// For speed reasons, use the unroll-loops option of your compiler
for(i = 0; i < 4; i++)
for(j = 0; j < 4; j++)
for(k = 0, mat[i][j] = 0; k < 4; k++)
mat[i][j] += mat1[i][k] * mat2[k][j]; //Wrong
mat[j][i] += mat1[j][k] * mat2[k][j]; //Right
return mat;
}

 // For speed reasons, use the unroll-loops option of your compiler
for(i = 0; i < 3; i++)
for(j = 0; j < 3; j++)
for(k = 0, mat[i][j] = 0; k < 3; k++)
mat[i][j] += mat1[i][k] * mat2[k][j]; //Wrong
mat[j][i] += mat1[j][k] * mat2[k][j]; //Right
return mat;
}

Quote:

Original post by Anonymous Poster Starts off talking like were newbies ( Which I am). Then starts talking about sin/cos bla bla blah. Completely losses track. Not usefull, sorry.

1  	0  	0  	0
0 	cos(x) 	-sin(x}	0
0 	sin(x) 	cos(x) 	0
0 	0 	0 	1

1  	0  	0  	0
0 	cos(3.1415) 	-sin(3.1415}	0
0 	sin(3.1415) 	cos(3.1415) 	0
0 	0 	0 	1

Quote:

Original post by Drew_Benton Quote: Original post by Anonymous Poster Starts off talking like were newbies ( Which I am). Then starts talking about sin/cos bla bla blah. Completely losses track. Not usefull, sorry. You learn the basics of sin/cos in Geometry and then the matricies in Algebra 2 (US Education Systems in TX at least). For us it was, Alg1, Geom, Alg2, PreCalc, Calc in high school. If you are looking into 3D Math, and do now know your basic trig (the sin/cos blah blah), then I highly reccomend going back and learning what you are missing. In those examples, it clearly shows what you have to do. If you want to rotate about the X axis, then for the X Rotation matrix, given as: 1 0 0 0 0 cos(x) -sin(x} 0 0 sin(x) cos(x) 0 0 0 0 1 You simply replace X with the radians/degress of what angle you want to rotate by (depending on your math systems), so if you want to rotate by 180 degress (which is PI radians) you will have: 1 0 0 0 0 cos(3.1415) -sin(3.1415} 0 0 sin(3.1415) cos(3.1415) 0 0 0 0 1 Now you have your matrix! Regardless of your programming API, there should be some math functions that can convert cos(3.1415) to -1 and sin(3.1415) to 0 and so on. That's all there is to it, it's very, very useful. For a conversion from degress to radians take a look at the Unit ciricle (something you should have to memorize in Pre-Calc). Other than that, it's just plug and chug stuff. For sin/cos/trig, all you need to know is SOHCAHTOA.

Quote:

Original post by Raziaar Quote: Original post by Drew_Benton Quote: Original post by Anonymous Poster Starts off talking like were newbies ( Which I am). Then starts talking about sin/cos bla bla blah. Completely losses track. Not usefull, sorry. You learn the basics of sin/cos in Geometry and then the matricies in Algebra 2 (US Education Systems in TX at least). For us it was, Alg1, Geom, Alg2, PreCalc, Calc in high school. If you are looking into 3D Math, and do now know your basic trig (the sin/cos blah blah), then I highly reccomend going back and learning what you are missing. In those examples, it clearly shows what you have to do. If you want to rotate about the X axis, then for the X Rotation matrix, given as: 1 0 0 0 0 cos(x) -sin(x} 0 0 sin(x) cos(x) 0 0 0 0 1 You simply replace X with the radians/degress of what angle you want to rotate by (depending on your math systems), so if you want to rotate by 180 degress (which is PI radians) you will have: 1 0 0 0 0 cos(3.1415) -sin(3.1415} 0 0 sin(3.1415) cos(3.1415) 0 0 0 0 1 Now you have your matrix! Regardless of your programming API, there should be some math functions that can convert cos(3.1415) to -1 and sin(3.1415) to 0 and so on. That's all there is to it, it's very, very useful. For a conversion from degress to radians take a look at the Unit ciricle (something you should have to memorize in Pre-Calc). Other than that, it's just plug and chug stuff. For sin/cos/trig, all you need to know is SOHCAHTOA. This is confusing. I know matrix algebra, and I know trigonometry and stuff... but I was hoping for an insightful article on matrices as they pertain to 3D Math. You didn't clarify at all why the matrix for rotation along the X axis is that, and why the matrix form of rotation along the Y axis is that... and so forth and so on. I'm looking at the matrix and I'm wondering why the rotation for the X axis has the trigonometric functions located in the center four elements. And why the Y rotation has the functions located where they are, and why the Z rotation has the functions located in the upper left four elements. Why is that the case? The article doesn't make it clear. Is that supposed to be something I should know, even though I know about vectors, trigonometry, and matrix algebra? What particular subject should discuss this aspect?

Well, with a bit of tinkering I'm sure you would have got it but lets look together. For our purposes, we will use a 2D example.

A point, P, has a position of (4,-3). If that is rotated 90 degrees around the Origin(0,0) what will it's new position be? 

P(4,-3) rotated 90 around Origin = P'(3,4). 

What just happened? Well, our x coordinate was replaced with; 

cos(90)*x + sin(90)*Y*(-1) 

and our y coordinate with:
sin(90)*X + cos(90)*Y.

hrmm... if only there was a way to store all this math... THE MATRIX!!!

or at least... A matrix.

Our vector [x,y] multiplied by a matrix [cos(theta), sin(theta)]
                                        [-sin(theta),cos(theta)]

gave us our vector rotated by (theta). now when we jump to 3d, it looks like this,

P[x,y,z] * M [cos(theta), sin(theta), 0]
             [-sin(theta),cos(theta), 0]
             [0,          0,          1]

That's right our trivial 2d rotation was actually a rotation around the z axis.
seen this way our matrix has a column for each axis, and since this is a zaxis rotation, the Z coordinate of our point doesn't change, hence:

 z'= x*0+y*0+z*1.