RotaTion
A 2D roration is applied to an object by repositioning it along a circular path in the xy plane.
We first determine the transformation equations for rotation of a point position P when the pivot point is at the coordinate origin.
Rotation of a point from position (x,
y) to position
(x'. y') through an angle a2 relative
to the coordinate origin
The original
angular displacement of the point from the x axis is a1
The constand distance of the point from the origin is r
Using standard trigonometric identities, we can express the transformed coordinates in terms of angles a1 and a2 as:
Rotated coordinates about the origin(0, 0): x'=r*cos(a1+a2)= r*cos(a1)*cos(a2) - r*sin(a1)*sin(a2) Original coordinates: x=r*cos(a1) |
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Therefore:
Rotated coordinates about the origin(0, 0): x¡¦= x*cos(a2) - y*sin(a2) |
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Let's apply the rotation to a digital image:
For example: The new position of point (4,2) with rotation angle=30 degree: x'= 4*cos(30) - 2*sin(30) =2.45
--> 2 |
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Handling Empty Pixels - Copying
Similar to scaling, rotation will create some "holes" in the resulting image.
Again, using the same solution --- Copy pixel values from neighbours
Common approach - just copy any one!
Result:
pivot point = (0, 0 )
Let's do it by using pen and graph paper:
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