File:GrahamScanDemo.gif
Summary
| Description |
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:
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- to remix – to adapt the work
- Under the following conditions:
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