Editing 184: Matrix Transform
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A {{w|Rotation matrix|rotational matrix transformation}} (i.e. the big brackets with "cos" and "sin" in them) is used in computer graphics to rotate an image. In general, to rotate a point [a1, a2] in a 2D space by z° clockwise, you can multiply it by the rotation matrix [[cos z°, sin z°], [-sin z°, cos z°]]. In this case, the left side of the equation is rotating [a1, a2] by 90°. Simplifying the trigonometry, the 90° clockwise rotation matrix is [[0, 1], [-1, 0]], so multiplying this by [a1, a2], you should get [a2, -a1]. | A {{w|Rotation matrix|rotational matrix transformation}} (i.e. the big brackets with "cos" and "sin" in them) is used in computer graphics to rotate an image. In general, to rotate a point [a1, a2] in a 2D space by z° clockwise, you can multiply it by the rotation matrix [[cos z°, sin z°], [-sin z°, cos z°]]. In this case, the left side of the equation is rotating [a1, a2] by 90°. Simplifying the trigonometry, the 90° clockwise rotation matrix is [[0, 1], [-1, 0]], so multiplying this by [a1, a2], you should get [a2, -a1]. | ||
| − | The joke is that the author performed the rotation transformation on the | + | The joke is that the author performed the rotation transformation on the image of the vector rather than just the vector itself. |
Rotational matrix transformations are a special case of the general linear matrix transform, which can do other things to images, including the other two affine transformations of scaling them or translating (moving) them. On a pedantic note, normally mathematics uses counterclockwise as a default, although computer graphics frequently use a clockwise default, so this may be an intentional reference. | Rotational matrix transformations are a special case of the general linear matrix transform, which can do other things to images, including the other two affine transformations of scaling them or translating (moving) them. On a pedantic note, normally mathematics uses counterclockwise as a default, although computer graphics frequently use a clockwise default, so this may be an intentional reference. | ||
