GrahamScanDemo.gif
Summary
Description GrahamScanDemo.gif |
English:
A demo of Graham's Scan, auto-generated by a Python program. The red lines connect the points in the stack. The blue line connects the observed point with the top of stack.
|
Date | |
Source | Own work |
Author | Shiyu Ji |
Python 3 Code
'''
Convex Hull Demo (SVG) for Graham's Scan.
Firstly use this code to generate SVG frames.
Then transform to bitmaps and convert to GIF.
'''
# range size
N = 300
margin = 50
def saveToSVG(nFrames, points, firmed, trying):
f = open('demo_'+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 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,N) for _ in [0, 1]]
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
nframe = 0;
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]]
saveToSVG(nframe, points, stack, [stack[-1], points[2]])
nframe += 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
if i<n:
saveToSVG(nframe, points, stack, [stack[-1], points[i]])
else:
saveToSVG(nframe, points, stack+[points[0]], [])
nframe += 1
return stack
# test 30 points temporarily
n = 30
pts = generatePoints(n)
graham(n, pts)
Licensing
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.