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Vector3 Part 2

Pre-requisites⚓︎

Before reading this tutorial, you should know about vector3s. An explanation of vector3 exists in the Lua-Learning folder. Or check out the Roblox docs.

Info⚓︎

In this tutorial, I will teach you what each Vector3 method does and some of its use cases.

Dot(other: Vector3): Vector3⚓︎

This method returns the scalar dot product between two vectors. The scalar dot formula is 

scalarDot = (x1 * x2) + (y1 * y2) + (z1 * z2)

How is it useful?⚓︎

Take this script for an example 

local part1 = script.Parent.Part1 -- blue part
local part2 = script.Parent.Part2 -- green part

local dirArrow = script.Parent.Dir  -- blue/yellow arrow

local function Update()
    -- this will be visualized by the light blue/yellow arrow
    local direction = (part2.Position - part1.Position).Unit

    -- this will be visualized by the black arrow
    local lv = part1.CFrame.lookVector 
    local dotProduct = direction:Dot(lv)

    print("Dot: "..dotProduct)

    if dotProduct > 0 then
        -- if part 1 can see part 2
        --turn blue
        dirArrow.Color = Color3.new(0.0352941, 0.537255, 0.811765)
    else
        -- if part 1 cannot  see part 2
        --turn yellow
        dirArrow.Color = Color3.new(1, 1, 0)
    end
    --makes the direction arrow point toward the direction
    dirArrow.CFrame = CFrame.lookAt(part1.Position + Vector3.new(0,.5,0), part1.Position + Vector3.new(0, .5, 0) + direction)

end


Update()
part2.Changed:Connect(Update)
What this script does is if the green part is in a 180-degree view of the blue part, then make the arrow blue. Else make the arrow yellow, which you can see from the gif below. It also prints a value between -1 and 1 if you look at the output on the right side. placeholder

This can be very useful in some use cases, such as checking if you are in the field of view of an NPC.

But what if I want the NPC's FOV to be narrower?

What you can do is replace this line

if dotProduct > 0 then
With 
if dotProduct > math.cos(math.rad(maxAngle)) then
placeholder

Why the math.cos you may ask?

Take this image as a reference

placeholder

The bold black arrow is the lookVector. The blue arrows/rays create the cone shape, whereas the pink curve is the range in which the green part is considered inside, and the red line is the red part in the gif.

Info

A reminder to everyone that forgot trigonometry, cosine is the x value, and sine is the y value, but in this case, we only care about the x value, which is cosine.

Angle(other: Vector3, axis: Vector3 | nil ): number⚓︎

This method returns the angle in radians between two vector3s. If an axis is provided, it will return an angle around the specified axis (default is Vector3.zAxis)

Example⚓︎

(without providing axis) 

local part1 = script.Parent.Part1 -- blue part
local part2 = script.Parent.Part2 -- green part

local dirArrow = script.Parent.Dir  -- blue/yellow arrow

local maxAngle = 45

local function Update()
    -- this will be visualized by the light blue/yellow arrow
    local direction = (part2.Position - part1.Position).Unit

    -- this will be visualized by the black arrow 
    local lv = part1.CFrame.lookVector 
    local Angle = direction:Angle(lv)

    print("Angle: "..math.deg(Angle))

    --makes the direction arrow point toward the direction
    dirArrow.CFrame = CFrame.lookAt(part1.Position + Vector3.new(0, .5, 0), part1.Position + Vector3.new(0, .5, 0) + direction)

end


Update()
part2.Changed:Connect(Update)
placeholder

(with axis argument = Vector3.xAxis) placeholder

Info

You can play around more in the test place that I will link at the bottom.

FuzzyEq(other: Vector3, epsilon: number): boolean⚓︎

This method returns true if the given vector3 is within the current vector3 by the epsilon.

