The Block Instance component will return a transform which will tell you everything you need to know about it’s scaling, translation, rotation, etc. Let’s look at an example (see below).
As a precursor, you might want to review some information about matrices and how they work.
Looking at the 4x4 matrix of values from the Original block, you can see that there are a series of values (1.0) starting in column 0, row 0 and working diagonally down to the bottom right of the matrix. All other values are set to 0.0. This is called an Identity Matrix and essentially means that it does nothing. There’s no scaling, rotation, or translation being applied to this block.
Now, let’s look at the Rotated block matrix. The last column has some large numbers (ie. 1525.84, -3164,74, etc.). The first three values in this column represent the translation values in X, Y, and Z. So, we know that this block has been moved 1525.84 units in the X-axis and -3164.74 in the Y-axis. Now, I know that I happened to have rotated this block 90 degrees counter clockwise about the z-axis. For rotation about the Z-axis, the matrix values that we care about look like this:
┌ ┐
| cos(⍺) -sin(⍺) 0 0 |
| sin(⍺) cos(⍺) 0 0 |
| 0 0 1 0 |
| 0 0 0 1 |
└ ┘
The cos(90) = 0.0 and the sin(90) = 1.0… so you can see that this fits for that pattern in the upper left hand corner of values for this matrix. Everything else remains the same as the identity matrix which means nothing else has changed. So, by reading this matrix, we can tell it’s been translated in the X and Y axis and rotated 90 degrees counter clockwise.
Now, let’s look at the Mirrored block instance matrix. Again, looking at the last column tells us that this block has also been translated along the X and Y axis. Now, I happen to know that I mirrored this block against the XZ plane. A reflection matrix that represents this would look like this:
┌ ┐
| 1 0 0 0 |
| 0 -1 0 0 |
| 0 0 1 0 |
| 0 0 0 1 |
└ ┘
In other words, The X and Z values stay the same but the Y values are mirrored (ie. -1). Looking at our matrix, you can see that it follows this exact pattern. If we had mirrored the block about the XY axis, then the third value in the third row and column would be -1 and the second value in the second row and column would go back to +1.
Anyway, learning how to read/manipulate matrices can be very useful. There are lots of online documents about how these can be composed/applied to transform geometry. I’ve really only scratched the surface.
