create a basicRenderView
add a cube to the root displayObject3D

the displayObject3D as a public transform matrix as member

displayObject3D.transform

if you modify the matrix, the object will be transformed moved or scaled, rotate etc.

A matrix3D is a composition of 1 matrix and 2 vector.

a matrix 3D for scale and rotation :

transform.n11 transform.n21 transform.n31
transform.n12 transform.n22 transform.n32
transform.n13 transform.n23 transform.n33

for n12 mean nXY coordinate of row and columns

look at that matrix whe can whrite that

X 0 0
0 Y 0
0 0 Z

changing X Y or Z will scale your transform matrix. When papervision will render one frame
the obejct will be scale (transform by scale)

if you want rotate arround X (roll) you will change your matrix like that :

1 0 0
0 cosA sin-A
0 sinA cosA

because to roll arround X the X vector must remain unchanged
and the X and Y must be moved (origin unchanged but and position moved)

rotate arround Y
cosA 0 sinA
0 1 0
sin-A 0 cosA

rotate arround Z
cosA sin-A 0
sinA cosA 0
0 0 1

the matrix3D use 2 vector in addition :

X 0 0 tX
0 Y 0 tY
0 0 Z tZ
X Y Z ?

tX, tY, tZ are used for translation
X Y Z are the coordinates
? is replaced by 1, but in fact isn’t used (I think)
in papervision the complete transform matrix3D is ordered like that

transform.n11 transform.n21 transform.n31 transform.n41
transform.n12 transform.n22 transform.n32 transform.n42
transform.n13 transform.n23 transform.n33 transform.n43
transform.n14 transform.n24 transform.n34 transform.n44

You have to map cursors on the transform matrix and you can map tweener.
BUT I think this demo use quaternion to avoid Euler gimbal lock
http://en.wikipedia.org/wiki/Gimbal_lock
Quaternion is another problem but if you don’t use thems X, Y and Z can lock.

Thx John for your demo. It has help me to understand Matrix and transformation matrix
and the render pipe of papervision. The response may contain errors or imprecisions,
in such case feel free to correct it.

gamedev
http://www.gamedev.net/reference/articles/article695.asp
http://www.gamedev.net/reference/list.asp?categoryid=259
Mathematic matrix :
http://en.wikipedia.org/wiki/Matrix_(mathematics)

your son is very loveliness