Or we can also define that when we refer to an image or picture, rotation is a feature that allows the user to rotate the picture in a clockwise or anticlockwise direction depending on the need. Shrinking will make image smoother.The rotation of an image or picture is a common image processing routine that allows the user to correctly display an image taken from a different angle to a camera, mobile or scanned document/ pictures. To overcome this, stretch image before rotation (400% is just fine), then shrink it back after. This causes rotated images to become "noisy", each pixel shifted by some random value.
When shearing image, Paint uses nearest-point approximation, moving each original pixel by integer amount. This gives overall transform very close to the true rotation, but image will be noisy because of big numbers of transforms. Using 3 and more shears can give even better approximation, however, each shear introduces distortions, caused by rounding and using to many of them may diminish effect of better approximation.Īnother example: to rotate by 45°, use the following sequence of 6 shears: H 4° H 19° V 10° V 28° H 4° H 19°. That's some 87 times better! Improved algorithm for rotation by 30° is:
This will give total shear angle of 26.570°, with relative error 0.018%. Thus to shear by 26.565°, instead of shearing by 27° (relative error is 1.6%) one may shear by 11° and then by 17°.
Where \(\alpha,\beta,\gamma\) are shear angles. The solution is to replace 1 shear with 2 or more consecutive shears in the same direction. This causes additional distortion, result is slightly different from exact rotation. Values, given by the formula above, are generally non-integer and must be rounded. Paint only shear shears by integer angle, if measured in degrees. To rotate by °: Further improvements Better angle approximation (You need to enable Java script to use it). Since Paint can only shear by integer angle, calculator automatically rounds results. Allowed interval is, but big shear angle can produce extremely large images. For the best result, angle should be in the interval. Calculator for shear anglesĮnter desired rotation angle and shear 3 times according to instruction. In other words, translating from math to English: to rotate by φ, shear horizontally by φ/2, then vertically by - arctan( sin( φ)), then again horizontally by φ/2. Mathematically, both rotation and shears are linear transformations, described by the square rank 2 matrices: However, 3 finely tuned shears can produce pure rotation, with all distortions cancelled out. It may seem that shearing twice can solve the problem, but alas, two shears are also not enough. If you shear a picture once, it will get distorted, not rotated. The key is the shear transform, which is supported by some reason (I guess, because it is simple to implement). Rotating image ( original) by 30° with 3 shears, useless but curious. Well, with mathematics, a workaround can be found: Rotating a picture by, for example, 30° is simply not possible, is it? But even the most prominent mspaint wizards will probably say that Paint can't rotate images by arbitrary angle: only rotations by 90°, 180° and 270° are supported. However, if you do it with MS Paint, the impression could be completely different. It is hard to impress people with computer drawing of a car nowadays.