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KurtCob
03-20-2001, 04:19 AM
Hello guys,

How can I multiply a vector by a matrix ?

Tnks
Kurt

Rudi_P
03-20-2001, 04:30 AM
Is it the maths your stuck on?

if so go to
http://147.4.150.5/~matscw/RealWorld/tutindex.html

Matrix multiplication

Bahamut_france
03-20-2001, 04:33 AM
Do you want do that?

[ a b c d
e f g h x [ x y z] ? http://www.opengl.org/discussion_boards/ubb/confused.gif
i j k l
m n o p]

Bahamut_france
03-20-2001, 04:35 AM
bad..... All caracters are not written....

I wrote: (matrice 4x4) x ( vector 1x3)

Do You want that ???

KurtCob
03-20-2001, 07:15 AM
Yes, is exactly what I want.

Tnks
Best Regards
Kurt

coredump
03-20-2001, 11:28 AM
multiplying a vector by a matrix will give you a vector.

Vold X Matrix = Vnew

the elements in Vnew are the dot products of Vold and each row/column in Matrix.

b

Randolph
03-20-2001, 12:44 PM
If you POST-multiply the matrix, then vector should be column. If you PRE-multiply the matrix vector is string. Surely, you will get same type of vector as a result. So, we have:
[a1 b1 c1 d1] [x1] [a1*x1+b1*x2+c1*x3+d1*x4]
[a2 b2 c2 d2]*[x2]=[a2*x1+b2*x2+c2*x3+d2*x4]
[a3 b3 c3 d3] [x3] [a3*x1+b3*x2+c3*x3+d3*x4]
[a4 b4 c4 d4] [x4] [a4*x1+b4*x2+c4*x3+d4*x4]
in occasion of post-multiplication, or analogically in pre-multiplication. The generic rule is that string is multiplied by column.

[This message has been edited by Randolph (edited 03-20-2001).]

john
03-20-2001, 05:31 PM
post multiply? pre multiply? vectors and matricies? surely you jest?

incidentially, you _can't_ multiply a 4x4 matrix by a 1x3 vector. furthermore, a 1x3 is a single ROW; you want a column vector (i.e. 3x1). Remember, its number_of_rows x number_of_columns (y dimension FIRST)

if you have two matricies, A and B of dimension a x b and c x d respectively, then in order to multiply A and B together then b MUST == c (and the dimension of the result is a x d). this is just matrix stuff, btw, nothing clever about opengl.

so, you CAN'T multiple 4x4 by a 1x3 (or a 3x1, for that matter) because 4!=3

but you CAN multiply a 4x4 by a 4x1:

ie. 4x4 * 4x1
| |
same!

uhm. yes. <tries to summon strength to explain matrix mul>
no, sod it. each element of the final vector is its corresponding ROW of the matrix multipled by the vector.

oh, and another thing: you can NOT premultiply a matrix with a vector.

cheers
John

[This message has been edited by john (edited 03-20-2001).]

KurtCob
03-21-2001, 01:37 AM
Tnks John,

So can you post how can I multiply a 4X4 Matrix by a 1X4 vector ? (Sorry, it looks really use, and I should know this), but I forgot how to do this.

So, any help will be apreciated.

Tnks
Best Regards
Kurt

jc
03-21-2001, 04:42 AM
Hi, if u want to multiply a vector by a matrice it should look like this:

Vector = V1 V2 V3 V4 And Matrix = M00 M01 M02 M03
M10 M11 M12 M13
M20 M21 M22 M23
M30 M31 M32 M33

Vector*Matrix = [a,b,c,d]

where
a = v1*m00 + v2*m10 + v3*m20 + v4*m30
b = v1*m01 + v2*m11 + v3*m21 + v4*m31
c = v1*m02 + v2*m12 + v3*m22 + v4*m32
d = v1*m03 + v2*m13 + v3*m23 + v4*m33


To multiply vector and matrices the dimensions of boths should look like this:

M [n m] * N[m t] = Res[n t]

Hope il will help

KurtCob
03-21-2001, 05:08 AM
Tnks JC,

Is it what I was looking for.

Does anyone know where could I find the matrix that OpenGL is using when we use glRotate and glTranslate ?

I want to multiply all the vertices of my model, using the way that OpenGL is rotating, scaling, translating and so one, because then when I export a file, I will have the right coordinates...Am I right ?

Tnks
Best regards
Kurt

coredump
03-21-2001, 06:28 AM
glRotate and glTranslate affect the modelview matrix, if in that mode. the matrix itself is a one dimensional array of 16 floats. using glMultMatrix you can use your own user-defined matrix.

b

KurtCob
03-21-2001, 07:02 AM
Ok, tnks again.

Just one more question, if I make a rotation in the X, Y or Z Axis, witch os the elements of the matriz will be the cos and sin ? or when I use glTranlate, witch element of the matriz will be the value translated in X, Y, Z...hope I'm clear enough, with my question.

