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Determine if two triangles overlap: Difference between revisions
Determine if two triangles overlap (view source)
Revision as of 01:32, 16 December 2016
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(Created page with "Category:Geometry Category:Collision detection {{draft task}}Determining if two triangles in the same plane overlap is an important topic in collision detection. ;Tas...") |
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=={{header|Python}}==
<lang python>from __future__ import print_function
import numpy as np
def CheckTriWinding(tri, allowReversed):
trisq = np.ones((3,3))
trisq[:,0:2] = np.array(tri)
detTri = np.linalg.det(trisq)
if detTri < 0.0:
if allowReversed:
a = trisq[2,:].copy()
trisq[2,:] = trisq[1,:]
trisq[1,:] = a
else: raise ValueError("triangle has wrong winding direction")
return trisq
def TriTri2D(t1, t2, eps = 0.0, allowReversed = False, onBoundary = True):
#Trangles must be expressed anti-clockwise
t1s = CheckTriWinding(t1, allowReversed)
t2s = CheckTriWinding(t2, allowReversed)
if onBoundary:
#Points on the boundary are considered as colliding
chkEdge = lambda x: np.linalg.det(x) < eps
else:
#Points on the boundary are not considered as colliding
chkEdge = lambda x: np.linalg.det(x) <= eps
#For edge E of trangle 1,
for i in range(3):
edge = np.roll(t1s, i, axis=0)[:2,:]
#Check all points of trangle 2 lay on the external side of the edge E. If
#they do, the triangles do not collide.
if (chkEdge(np.vstack((edge, t2s[0]))) and
chkEdge(np.vstack((edge, t2s[1]))) and
chkEdge(np.vstack((edge, t2s[2])))):
return False
#For edge E of trangle 2,
for i in range(3):
edge = np.roll(t2s, i, axis=0)[:2,:]
#Check all points of trangle 1 lay on the external side of the edge E. If
#they do, the triangles do not collide.
if (chkEdge(np.vstack((edge, t1s[0]))) and
chkEdge(np.vstack((edge, t1s[1]))) and
chkEdge(np.vstack((edge, t1s[2])))):
return False
#The triangles collide
return True
if __name__=="__main__":
t1 = [[0,0],[5,0],[0,5]]
t2 = [[0,0],[5,0],[0,6]]
print (TriTri2D(t1, t2), True)
t1 = [[0,0],[0,5],[5,0]]
t2 = [[0,0],[0,6],[5,0]]
print (TriTri2D(t1, t2, allowReversed = True), True)
t1 = [[0,0],[5,0],[0,5]]
t2 = [[-10,0],[-5,0],[-1,6]]
print (TriTri2D(t1, t2), False)
t1 = [[0,0],[5,0],[2.5,5]]
t2 = [[0,4],[2.5,-1],[5,4]]
print (TriTri2D(t1, t2), True)
t1 = [[0,0],[1,1],[0,2]]
t2 = [[2,1],[3,0],[3,2]]
print (TriTri2D(t1, t2), False)
t1 = [[0,0],[1,1],[0,2]]
t2 = [[2,1],[3,-2],[3,4]]
print (TriTri2D(t1, t2), False)
#Barely touching
t1 = [[0,0],[1,0],[0,1]]
t2 = [[1,0],[2,0],[1,1]]
print (TriTri2D(t1, t2, onBoundary = True), True)
#Barely touching
t1 = [[0,0],[1,0],[0,1]]
t2 = [[1,0],[2,0],[1,1]]
print (TriTri2D(t1, t2, onBoundary = False), False)</lang>
{{out}}
<pre>True True
True True
False False
True True
False False
False False
True True
False False</pre>
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