Michael von Aichberger <[EMAIL PROTECTED]> wrote:
> Suppose you have two straight lines, defined by two points:
>
> Let's say
>
> point(x1, y1) and point(x2, y2) for line 1
>
> and
>
> point(x3, y3) and point(x4, y4) for line 2.
>
> What's the algorithm for calculating the point where these two lines
> intersect?
Hi Michael,
The mathematics are quite simple, but there are a number of special cases
(vertical and horizontal lines) that need to be taken into consideration.
You'll find below my handlers for this. You could use the following syntax:
line1 = lineEquation(point(x1, y1), point(x2, y2))
line2 = lineEquation(point(x3, y3), point(x4, y4))
intersection = lineCutsLine(line1, line2)
put intersection
Cheers,
James
----------------------------------------------------------------------------
on lineCutsLine(line1, line2) ----------------------------------------
-- ACTION: Finds the intersection points for two infinite lines
--
-- INPUT:
-- <line1> and <line2> must be property lists with one of the
-- following formats:
-- [#slope: <float>, #zeroX: <float>] --> y = ax + b
-- [#x: <float>] --> vertical line
-- See the lineEquation() handler for details.
--
-- RETURNS: point(<integer or float>, <integer or float>) if the
-- lines intersect, or #parallel if they do not.
--------------------------------------------------------------------
if voidP(line1[#slope]) then
-- line1 is vertical
if voidP(line2[#slope]) then
-- line2 is also vertical
return #parallel
else
-- Intersection with line2 will occur at line1.x
x = line1.x
y = line2.slope * x + line2.zeroX
return point(x, y)
end if
else if voidP(line2[#slope]) then
-- line2 is vertical: Swap line1 and line2 and try again
return lineIntersection(line2, line1)
else -- Both lines slope
slopeDifference = line1.slope - line2.slope
if slopeDifference = 0 then
return #parallel
end if
x = (line2.zeroX - line1.zeroX) / slopeDifference
y = line1.slope * x + line1.zeroX
return point(x, y)
end if
end lineCutsLine
on lineEquation(point1, point2) --------------------------------------
-- ACTION: Converts a 2D line defined by two points into a formula
-- corresponding to:
-- y = ax + b (or in Lingo : v = slope * h + zeroX).
--
-- The two points used to define the line may be considered to be
-- the end points of a segment, or one of them may be the end point
-- of a ray.
--
-- INPUT:
-- <point1> and <point2> should be point objects.
--
-- RETURNS: a list with one of the following formats::
--
-- [#slope: <float>, #zeroX: <float>, #x1: <float>, #x2: <float>]
-- [#x: <float>, #y1: <float>, #y2: <float>] -- vertical line
--
-- In the first version, #slope corresponds to "a", #zeroX
-- corresponds to "b" and #x1 and #x2 correspond to the values for
-- x at the ends of the line segment.
--
-- The second version is a special case for a vertical line.
-- #x corresponds to the constant value of x for all values of y.
-- #y1 and #y2 give the y values at the ends of the line segment.
--------------------------------------------------------------------
-- Check parameters
if ilk(point1) <> #point then
return #invalidPoint
else if ilk(point2) <> #point then
return #invalidPoint
else if point1 = point2 then
return #identicalPoints
end if
-- End of checking
h1 = point1.locH
v1 = point1.locV
h2 = point2.locH
v2 = point2.locV
deltaH = h1 - h2
if deltaH = 0 then -- The line is vertical
tEquation = [#x: h1]
tEquation[#y1] = v1
tEquation[#y2] = v2
else -- The line is horizontal or sloping
b = float((h1 * v2) - (h2 * v1)) / (h1 - h2)
if h1 = 0 then
a = (v2 - b) / h2
else
a = (v1 - b) / h1
end if
tEquation = [#slope: a, #zeroX: b]
tEquation[#x1] = h1
tEquation[#x2] = h2
end if
return tEquation
end lineEquation
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