Lets say that i want to know where 2 lines intersect (Resulting in Vector3).
The lines are just two Vector3 position (start, end).
Ignore Y axis.
How to i should calculate that in a script?
This Thead dont provided script examples and I dont understand it.
So, each line has two Vector3 positions (the start and end) associated with it? Making for 4 total Vector3 positions?
I expected this to be a simple vector problem, but I actually couldn’t think of anything myself. Here’s a video explaining it and it links to the code in the description. You’ll have to translate it into lua. https://youtu.be/wCR48FqkI4w
EDIT: @Bakkikins Yeah, that’s my impression of what he said.
Here’s the code that calculates it, assuming my previous comment’s assumption is true.
function intersection_point(line_1_start, line_1_end, line_2_start, line_2_end)
local line_1_m = (line_1_end.Z - line_1_start.Z) / (line_1_end.X - line_1_start.X)
local line_2_m = (line_2_end.Z - line_2_start.Z) / (line_2_end.X - line_2_start.X)
local line_1_b = line_1_start.Z - (line_1_m * line_1_start.X)
local line_2_b = line_2_start.Z - (line_2_m * line_2_start.X)
local intersect_x = (line_2_b - line_1_b) / (line_1_m - line_2_m)
local intersect_z = (line_1_m * intersect_x) + line_1_b
return Vector3.new(intersect_x, line_1_start.Y, intersect_z)
end
Explaining how it works would involve me explaining quite a bit of algebra and calculus, and would take way too long for something this simple. I’ve tested it and, to my knowledge, it should work.
EDIT: Here’s some lines to test it out with (these are the ones I actually used). Pick any x and y values on either side of the point where they intersect for each line (these will be your Vector3 x and z values) and plug it in, and it should work.
The solution given is not 100% accurate what if a there is a cross point on a vertical line? Vertical lines have no slope. This modified code will include all cross points of any lines.
Note This code was compiled from typescript to lua
local function intersection_point(startPoint1, endPoint1, startPoint2, endPoint2)
local point_1_x1 = startPoint1.X
local point_1_y1 = startPoint1.Z
local point_1_x2 = endPoint1.X
local point_1_y2 = endPoint1.Z
local point_2_x1 = startPoint2.X
local point_2_y1 = startPoint2.Z
local point_2_x2 = endPoint2.X
local point_2_y2 = endPoint2.Z
-- m = (y1 - y2) / (x1 - x2)
local line_1_m = 0
local line_2_m = 0
-- b = -(mx1) + y1
local line_1_b = 0
local line_2_b = 0
local intersect_x = 0
local intersect_z = 0
local isLineOneVertical = ((point_1_x1 / point_1_x2) % 2) == 1
local isLineTwoVertical = ((point_2_x1 / point_2_x2) % 2) == 1
if isLineOneVertical and isLineTwoVertical then
error(error("There is no cross point"))
end
-- Line 1
if isLineOneVertical then
line_2_m = (point_2_y1 - point_2_y2) / (point_2_x1 - point_2_x2)
line_2_b = -(line_2_m * point_2_x1) + point_2_y1
intersect_x = point_1_x1
intersect_z = (line_2_m * intersect_x) + line_2_b
-- Line 2
elseif isLineTwoVertical then
line_1_m = (point_1_y1 - point_1_y2) / (point_1_x1 - point_1_x2)
line_1_b = -(line_1_m * point_1_x1) + point_1_y1
intersect_x = point_2_x1
intersect_z = (line_1_m * intersect_x) + line_1_b
else
line_1_m = (point_1_y1 - point_1_y2) / (point_1_x1 - point_1_x2)
line_2_m = (point_2_y1 - point_2_y2) / (point_2_x1 - point_2_x2)
if line_1_m == line_2_m then
error(error("There is no cross point"))
end
line_1_b = -(line_1_m * point_1_x1) + point_1_y1
line_2_b = -(line_2_m * point_2_x1) + point_2_y1
intersect_x = (line_2_b - line_1_b) / (line_1_m - line_2_m)
intersect_z = (line_1_m * intersect_x) + line_1_b
end
return Vector3.new(intersect_x, point_1_y1, intersect_z)
endSorry to bump this, but this also doesn’t work on all line intersections 
Removing these error messages makes it work, but it’ll sometimes get intersections that don’t exist
Upon further testing, this seems to extrapolate lines, and thus creates a point of intersection
Because of
I thought it’d only get from start-end of lines
That’s what the errors were for. You should be able to switch them out with return to return nothing when there’s no cross point.
