Move, turn and stretch an object by dragging the numbers that do it, and watch the matrix fill in as you go.
What you should come away with: Why a matrix chain reads right to left, and why the columns are the object’s own axes.
X
Y
Z
drag to orbit
The matrix
T translate
1.00
0.00
0.00
1.40
0.00
1.00
0.00
0.50
0.00
0.00
1.00
0.00
0.00
0.00
0.00
1.00
·
R rotate
0.91
0.00
0.42
0.00
0.00
1.00
0.00
0.00
-0.42
0.00
0.91
0.00
0.00
0.00
0.00
1.00
·
S scale
1.00
0.00
0.00
0.00
0.00
1.00
0.00
0.00
0.00
0.00
1.00
0.00
0.00
0.00
0.00
1.00
M = T · R · S
0.91
0.00
0.42
1.40
0.00
1.00
0.00
0.50
-0.42
0.00
0.91
0.00
0.00
0.00
0.00
1.00
The first three columns of M are the cube’s own axes after the transform — that is exactly what the red, green and blue arms on the canvas are drawing. The fourth column, in amber, is where its origin ended up. Drag a translate slider and watch only that column move.