Big brain maths question that sadly IDK!

anon_j1124 · December 7, 2022, 2:38pm

This might help.

You can substitute angle a for 90, sides a and c for the sides labelled in the diagram.

Qinrir · December 7, 2022, 2:38pm

how?

Qinrir · December 7, 2022, 2:55pm

ok this is my code

	local primpartpos = CWorkspace.PrimaryPart.Position -- mirror positon
	local campos = workspace.CurrentCamera.CFrame.Position
	local _,y,_  = CFrame.new(campos,primpartpos):ToOrientation()
	Camera.CFrame = CFrame.new(primpartpos)*CFrame.Angles(0,90-y,0)
	workspace.Pointer.Orientation = Vector3.new(0,(90-math.deg(y))+45,0) -- this is for angle visualization and +45 to make it accurate as possible.

Qinrir · December 7, 2022, 2:56pm

I got the angle of incidence but uhh nothing else

anon_j1124 · December 7, 2022, 3:01pm

Then you can do 90 - angleIncidence to work out theta.

Qinrir · December 7, 2022, 4:53pm

I am doing that 90-y and y being angle of incidence

anon_j1124 · December 7, 2022, 4:59pm

Yep - that’ll give you the angle theta you labelled in your original diagram.

msix29 · December 7, 2022, 5:04pm

So, to make a mirror, you will follow the law of reflection, it has some easy to follow rules.

The angle between the incident ray and the normal is equal to the angle between the reflected ray and the normal.
The incident ray, the normal and the reflected ray are all in the same plane.
Incident ray and refracted ray are on different sides of the normal.

Here’s a picture to help you understand.

The law of reflection states that the angle of reflection equals the angle of incidence θr = θi . The angles are measured relative to the perpendicular to the surface at the point where the ray strikes the surface.
now if you look, you can create a triangle by each “half” from the image (any side of the perpendicular) and from there you can easily get the angles, here for example.

If you were to compare the images, YZ is the normal and the angle and Z is the point where the normal touches the surface of the mirror, the angle we need is c, to get a we need the length of YZ and YX or XZ, you can choose the side that’s easier for you to find and use these formulas.

-- YX
local c = math.atan(YZ / YX)

-- XZ
local a = math.acos(YZ / XZ)

And ya, I think that’s everything. If I missed anything or you need more explanation on a point, feel free to tell me.

anon_j1124 · December 7, 2022, 5:12pm

Better explanation than I could have come up with, though you may want to edit:

… for reflection, rather than refraction; a whole different kettle of fish.

msix29 · December 7, 2022, 5:19pm

I would rather not mention refraction as some might get confused about which one I’m talking about. Thanks tho.

Qinrir · December 8, 2022, 11:27am

alright that explaination is very good i like it. I understand that the laws of reflections stats that Thetai = ThetaR I got it but the thing is there is always some sort of inversion like its opposite yknow how would I do that? My idea is to make the angle be relative to the surface but how can I do that in Roblox?

Qinrir · December 8, 2022, 12:24pm

@msix29 and @anon_j1124 sorry for the ping but I THINK I GOT IT!

Stayroh · December 8, 2022, 12:36pm

The angle ist equel to the arccosine of the dot product of the unit vector from the Hit Position to the camera position and Hit.Normal.

Theta = math.acos((Camera.CFrame.Position - Hit.Position).Unit:Dot(Hit.Normal))

Edit:
You can also directly get the reflection vector.

local d = (Hit.Position - Camera.CFrame.Position).Unit
RefVector = d - 2 * d:Dot(Hit.Normal) * Hit.Normal

Qinrir · December 8, 2022, 1:27pm

for some reason your formula is doing refraction like effect

this one ig is better or maybe not? IDK MATHS OK!

local part = workspace.Part
local port = workspace.port
game:GetService("RunService").Heartbeat:Connect(function()
	local startCFrame  = part.CFrame -- Where we derive our position & normal
	local normal = startCFrame.lookVector
	local position = startCFrame.p
	local ray = Ray.new(position, normal * 500)
	local hit, position, surfaceNormal = game.Workspace:FindPartOnRay(ray)
	local reflectedNormal = (normal - (2 * normal:Dot(surfaceNormal) * surfaceNormal))
	local Y = math.acos(reflectedNormal.Y)
	port.CFrame = CFrame.new(position)*CFrame.Angles(0,Y,0)*CFrame.new(0,0,-10)
end)

code to test

msix29 · December 8, 2022, 1:38pm

well, you will get the position correct by getting the angle and ending position, by inversion I think you mean the character being inversed so people commonly think of the reflection as being reversed left to right; however, this is a misconception, but I’ll try to help you get as close as possible to it.
You can do calculate starting position and ending position of every part of the player’s character and clone that part and place it there, then destroy it and redo that every frame, make sure to do that client-side so it doesn’t completely break the game from lag.

Qinrir · December 8, 2022, 2:05pm

welp man THANK YOU SO MUCH! AND
how can i forget about you anon! thank you both of you soooo much for the help! I figured it out and now it works!

Stayroh · December 8, 2022, 2:06pm

Try this:

local part = workspace.Part
local port = workspace.port
game:GetService("RunService").Heartbeat:Connect(function()
	local startCFrame = part.CFrame -- Where we derive our position & normal
	local Direction = startCFrame.lookVector
	local position = startCFrame.p
	local ray = Ray.new(position, Direction * 500)
	local hit, position, surfaceNormal = game.Workspace:FindPartOnRay(ray)
	local reflectedNormal = (Direction - (2 * Direction:Dot(surfaceNormal) * surfaceNormal))
	port.CFrame = CFrame.lookAt(Vector3.zero, reflectedNormal) + position + reflectedNormal * 10
end)

Qinrir · December 8, 2022, 2:07pm

what does vector3.zero do? is it just Vector3.new(0,0,0??

Stayroh · December 8, 2022, 2:08pm

Yes. There is also vector3.one wich is just the same as vector3.new(1,1,1)

Qinrir · December 8, 2022, 2:09pm

good for lazy devs like me lol