That’s what I ended up doing, but the intersections are still detected and created
local function GetLineIntersection(startPoint1, endPoint1, startPoint2, endPoint2)
local point_1_x1 = startPoint1.X
local point_1_y1 = startPoint1.Z
local point_1_x2 = endPoint1.X
local point_1_y2 = endPoint1.Z
local point_2_x1 = startPoint2.X
local point_2_y1 = startPoint2.Z
local point_2_x2 = endPoint2.X
local point_2_y2 = endPoint2.Z
-- m = (y1 - y2) / (x1 - x2)
local line_1_m = 0
local line_2_m = 0
-- b = -(mx1) + y1
local line_1_b = 0
local line_2_b = 0
local intersect_x = 0
local intersect_z = 0
local isLineOneVertical = ((point_1_x1 / point_1_x2) % 2) == 1
local isLineTwoVertical = ((point_2_x1 / point_2_x2) % 2) == 1
if isLineOneVertical and isLineTwoVertical then
print("error")
return
--error("There is no cross point")
end
-- Line 1
if isLineOneVertical then
print(1)
line_2_m = (point_2_y1 - point_2_y2) / (point_2_x1 - point_2_x2)
line_2_b = -(line_2_m * point_2_x1) + point_2_y1
intersect_x = point_1_x1
intersect_z = (line_2_m * intersect_x) + line_2_b
-- Line 2
elseif isLineTwoVertical then
print(2)
line_1_m = (point_1_y1 - point_1_y2) / (point_1_x1 - point_1_x2)
line_1_b = -(line_1_m * point_1_x1) + point_1_y1
intersect_x = point_2_x1
intersect_z = (line_1_m * intersect_x) + line_1_b
else
print(3)
line_1_m = (point_1_y1 - point_1_y2) / (point_1_x1 - point_1_x2)
line_2_m = (point_2_y1 - point_2_y2) / (point_2_x1 - point_2_x2)
print(line_1_m, line_2_m)
if line_1_m == line_2_m then
print("error")
return
--error("There is no cross point")
end
line_1_b = -(line_1_m * point_1_x1) + point_1_y1
line_2_b = -(line_2_m * point_2_x1) + point_2_y1
intersect_x = (line_2_b - line_1_b) / (line_1_m - line_2_m)
intersect_z = (line_1_m * intersect_x) + line_1_b
end
print(startPoint1, endPoint1, startPoint2, endPoint2)
print(Vector3.new(intersect_x, startPoint1.Y, intersect_z))
return Vector3.new(intersect_x, startPoint1.Y, intersect_z)
end
20:23:35.511 3 - Server - Script:47
20:23:35.511 -0 -1 - Server - Script:50
20:23:35.512 -52, 6, -19 3, 6, -19 -12, 6, -64 -47, 6, -29 - Server - Script:62
20:23:35.512 -57, 6, -19 - Server - Script:63
Only errors when the 2 lines are parralel to each other
I’m not too sure what’s going on in that function so I can’t really modify it, but I came up with this typed function which should be what you’re looking for:
function FindLineIntersection2D(l1p1: Vector2, l1p2: Vector2, l2p1: Vector2, l2p2: Vector2, l1Seg: boolean?, l2Seg: boolean?): Vector2?
