I'm rotating using matrix. When I rotate a vector using matrix, I will get new coordinates. But I will not get angle (which that vector was rotated around itself - itself means around axis which this vector now describes).

I've edit my answer to make more explicit the restoration of the rotation angle from the vectors before and after a rotation transform. Do check it out!

I have input vector A. I have rotation matrix which produce output vector B. To insert "physical component" in some 3D app, I need to give an postion, a direction (that produced vector B) and the angle. Everything I havem but not angle :( I must use these 2 inputs (vector A and matrix) to obtain pos, dir and angle :/

I believe you want to write something which allows the user to interact with your model and to rotate it about?

If you have the input vector $\vec{A}$, and the rotation matrix $\textbf{R}$, you could simply compute the output vector $\vec{B}$ by multiplying $\vec{A}$ with $\textbf{R}$, and use the dot product approach mentioned in the amended answer.

I have methods: InsertComponent (position, direction, angle). 1) position = start position, direction = normalized vector which indicates 'head' direction (if dir = (0,0,1) it means human head direction in targeted to sky). And angle means rotation around 'backbone' (0, 0, 1) = Z axis. And input values i have is default direction, and rotation matrix. I can easly produce final direction (matrix*direction), but I cannot get angle.

Good evening!

hi

Lets move on

srry about my english, I cannot describe my problem properly

it is alright!

let me start again

sure thing

I have a vector (0, 0, 1), and matrix which rorate this vector around Z axis 40 degrees

so result will be the same vecttor right?

0, 0, 1

yep

and now I need to extract that '40' value

unfortunately it's impossible if you are rotating an axis by itself

if rotation is made on one axis or input vector is placed on X, Y or Z axis this is easy

okay what if I add 1 more vector ?

because the vector wont have rotated t all

and i will transform it via the same matrix

for example i will add vecotr (1, 0 , 0)

so when i lokk at this vector i will know the angle, but its simple scenario

yeah i know

the final vector has to be different from the initial vector, or else one can say that nothing has changed

if you rotate (1, 0, 0) about Z-axis by 40 degrees

yes, but if i add more vector with different direction, maybe the other vectors will tell that angle ?

yes, it will!

lets take a simpler case

ok

we consider rotating the (1, 0, 0) about (0, 0, 1) by 45 degrees

the result will be (sqrt(2), sqrt(2), 0)

yes

let the rotation angle (45 degrees in this case) be, say, t

we assume that we dont know that t is 45 degrees

ok

but what we know is that the dot product of the initial vector, A, and the final vector, B, gives

A dot B = |A||B|cos(t)

yes

since |A| = |B| = 1, this simplifies to

sqrt(2) = cos(t)

i have function AngleBetween (vec1, vec2) and it computes angle, so its in my 3d library already

thats awesome

but problem is when i try to rotate about 3 axis

sorry, the final vector should be (1/sqrt(2), 1/sqrt(2), 0)

feel free to use programming jargon, i'm a programmer as well

but what if we rotate like we did, and also we rotate around different angle? that function anglebetween is useless in this case

look at picutre

wait

so what's the aim of your program?

im converting some stuff from one 3d model to another

to only compute the rotation angle from the initial and final vector, or to rotate a vector about some axis by some angle?

dont understand but imagine:

you need to place 3d component in 3d space

you need to provide: position, direction , and angle

(agnle = rotation aorund direction)

but you have as input: position (OK)

whats the position, direction and angle for?

direction = local direction + matrix = absolute direction

for method that will insert a component in 3d space

hmm.. alright

imagine a human body in local space

Position is 0,0,0

direction is 0,0,1 (head is targeting sky)

and angle is 0 (standing infront)

and u have transformation amtrix

so u apply

position will remain same 0,0,0

direction will remain same 0,0,1

but human body will not be infront anymore

you will okk at body from back

so i need to receive that 180 deg angle

i think i understand

:D

the flaw of your positioning system is that it does not have enough parameters

see this

basically, you need 4 parameters instead of just 3

1 for 3d cartesian coordinates (the position)

yeah

the other 3 (euler angles) for orientation. its in the link i gave.

okay

and i will find everything at this wikipedia atricle ?

for describing 3d orientation, yes

but the link in my answer in the man thread has some goodies on rotation transforms in 3ds

inn 3d*

in* 3d*

that is, if you ever need it^^

ok thanks, will try to do this damn vectors stuff. see you, answer accepted.

vectors are fun! I've recently completed a high school project whereby we have to write an interactive 3D sphere. You really learn a lot from it. Thanks and see you too!