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Now you have to think mathematically. Consider the base-factor you are presently using, and the number of "points" you are trying to achieve. By replicating a tile at 2 angle-unit intervals, you will always end up with as many points as the base-factor, but one need not limit themselves. In base-factor 9, for example, and allowing for increments of 1/2 angle units, there are 36 distinct areas uniformly distributed.
Many distinct numbers can be represented in our target design. Through careful planning, 2, 3, 4, 6, 8, 9, 12, 18, 24, and 36 can ALL be found in base-factor 9. Once you've decided how many points you're hoping to achieve, determine how to accomplish it. TileDreams allows you to rotate clockwise or counter-clockwise in increments equal to:
So to show 12, in base factor 9, we need to rotate the tile 3 1/2 steps each time. At the end of step 1, you created a composite tile. Select the tile by right-clicking/dragging around the selected area. Release the mouse button when you've selected anything you want to replicate. It will become highlit. Copy it to the clipboard (Ctrl + C). Paste it into the display area (Ctrl+V and click the display to place it generally). Rotate the pasted copy the required 3 1/2 steps (Ctrl + F7) You can precisely align it relative to the original tile using the mouse and/or the keyboard commands. Paste from the clipboard again, only this time rotate it 3 1/2 steps in the opposite direction (Ctrl + F6). Align as necessary, using the mouse and/or the keyboard. You should now have three tiles, counting your original tile, with the original in the center. Rotating tiles within the display area requires TileDreams to round the results of standard trigonometric algorithms, projecting the points of the shapes X degrees in one direction or another. These points were already rounded, most likely, so the degeneration of geometric precision is a serious concern. To minimize the degeneration, and keep the design as symmetrical as possible, it is crucial to minimize the number of rotations a tile or group of tiles is subjected to. Paste from the clipboard again, only this time, you should shift it's position by adding another increment of rotation. Copy the composite tile from the end of Step 1, and paste a copy of it into your display area. Rotate it two angle units by using the Shift+F8 combination, or pressing F8 twice. Paste it a second time, only this time rotate the copy two angle units in the opposite direction by using Shift+F5, or |
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