Rosetta Code task: Find the intersection of two lines

[David Drake]

I created the code below for the Rosetta Code task "Find the intersection of two lines" (found here: rosettacode.org/wiki/Find_the_intersection_of_two_lines).

The task states: Finding the intersection of two lines that are in the same plane is an important topic in collision detection. Find the point of intersection of two lines in 2D.


The 1st line passes though (4,0) and (6,10) .

The 2nd line passes though (0,3) and (10,7) .




'Find the intersection of lines
'y1=mx1+b1
'y2=mx2+b2
'calulate b1,b2
'calculate m1,m2

on error goto [errorHandler] 'parallel lines

x11=4:y11=0 'line 1, point 1
x12=6:y12=10 'line 1, point 2
x21=0:y21=3 'line 2, point 1
x22=10:y22=7 'line 2, point 2

m1=(y12-y11)/(x12-x11) ' calculate Line 1 slope
m2=(y22-y21)/(x22-x21)  ' calculate Line 2 slope
b1=y11-m1*x11 ' calculate Line 1 intercept
b2=y21-m2*x21 'calculate Line 2 intercept

print "Find intersecting coordinate for these lines: ";
print
print "Line 1: y = ";m1;"x + ";b1
print "Line 2: y = ";m2;"x + ";b2

'Note error handler will catch if parallel slopes lead to division by zero

xint = (b2-b1)/(m1-m2) ' calculate value of intersecting x coordinate
yint = m1*xint+b1 ' calculate value of intersecting y coordinate
print
print "Intersecting coordinate is ";xint;", ";yint
print

end

[errorHandler]
print "An error has occurred."
if Err = 11 then print "Division by zero.  Likely the lines are parallel."
end



Looking forward to seeing your corrections and suggestions.

[tsh73]

As a sub, along c# example
'Find the intersection of lines
'along c# example
data 4,0, 6,10,  0,3, 10, 7
data 0,0, 1,1,   1,2, 4,5

for i = 1 to 2
read s1x, s1y, e1x, e1y     'first line start, end
read s2x, s2y, e2x, e2y     'second line
print "First line is  (";s1x;","; s1y;")-("; e1x;","; e1y;")"
print "second line is (";s2x;","; s2y;")-("; e2x;","; e2y;")"

call findIntersection  s1x, s1y, e1x, e1y, s2x, s2y, e2x, e2y, x, y, isParallel
if  isParallel then
   print "is parallel"
else
   print "intersects at (";x;","; y;")"
end if

print
next

end

sub findIntersection  s1x, s1y, e1x, e1y, s2x, s2y, e2x, e2y, byRef x,  byRef y, byRef isParallel
   a1 = e1y - s1y
   b1 = s1x - e1x
   c1 = a1 * s1x + b1 * s1y

   a2 = e2y - s2y
   b2 = s2x - e2x
   c2 = a2 * s2x + b2 * s2y

   delta = a1 * b2 - a2 * b1
   'if lines are parallel
   if delta =0 then isParallel=1: exit sub
   x = (b2 * c1 - b1 * c2) / delta
   y = (a1 * c2 - a2 * c1) / delta
end sub

results
First line is  (4,0)-(6,10)
second line is (0,3)-(10,7)
intersects at (5,5)

First line is  (0,0)-(1,1)
second line is (1,2)-(4,5)
is parallel


[tsh73]

Also - it is not required but really could gеt handy - how to tell if intersection point actually on segment(s) provided
'Find the intersection of lines
'along c# example
data 4,0, 6,10,  0,3, 10,7
data 4,0, 6,10,  0,3, 4,5
data 4,0, 5,4,   0,3, 10,7
data 4,0, 5,4,   0,3, 4,5
data 0,0, 1,1,   1,2, 4,5

for i = 1 to 5
read s1x, s1y, e1x, e1y     'first line start, end
read s2x, s2y, e2x, e2y     'second line
print "First line is  (";s1x;","; s1y;")-("; e1x;","; e1y;")"
print "second line is (";s2x;","; s2y;")-("; e2x;","; e2y;")"

call findIntersection  s1x, s1y, e1x, e1y, s2x, s2y, e2x, e2y, x, y, isParallel
if  isParallel then
   print "is parallel"
else
   print "intersects at (";x;","; y;")"
   if (x-s1x)*(x-e1x)<0 and (y-s1y)*(y-e1y)<0 then print "on the 1st segment"
   if (x-s2x)*(x-e2x)<0 and (y-s2y)*(y-e2y)<0 then print "on the 2nd segment"
end if

print
next

end

sub findIntersection  s1x, s1y, e1x, e1y, s2x, s2y, e2x, e2y, byRef x,  byRef y, byRef isParallel
   a1 = e1y - s1y
   b1 = s1x - e1x
   c1 = a1 * s1x + b1 * s1y

   a2 = e2y - s2y
   b2 = s2x - e2x
   c2 = a2 * s2x + b2 * s2y

   delta = a1 * b2 - a2 * b1
   'if lines are parallel
   if delta =0 then isParallel=1: exit sub
   x = (b2 * c1 - b1 * c2) / delta
   y = (a1 * c2 - a2 * c1) / delta
end sub

result
First line is  (4,0)-(6,10)
second line is (0,3)-(10,7)
intersects at (5,5)
on the 1st segment
on the 2nd segment

First line is  (4,0)-(6,10)
second line is (0,3)-(4,5)
intersects at (5.11111111,5.55555556)
on the 1st segment

First line is  (4,0)-(5,4)
second line is (0,3)-(10,7)
intersects at (5.27777778,5.11111111)
on the 2nd segment

First line is  (4,0)-(5,4)
second line is (0,3)-(4,5)
intersects at (5.42857143,5.71428571)

First line is  (0,0)-(1,1)
second line is (1,2)-(4,5)
is parallel


[David Drake]

Okay, team, which version should be posted to Rosetta Code? I like all three (the first is, I think easier to understand, the second and third have more features).