Hello,
I have dig a little bit in matrix for screen coordinates manipulation with modelMatrix() and I am sure one may be interresting of understanding how this is working…
First of all the matrix return by modelMatrix() is a 4 x 4 matrix { 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16 }
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
representing the transformation made by call to translate() , scale() or rotate() …
Sx Xy Xz 0
Yx Sy Yz 0
Zx Zy Sz 0
Tx Ty Tz 1
or
Xx Xy Xz 0
Yx Yy Yz 0
Zx Zy Zz 0
Tx Ty Tz 1
where Sx, Sy, Sz are the scale applied to each axes (x,y,z)
and Tx Ty Tz are the scale applied to each axes (x,y,z)
For rotation, it is a bit more complex, the matrix indicate the portion of each X,Y,Z to apply to each axes (x,y,z).
You will note that Sx=Xx , Sy=Yy and Sz=Zz this mean that rotation and scale are sharing the same value, so if you have both a scale and a rotation, you can not separate them looking at the matrix.
So the simple translation matrix is a multiplication (*) by this matrix:
0 0 0 0
0 0 0 0
0 0 1 0
Tx Ty Tz 1
The simple scaling matrix is a multiplication by this one:
0 0 0 0
0 0 0 0
0 0 1 0
Tx Ty Tz 1
And the rotation part is done using multiplication by the rotation matrix, for a rotation on z of angle r :
cos r - sin r 0 0
sin r cos r 0 0
0 0 1 0
0 0 0 1
For an easy use, codea as some quick multiplication by each of those using :
m=m:translate(Tx,Ty,Tz)
m=m:scale(Sx,Sy,Sz)
m=m:rotate(r) (for a rotation on axe z, case for a 2D transformation for example)
To convert a World Wx,Wy,Wz coordinate to Screen coordinate X,Y,Z you just need to multiply the matrix returned by modelMatrix() by the 4 dimentions vector (Wx,Wy,Wz,0)
The formula is :
X=WxSx + WyYx + WzZx + Tx
Y=WxXy + WySy + WzZy + Ty
Z=WxXz + WyYz + Wz*Sz + Tz
It works in 2D, but you just have more 0 in the matrix !
The beauty of Matrix is that you just have to multiply then to merge transformation.
The inverse of a Matrix will do a reverse transformation (only if determinant is non null)
If you want to play a little with it in 2D, here is a sample program :
– matrix
-- Use this function to perform your initial setup
function setup()
iparameter("tx",0,100) -- transpose X
iparameter("ty",0,100) -- transpose Y
parameter("sx",0,2,1) -- scale X
parameter("sy",0,2,1) -- scale Y
iparameter("r",0,360) -- rotation around Z
iparameter("mode",0,1,0) -- When 0 show transformation automatic, when 1 show manual calculation
end
-- This function gets called once every frame
function draw()
-- This sets a dark background color
background(40, 40, 50)
-- This sets the line thickness
strokeWidth(5)
-- Do your drawing here
tm=matrix()
tm=tm:translate(tx,ty)
tm=tm:scale(sx,sy)
tm=tm:rotate(r)
if mode==0 then
translate(tx,ty)
scale(sx,sy)
rotate(r)
stroke(255, 221, 0, 255)
line(250,200,400,450)
else
stroke(91, 28, 241, 255)
a=toscreen(tm,vec2(250,200))
b=toscreen(tm,vec2(400,450))
line(a.x,a.y,b.x,b.y)
end
m=modelMatrix()
resetMatrix()
resetStyle()
for i = 1,16 do
text(i.."="..m[i],100,40*i)
text(i.."="..tm[i],200,40*i)
end
end
function toscreen(mat,ve)
x=mat[1]*ve.x+mat[5]*ve.y+mat[13]
y=mat[2]*ve.x+mat[6]*ve.y+mat[14]
return vec2(x,y)
end
). Btw, I’am not sure from running your example that it is really 2D, but never mind. If you get deeper understanding about this matrix stuff (i’m not talking about quaternions theory, but practical things), please keep sharing, i’m sure it will help a lot of people.
But they are perfect to create a transition from one rotation matrix to another. With simple matrix transition the object would be stretched, but with quaternions it rotates.