local a1: number = l1p2.Y - l1p1.Y
local b1: number = l1p1.X - l1p2.X
local a2: number = l2p2.Y - l2p1.Y
local b2: number = l2p1.X - l2p2.X
local c1: number = a1 * l1p1.X + b1 * l1p1.Y
local c2: number = a2 * l2p1.X + b2 * l2p1.Y
local determinant: number = a1 * b2 - a2 * b1
if (determinant == 0) then
return -- lines are parallel
end
local x: number = (b2 * c1 - b1 * c2) / determinant
local y: number = (a1 * c2 - a2 * c1) / determinant
if (l1Seg or l2Seg) then
if l1Seg and not (math.min(l1p1.X, l1p2.X) <= x
and x <= math.max(l1p1.X, l1p2.X)
and math.min(l1p1.Y, l1p2.Y) <= y
and y <= math.max(l1p1.Y, l1p2.Y))
or l2Seg and not (math.min(l2p1.X, l2p2.X) <= x
and x <= math.max(l2p1.X, l2p2.X)
and math.min(l2p1.Y, l2p2.Y) <= y
and y <= math.max(l2p1.Y, l2p2.Y)) then
return -- lines dont intersect
end
end
return Vector2.new(x, y)
end
If you want the function to take the lengths of the lines or one of the lines into account, simply pass l1Seg and l2Seg as true respectively.
function V3ToV2(vector: Vector3): Vector2
-- ignore Y component
return Vector2.new(vector.X, vector.Z)
end
local l1, l2 = workspace.l1, workspace.l2
local p: Part = Instance.new("Part")
p.Shape = Enum.PartType.Ball
p.Anchored = true
p.Parent = workspace
p.Size = Vector3.new(2, 2, 2)
task.spawn(function()
while task.wait() do
local p1, p2, p3, p4 =
(l1.CFrame * CFrame.new(0, 0, -l1.Size.Z/2)).Position,
(l1.CFrame * CFrame.new(0, 0, l1.Size.Z/2)).Position,
(l2.CFrame * CFrame.new(0, 0, -l2.Size.Z/2)).Position,
(l2.CFrame * CFrame.new(0, 0, l2.Size.Z/2)).Position
local point = FindLineIntersection2D(V3ToV2(p1), V3ToV2(p2), V3ToV2(p3), V3ToV2(p4), true, true)
p.Transparency = point and 0 or 1
if point then
p.Position = Vector3.new(point.X, p1.Y, point.Y)
end
end
end)
Hello, it has been a little over a year, but recently I came across this post. If anyone was looking to find the interception of 3D vectors, here is the code. I want to say it took me hours to find it 
local start1, end1 = workspace.Terrain.Attachment1.WorldPosition, workspace.Terrain.Attachment2.WorldPosition
local start2, end2 = workspace.Terrain.Attachment11.WorldPosition, workspace.Terrain.Attachment22.WorldPosition
-->> for checking intersections
local function IntersectingLines3D(line1Point, line1Direction, line2Point, line2Direction)
local u = line1Direction:Cross(line2Direction)
local denominator = u:Dot(u)
-- Check if the lines are parallel
if denominator == 0 then
return false, Vector3.new() -- No intersection
end
local v = line2Point - line1Point
local t = v:Cross(line2Direction):Dot(u) / denominator
local intersectionPoint = line1Point + line1Direction * t
return true, intersectionPoint -- Intersection point
end
-->> finds the intersect of 2 3D segment lines
local function intersect(point1Start, point1End, point2Start, point2End)
local distanceAmountToBeTouching = .05 -- min distance to be seen as interceting
local vectDirection1 = (point1End-point1Start) -- direction from point 1
local vectDirection2 = (point2End-point2Start) -- direction from point 2
local failed1, pointOnLine1 = IntersectingLines3D(point1Start, vectDirection1, point2Start, vectDirection2) -- point on ray relative to second ray
local failed2, pointOnLine2 = IntersectingLines3D(point2Start, vectDirection2, point1Start, vectDirection1) -- point on ray relative to first ray
if (not failed1) or (not failed2) then return false end -- failed to find one return false
-->> if the manigute does exceed the segment return false
if (pointOnLine1-(point1Start+(vectDirection1/2))).Magnitude > vectDirection1.Magnitude/2 then return false end
if (pointOnLine2-(point2Start+(vectDirection2/2))).Magnitude > vectDirection2.Magnitude/2 then return false end
-->> plots points
workspace.Terrain.Attachment01.WorldPosition = pointOnLine1
workspace.Terrain.Attachment02.WorldPosition = pointOnLine2
-->> if the distance from each other is close enough
return (pointOnLine1-pointOnLine2).Magnitude <= distanceAmountToBeTouching
end
local intersected = intersect(start1, end1, start2, end2)
print(intersected)