File:ChanAlgDemo.gif
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Size of this preview: 799 × 282 pixels. Other resolutions: 320 × 113 pixels | 918 × 324 pixels.
Original file (918 × 324 pixels, file size: 1.06 MB, MIME type: image/gif, looped, 61 frames, 49 s)
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Summary[edit]
DescriptionChanAlgDemo.gif |
English: A demo of Chan's algorithm to find a 2D convex hull. |
Date | |
Source | Own work |
Author | Shiyu Ji |
Python 3 Code[edit]
'''
Convex Hull Demo (SVG) for Chan's algorithm.
Firstly use this code to generate SVG frames.
Then transform to bitmaps and convert to GIF.
'''
# range size
N, M = 300, 900
margin = 20
def saveToSVG(nFrames, points, partitions, firmed, trying):
f = open('demo_'+'0'*(3-len(str(nFrames)))+str(nFrames)+'.svg', 'w')
f.write("<svg xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n")
for p in points:
f.write("<circle cx=\"" +str(p[0]+margin)+ "\" cy=\""+ str(N-p[1]+margin) +"\" r=\"5\" fill=\"white\" stroke=\"black\"/>\n")
for par in partitions:
for i in range(len(par)-1):
f.write("<line x1=\"" +str(par[i][0]+margin)+ "\" y1=\""+ str(N-par[i][1]+margin) +"\" x2=\"" + str(par[i+1][0]+margin) + "\" y2=\"" + str(N-par[i+1][1]+margin) + "\" stroke=\"grey\" stroke-width=\"3\"/>\n")
f.write("<line x1=\"" +str(par[-1][0]+margin)+ "\" y1=\""+ str(N-par[-1][1]+margin) +"\" x2=\"" + str(par[0][0]+margin) + "\" y2=\"" + str(N-par[0][1]+margin) + "\" stroke=\"grey\" stroke-width=\"3\"/>\n")
for i in range(len(firmed)-1):
f.write("<line x1=\"" +str(firmed[i][0]+margin)+ "\" y1=\""+ str(N-firmed[i][1]+margin) +"\" x2=\"" + str(firmed[i+1][0]+margin) + "\" y2=\"" + str(N-firmed[i+1][1]+margin) + "\" stroke=\"red\" stroke-width=\"5\"/>\n")
for i in range(len(trying)-1):
f.write("<line x1=\"" +str(trying[i][0]+margin)+ "\" y1=\""+ str(N-trying[i][1]+margin) +"\" x2=\"" + str(trying[i+1][0]+margin) + "\" y2=\"" + str(N-trying[i+1][1]+margin) + "\" stroke=\"blue\" stroke-width=\"5\"/>\n")
f.write("</svg>\n")
f.close()
def generatePoints(n):
import random as r
r.seed(100)
res = []
for i in range(n):
pt = [r.randint(0,M), r.randint(0,N)]
if [pt] not in res:
res += [pt]
return res
def norm(x, y):
return (x*x+y*y)**.5
def dotProductNormed(x1, y1, x2, y2):
return (x1*x2+y1*y2)/norm(x1, y1)/norm(x2, y2)
def cross(x1, y1, x2, y2):
return x1*y2 - x2*y1
def graham(n, points):
if n<3: return
points.sort(key = lambda x: x[1])
first = points[0]
rest = points[1:]
rest.sort(key = lambda x: -dotProductNormed(x[0]-points[0][0], x[1]-points[0][1], 1, 0))
points = [first] + rest
stack = [points[0], points[1]]
i=2
while i<n:
x0, y0 = stack[-2][0], stack[-2][1]
x1, y1 = stack[-1][0], stack[-1][1]
x2, y2 = points[i][0], points[i][1]
if cross(x1-x0, y1-y0, x2-x0, y2-y0)<0:
stack.pop()
else:
stack += [points[i]]
