literature

# Cpow3 without overlaps

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## Literature Text

All the needed plugins can be found in Essential Plugin Pack

# Input

You need a shape with a hole of same shape in the middle (it doesn't really have to be in the middle, but that is trickier )

# Parameters

Cpow3_d is the ratio of the hole to the whole shape. For example, if the hole is a circle of radius 0.5 and the shape is a circle of radius 1, cpow3_d is 0.5 / 1 = 0.5. If the hole is a square of side 1, and the shape is a square of side 3, cpow3_d is 1 / 3 = 0.333333.

Cpow3_r is equal to 360 / (rotation of hole). Lets see a few examples:

1. A circle with a circular hole. In this case, the hole can be rotated any angle compared to main shape, and it will still remain the same. So cpow3_r can take any value without creating overlaps.

2. A square with a square hole, such as below. Observe that the rotation can be 90, 180, 270, 360, 450 degrees and so on, which means you can use cpow3_r values such as 360 / 90 = 4, 360 / 180 = 2, 360 / 270 = 1.333333, 360 / 360 = 1, 360 / 450 = 0.8 and so on.

3. A square with a square hole, such as below, rotated by 30 degrees in relation to the main shape. Now, possible rotations are 30 (0 + 30 degrees), 120 (90 + 30 degrees), 210, 300, 390, 480 and so on. The corresponding cpow3_r values are 12, 3, 1.714286, 1.2, 0.923077, 0.75 and so on.

4. A triangle with a triangle shaped hole, such as below. The possible rotations here are 60, 180, 300, 420, 540, so the cpow3_r values are 6, 2, 1.2, 0.857143, 0.666667 and so on.

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