Scripting Helpers is winding down operations and is now read-only. More info→

How is CFrame able to do multiplication with Vector3? [SOLVED]

Asked by

DeceptiveCaster 3761

5 years ago

Edited 5 years ago

CFrame and Vector3 are both matrices, but they have a different number of rows and columns. A CFrame is 4x4 matrix and a Vector3 is a 3x1 matrix. According to the standard rules of matrix multiplication, you can only multiply a matrix by another matrix if they have either the same number of rows or the same number of columns (or both). This is where I start to question CFrame's ability to do multiplication with Vector3. Since they have an unequal amount of rows and an unequal amount of columns, I still wonder how they are able to perform multiplication with each other. Maybe it's because Vector3 is, well, a vector, but I still don't know.

local new_mtrx = script.Parent.Base.Position * script.Parent.Joint1.Position

But CFrame is a bit unusual with this. Even though its number of rows and columns is not the same as Vector3's, it can still multiply itself by a Vector3 and evaluate to a Vector3:

local new_vctr = script.Parent.CFrame * script.Parent.Base.Position

And this evaluates to a Vector3. So, my question is:

How is CFrame able to multiply itself by a Vector3, and why does it evaluate to a Vector3 instead of throwing an error?

1 answer

Answered by

NeutralEnergy -1

5 years ago

!enter image description here

Like this. The 4x4 matrix can be multiplied with a 3x1. The top left is the cframe matrix multiplied by the 3x1 vector matrix on the right.

That also does not answer my question. The question is "How is it possible?", not "How does it work?". I already know how it works, and I'm asking WHY it works, not HOW it works. DeceptiveCaster 3761 — 5y

Hmm, not something I can answer. I am going on a limb here and saying that the vector3 actually gets another value added to make it have 4 when it is multiplied. So the CFrame can actually multiply with a vector3 cause of the equal number of rows. NeutralEnergy -1 — 5y

The explanation is fase. The vector is a 4x1 matrix, not a 3x1 matrix. ScriptGuider 5640 — 5y

Reasonable. DeceptiveCaster 3761 — 5y

View all comments (3 more)

On your educated guess, what do you think the explanation is then? NeutralEnergy -1 — 5y

The explanation is that the two matrices are allowed to be multiplied because, in fact, a vector is a 4x1 column matrix instead of 3x1. The 4th row of the CFrame matrix exists to zero-out the position components so that the product 4x1 matrix can reserve it's [x y z 1] structure. And this isn't an educated guess, this is mathematically true. ScriptGuider 5640 — 5y

Hmm, so my explanation wasn't wrong. NeutralEnergy -1 — 5y

How is CFrame able to do multiplication with Vector3? [SOLVED]

1 answer

Answer this question