i+=1
return stack
# TODO: may be improved.
def tangentPoint(t, hull):
n = len(hull)
if t in hull:
for i in range(len(hull)):
if hull[i] == t:
return hull[(i+1)%n]
if cross(hull[0][0]-t[0], hull[0][1]-t[1], hull[-1][0]-t[0], hull[-1][1]-t[1])>=0 and cross(hull[1][0]-t[0], hull[1][1]-t[1], hull[0][0]-t[0], hull[0][1]-t[1])<=0:
return hull[0]
if cross(hull[0][0]-t[0], hull[0][1]-t[1], hull[-1][0]-t[0], hull[-1][1]-t[1])<=0 and cross(hull[-1][0]-t[0], hull[-1][1]-t[1], hull[-2][0]-t[0], hull[-2][1]-t[1])>=0:
return hull[-1]
low, high = 1, n-2
while low+1<high:
i = low + (high-low)//2
if cross(hull[i][0]-t[0], hull[i][1]-t[1], hull[i-1][0]-t[0], hull[i-1][1]-t[1])>=0 and cross(hull[i+1][0]-t[0], hull[i+1][1]-t[1], hull[i][0]-t[0], hull[i][1]-t[1])<=0:
return hull[i]
if cross(hull[i][0]-t[0], hull[i][1]-t[1], hull[i-1][0]-t[0], hull[i-1][1]-t[1])>=0 and cross(hull[i+1][0]-t[0], hull[i+1][1]-t[1], hull[i][0]-t[0], hull[i][1]-t[1])>=0:
if cross(hull[i][0]-t[0], hull[i][1]-t[1], hull[low][0]-t[0], hull[low][1]-t[1])<=0:
if cross(hull[high+1][0]-t[0], hull[high+1][1]-t[1], hull[high][0]-t[0], hull[high][1]-t[1])>=0 and cross(hull[high][0]-t[0], hull[high][1]-t[1], hull[high-1][0]-t[0], hull[high-1][1]-t[1])>=0:
high = i
else: low = i
else: low = i
else:
if cross(hull[i][0]-t[0], hull[i][1]-t[1], hull[low][0]-t[0], hull[low][1]-t[1])>=0:
if cross(hull[low+1][0]-t[0], hull[low+1][1]-t[1], hull[low][0]-t[0], hull[low][1]-t[1])<=0 and cross(hull[low][0]-t[0], hull[low][1]-t[1], hull[low-1][0]-t[0], hull[low-1][1]-t[1])<=0:
low = i
else: high = i
else: high = i
for i in range(n):
j = (low+i)%n
if cross(hull[j][0]-t[0], hull[j][1]-t[1], hull[j-1][0]-t[0], hull[j-1][1]-t[1])>=0 and cross(hull[j+1][0]-t[0], hull[j+1][1]-t[1], hull[j][0]-t[0], hull[j][1]-t[1])<=0:
return hull[j]
def javis(s, hulls):
n = len(hulls)
t = s
res = [s]
nframe = 1
while True:
next_pt = t
for hull in hulls:
p = tangentPoint(t, hull)
saveToSVG(nframe, pts, hulls, res, [res[-1], p])
nframe+=1
if next_pt == t or cross(p[0]-t[0], p[1]-t[1], next_pt[0]-t[0], next_pt[1]-t[1])>0 :
next_pt = p
if next_pt == s:
res += [s]
break
else:
t = next_pt
res += [next_pt]
saveToSVG(nframe, pts, hulls, res, [])
nframe+=1
saveToSVG(nframe, pts, hulls, res, [])
return res
# test 120 points temporarily
n = 120
pts = generatePoints(n)
pts.sort(key = lambda x: x[0])
nPartition = 4
hulls = []
for i in range(nPartition):
hulls.append(graham(n//nPartition, pts[i*n//nPartition:(i+1)*n//nPartition]))
saveToSVG(0, pts, hulls, [], [])
start = hulls[0][0]
for hull in hulls:
for pt in hull:
if pt[1]<start[1] or (pt[1]==start[1] and pt[0] < start[0]):
start = pt
javis(start, hulls)
Licensing[edit]
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 12:52, 24 December 2016 | 918 × 324 (1.06 MB) | Shiyu Ji (talk | contribs) | User created page with UploadWizard |
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