How it works⚓︎

Source 

function fuzzyEq(a, b, epsilon)
    return a == b or math.abs(a - b) <= (math.abs(a) + 1) * epsilon
end

function fuzzyEqVec(v1, v2, epsilon)
    for _, axis in ipairs({"X", "Y", "Z"}) do
        if not fuzzyEq(v1[axis], v2[axis], epsilon) then
            return false
        end
    end

    return true
end

Use cases⚓︎

You can use it to detect when the player stopped moving using their MoveDirection 

local humanoid: Humanoid = script.Parent.Humanoid

humanoid:GetPropertyChangedSignal("MoveDirection"):Connect(function()
    --if it is close by .001 
    if humanoid.MoveDirection:FuzzyEq(Vector3.zero, .001) then
        print("Player Stopped Moving")
    end

end)

Cross(other: Vector3): Vector3⚓︎

This method returns the cross product of the two vectors

Example⚓︎

The blue arrow is the the direction(self), the yellow arrow is the cross(result), the black arrow is the lookVector(other) 

local part1 = script.Parent.Part1 -- blue part
local part2 = script.Parent.Part2 -- green part

local dirArrow = script.Parent.Dir  -- blue arrow
local crossArrow = script.Parent.Cross  -- yellow arrow

local function Update()
    -- this will be visualized by the light blue arrow
    local direction = (part2.Position - part1.Position).Unit
    -- this will be visualized by the black arrow 
    local lv = part1.CFrame.lookVector 
    local Cross = direction:Cross(lv)
    print("Cross:", Cross)

    --makes the direction arrow point toward the direction
    dirArrow.CFrame = CFrame.lookAt(part1.Position + Vector3.new(0, .5, 0), part1.Position+Vector3.new(0, .5, 0) + direction)
    crossArrow.CFrame = CFrame.lookAt(part1.Position + Vector3.new(0, .5, 0), part1.Position+Vector3.new(0, .5, 0) + Cross)

end


Update()
part2.Changed:Connect(Update)
placeholder

Lerp(goal: Vector3, alpha: number): Vector3⚓︎

This method returns a Vector3 that is interpolated to the goal by the alpha or percent.

How it works⚓︎

function Lerp(start,goal,alpha)
    return start + (goal - start) * alpha
end

function Vector3Lerp(start,goal,alpha)
    return Vector3.new(
        Lerp(start.X, goal.X, alpha),   
        Lerp(start.Y, goal.Y, alpha),
        Lerp(start.Z, goal.Z, alpha),
    )
end

Use Case⚓︎

you can use it to make parts move smoothly 

local start = script.Parent.Part1 -- blue part
local end = script.Parent.Part2 -- green part
local move = script.Parent.Move -- grey part

while true do
    -- lerp forward
    for i = 0, 1, .01 do-- go from 0-1
        task.wait()
        Move.Position = Start.Position:Lerp(End.Position,i)
    end

    task.wait(2)
    -- lerp back
    for i = 0, 1, .01 do -- go from 0-1
        task.wait()
        Move.Position = End.Position:Lerp(Start.Position, i)
    end
    task.wait(2)
    --repeat 
end
(gif might be a bit laggy)

placeholder

Difference between Lerp and TweenService

Tween service is a roblox Service that only works on Instances while with Lerping you don't need instances and all you need is just two values.

Min(vector: Vector3): Vector3⚓︎

This method returns a Vector3 with each component being the lowest value for both Vectors 

local vector1 = Vector3.new(5,2,7)
local vector2 = Vector3.new(1,5,3)

print("Min: ", vector2:Min(vector1)) -- "Min: 1,2,3"

Max(vector: Vector3): Vector3⚓︎

This method returns a Vector3 with each component as the highest for both Vectors 

local vector1 = Vector3.new(5,2,7)
local vector2 = Vector3.new(1,5,3)

print("Max: ", vector2:Min(vector1)) -- "Max: 5,5,7"

Conclusion⚓︎

I hope this helps you understand these methods better and what they do. The link to the example will be here. To view the code, simply make a copy of the game by pressing the 3 dots on the top right and clicking edit. Once you are in, you can move the green parts around to see different results. Anyways bye! (It is currently 4:18 AM, I spent 3 hours on this)

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