CALCULATION METHOD OF ROTATION MATRIX

The figure above shows the rotation matrix of the Tetris block.
How does this result in the following…
I don't know how to calculate it.
How is xr-3/2 and x-3/2 on the right calculated?
This may be a rudimentary question, but please let me know m(__)m

procession

2022-09-30 18:08

1 Answers

sin 90° is 1 and cos 90° is 0 so
The applicable expression is

 | xR-3/2 | | 0-1 | | x-3/2 |
|      | = |     | |     |
| yR-3/2 | | 10 | | y-3/2 |

By the way, the multiplication of 2 行列2 and 2 行列1 matrices is

 | ab | | A | | aA + bB |
|    | |   | =  |         |
| cd | | B | | cA + dB |

|xR-3/2||-1(y-3/2)||-y+3/2|
|      | = |         | = |        |
|yR-3/2 | | 1 (x-3/2) | | x + 3/2 |
         The term multiplied by zero disappears.

will be .

on both sides

|3/2|
|     |
| 3/2 |

Add to

|xR-3/2+3/2||-y+3/2+3/2||-y+3|
|          | = |            | = |        |
|yR-3/2 + 3/2 | | x-3/2 + 3/2 | | x |

| xR | | -y + 3 |
|    | = |        |
| yR||x|

will be

2022-09-30 18:08

If you have any answers or tips

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