
"""
try:
pos = {"posX": [], "posY": []}
for edge in self.edgeContainer:
pos["posX"].append(edge[0].posX)
pos["posX"].append(edge[1].posX)
pos["posY"].append(edge[0].posY)
pos["posY"].append(edge[1].posY)
CHLogger.info("get edge pos nums:%d" % len(self.edgeContainer))
return pos
except Exception as error:
CHLogger.error(error)
return None
def jarvis(self):
"""
to find the convex hull with jarvis method
"""
if len(self.pointContainer) < 3:
CHLogger.warning("not enough point in the set")
return None, None
try:
pointZero = self.LTLTest()
pointStart = pointZero
"""
find the TLT point as the first extreme point noted as pointZero
and start with pointZero
"""
while True:
pointEndTem = pointZero
for pointTest in self.pointContainer:
"""
search for a point that lies on the left of the tem line
"""
if pointTest == pointEndTem or pointTest == pointStart:
continue
else:
flag = self.toLeftTest(
pointStart, pointEndTem, pointTest)
"""
to left test
"""
if flag:
pass
else:
pointEndTem = pointTest
pointEndTem.extreme = True
self.appendEdge(pointStart, pointEndTem)
pointStart = pointEndTem
"""
find a EE and add it to edge container and set the EP as next turn start point
"""
if pointZero == pointEndTem:
"""
leave when the next extreme point is the LTL point
"""
break
else:
continue
CHLogger.info("jarvis")
edgePos = self.getEdgePos()
return edgePos
except Exception as error:
CHLogger.error(error)
def toLeftTest(self, pointStart, pointEnd, pointTest):
"""
to left test.
to calculate the det of area array
"""
try:
areaArray = numpy.array([[pointStart.posX, pointStart.posY, 1],
[pointEnd.posX, pointEnd.posY, 1],
[pointTest.posX, pointTest.posY, 1]])
signedArea = numpy.linalg.det(areaArray)
"""
signed area>0 means test point lies on the left
"""
if signedArea > 0:
flag = True
else:
flag = False
CHLogger.info("to left test (%f,%f)(%f,%f)(%f,%f) %s" % (
pointStart.posX, pointStart.posY, pointEnd.posX, pointEnd.posY, pointTest.posX, pointTest.posY, flag))
return flag
except Exception as error:
CHLogger.error(error)
def LTLTest(self):
"""
LTL(lowest-then-leftmost) test
"""
try:
pointLTL = self.pointContainer[0]
for pointTest in self.pointContainer:
if pointTest.posY < pointLTL.posY:
pointLTL = pointTest
elif pointTest.posY == pointLTL.posY:
if pointTest.posX < pointLTL.posX:
pointLTL = pointTest
else:
pass
else:
continue
CHLogger.info("find the LTL poing")
return pointLTL
except Exception as error:
CHLogger.error(error)
return None
class Point():
"""
class of point
"""
def __init__(self, posX, posY, extreme=False):
self.posX = posX
self.posY = posY
self.extreme = extreme
class Edge():
"""
class of edge
"""
def __init__(self, pointStart, pointEnd, extreme=False):
self.pointStart = pointStart
self.pointEnd = pointEnd
self.extreme = extreme
if __name__ == "__main__":
class MainTest(unittest2.TestCase):
"""
test case
"""
def drawPoint(self):
pos = self.pointList.getPointPos()
pyplot.plot(pos["posX"], pos["posY"], "o")
def setUp(self):
self.pointList = PointBasket()
for index in range(10): # @UnusedVariable
self.pointList.appendPoint(
self.pointList.Point(random.uniform(0, 10), random.uniform(0, 10)))
def tearDown(self):
pass
def test_drawPoint(self):
pos = self.pointList.getPointPos()
pyplot.plot(pos["posX"], pos["posY"], "*")
pyplot.title("draw point")
pyplot.show()
def test_drawEdge(self):
self.pointList.appendEdge(
self.pointList.pointContainer[0], self.pointList.pointContainer[1])
pos = self.pointList.getEdgePos()
self.drawPoint()
pyplot.plot(pos["posX"], pos["posY"])
pyplot.title("draw edge")
pyplot.show()
def test_LTL(self):
pointLTL = self.pointList.LTLTest()
self.drawPoint()
pyplot.annotate("LTL", xy=(pointLTL.posX, pointLTL.posY))
pyplot.title("LTL test")
pyplot.show()
def test_toLeft(self):
self.drawPoint()
li = self.pointList.pointContainer[:3]
flag = self.pointList.toLeftTest(li[0], li[1], li[2])
pyplot.plot(
[point.posX for point in li], [point.posY for point in li], "*")
pyplot.plot(
[point.posX for point in li[:2]], [point.posY for point in li[:2]])
pyplot.annotate("start", xy=(li[0].posX, li[0].posY))
pyplot.annotate("end", xy=(li[1].posX, li[1].posY))
pyplot.annotate(flag, xy=(li[2].posX, li[2].posY))
pyplot.title("to left test")
pyplot.show()
def test_jarvis(self):
self.drawPoint()
pos = self.pointList.jarvis()
pyplot.plot(pos["posX"], pos["posY"])
pyplot.title("jarvis test")
pyplot.show()
unittest2.main()