I'm not really sure what this is called

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#1

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As you can see from the image, I want the mouse hit to not go beyond the origin’s position. If anyone knows about this, I’d like to know.

#2

Are you trying to translate the mouse hit position to a similar relative position on the yellow box?

You could get the Mouse’s relative position like this:

local posX = mouse.X
local posY = mouse.Y

And then apply it to the position relative to a part:

point.CFrame = CFrame.new(posY, posX, origin.Z)

This works if its scaled 1:1 with the screen dimensions (ViewSizeX, ViewSizeY), but if not, you can just apply a scaling factor to the respective positions and it will work as intended.

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#3

Your question is almost exactly like this and you might be able to use the answer I gave here: How would I be able to get a point where a line intersect

As for what this is called, this would usually be called projecting a vector on to a plane.

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#4

That’s because I’m still the one who asked the question.

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#5

Oops. Is your plane always aligned with one of the world space planes? I.e. is it always the world XY, or XZ plane? This simplifies the solution slightly if so.

#6

The plane depends on the surface GUI’s normal ID; for front and back, it is XY, while left and right are ZY, and top and bottom are ZX.

#7

I will answer your question more directly but I did do something similar to this a while ago to create a holographic sight. In fact, it does what you’re asking but in reverse to give the illusion of a holographic object at a constant position relative to the plane. Check it out and see if the math makes sense: Holographic Sight - Roblox

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#8

The part that’s relevant to you is here:

	--Draw a line from the virtual position to the camera
	--Local space
	local dir = virtualReticlePos - glass.CFrame:PointToObjectSpace(workspace.CurrentCamera.CFrame.Position)
	
	--Find where this line intersects the glass
	local intersection = (dir / dir.Z) * focalPlaneDist

Note that on the first line we make sure all our vectors are in local space relative to the part. This could be any CFrame whose Z direction is the normal of the plane we care about, it just happens to be a part’s front surface in this case. dir is a vector (in local space) that goes from the camera to a point on the other side of the part, crossing through the plane. By dividing it by its own Z component, we get a shortened vector with the same direction, whose Z component is 1. Since it’s 1, if we multiply it by the distance to the plane, the Z component must now be exactly that distance, and thus our vector must point directly onto the plane, while having the same direction.

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#9

Here’s is what I came up with:

local diff = a - b
local position = origin + diff / diff.Z

All that is left to do is get the difference of origin and the new position then get the magnitude and subtract that to the target’s position.

#10

You’re missing the multiplication step:

local position = origin + (diff / diff.Z) * distanceToPlane

where distanceToPlane must be the projected distance from origin to the plane. That is the shortest distance from a point to a plane, which always forms a right angle on the plane. You can get this by taking the dot between the plane normal and the difference vector between camera pos and any point on the plane:
image

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#11

I don’t think this is the solution. It does not stay on a constant Z axis relative to the origin, but it is close, so I’ll keep testing and see what I get.