Tnks
Best regards
Kurt

DaViper
03-21-2001, 07:20 AM
everything you are looking for us here: http://shiva.missouri.edu:88/SGI_Developer/OpenGL_PG/27690#X

hope that helps
Chris

Randolph
03-21-2001, 01:04 PM
TO John:
You wrote: "you can NOT premultiply a matrix with a vector". Beforehands, you explained, how it should be done. If i can multiply 4*4 by 4*1, I surely can multiply 1*4 by 4*4! The result surely will be 1*4. I think that 1*4 is vector. You dont?

john
03-21-2001, 03:08 PM
quote:
TO John:
You wrote: "you can NOT premultiply a matrix with a vector". Beforehands, you explained, how it should be done. If i can multiply 4*4 by 4*1, I surely can multiply 1*4 by 4*4! The result surely will be 1*4. I think that 1*4 is vector. You dont?


yes, you can, and that's right. but the guy was talking about column vectors.. okay, so maybe he wasn't and it was just a massive assumption on my part =) but, given that verticies are specified by a column vector, then you can NOT premultiply a column vector by a matrix, but you CAN premultiply the transpose of a column vector by a matrix. subtle difference in that you need to do an extra step

ie. if V = [ 1 2 3 4 ] ' and M is a 4x4 matrix, then

MV works

VM does NOT work

but

V'M DOES work

(where ' is the transpose operator)

(oh, and V'V is a scalar, and MM is a 4x4 matrix and VV' does nto work, either)

cheers,
John

ffish
03-21-2001, 04:46 PM
I agree with everything John says. One thing that may help people with questions on the topic is a good linear algebra book. Our first year undergrad book was Gilbert Strang's "Introduction to Linear Algebra" and I highly recommend it. I still refer to it if I have problems. Early chapters are easy to understand and you can really expand your LA knowledge in some of the later chapters. It's also very readable.

KurtCob
04-02-2001, 04:41 AM
Ok guys, so witch is the right way ?

This posted by Randolph

[a1 b1 c1 d1] [x1] [a1*x1+b1*x2+c1*x3+d1*x4]
[a2 b2 c2 d2]*[x2]=[a2*x1+b2*x2+c2*x3+d2*x4]
[a3 b3 c3 d3] [x3] [a3*x1+b3*x2+c3*x3+d3*x4]
[a4 b4 c4 d4] [x4] [a4*x1+b4*x2+c4*x3+d4*x4]
????

or this one posted by JC

a = v1*m00 + v2*m10 + v3*m20 + v4*m30
b = v1*m01 + v2*m11 + v3*m21 + v4*m31
c = v1*m02 + v2*m12 + v3*m22 + v4*m32
d = v1*m03 + v2*m13 + v3*m23 + v4*m33

???

Any help will be apreciated.
Thank you for the moment
Best regards

Kurt

KurtCob
04-02-2001, 09:43 AM
Ok guys, so witch is the right way ?
This posted by Randolph

[a1 b1 c1 d1] [x1] [a1*x1+b1*x2+c1*x3+d1*x4]
[a2 b2 c2 d2]*[x2]=[a2*x1+b2*x2+c2*x3+d2*x4]
[a3 b3 c3 d3] [x3] [a3*x1+b3*x2+c3*x3+d3*x4]
[a4 b4 c4 d4] [x4] [a4*x1+b4*x2+c4*x3+d4*x4]
????

or this one posted by JC

a = v1*m00 + v2*m10 + v3*m20 + v4*m30
b = v1*m01 + v2*m11 + v3*m21 + v4*m31
c = v1*m02 + v2*m12 + v3*m22 + v4*m32
d = v1*m03 + v2*m13 + v3*m23 + v4*m33

???

Any help will be apreciated.
Tnks
Best regards

Kurt

FoxDie
04-02-2001, 10:06 AM
A is matrix 4X4
B is matrix 4x1

A=(0,5,4,3)
(1,0,0,8)
(8,4,4,5)
(1,-2,3,1);
B=(0)
(8)
(0)
(2);

If you multiplying matrixes the rows of
matrix A must be same as columns of matrix B.
C=A*B

I-row index
J-column index

C[I,J]=A[I,J]*B[J,I]+A[I+1,J+1]+1*B[J+1,I+1].....

KurtCob
04-04-2001, 01:12 AM
Sorry, but i didn't understand.

Tnks
Best regards

Kurt

fleejay
04-04-2001, 06:22 AM
KurtCob the two methods are identical, bothj producing the same results, in the top method there is a name for each element in the matrix, in the bottom method each element in the matrix is accessed by a 2-dimensional index (think of a 2d array).

---

Fleejay

KurtCob
04-04-2001, 06:55 AM
Ok,
Thank you.

Best regards
Kurt