[AD] Angular precision?

[R C-R]

I have been experimenting with general methods of creating radially symmetric circular designs with an arbitrary number of planes of symmetry, particularly with ones that are not evenly divisible into 360°. My method is explained in detail below but the general idea is to enter fractions in the rotate field in the Transform panel to rotate elements of the design as precisely as possible.

 

The problem is this leaves tiny gaps between the rotated objects unless I add a thin stroke to them. Experimentally, about a 0.2 to 0.3 px stroke width seems to be enough to fill the gaps, but this may vary depending on the canvas size.

 

I assume this is due to the inability of the app to work with irrational numbers to a sufficiently high degree of precision, but I sometimes see this even with rational numbers entered as fractions, like 360/9.

 

Is there any way to avoid this?

 

--------- My method -----------

1. I start by creating a vertical line with the Pen tool in Line Mode with snapping enabled so it begins at the exact center of the canvas.

2. I duplicate it with CMD-J, set the the lower right anchor point in the Transform panel, & enter (for example 360/7) in the rotate field.

3. I select both lines with the Node tool & use Join Curves & Close Curves to create a closed, pie slice shaped curve.

4. I duplicate that, & use the same method to rotate it in the Transform panel, again entering the same fraction as in step 2.

5. I then power duplicate to complete the design.

 

Attached is an example of the result (history included), showing the gaps for a 7 way symmetric design.

 

EDIT: I know about using various multisided shapes as templates for this sort of work but my question is about precision in angular text entry fields.

radial symetry issue.afdesign

Edited March 25, 2017 by R C-R

[R C-R]

After noticing that the Pie tool will accept fractions in the total angle field I simplified the above method using pie shaped wedges to combine steps 1 through 3. But I get the same gaps for various multi-way symmetries. Also, by using different start angles, rescaling the document to various pixel dimensions, & zooming to different levels, it became obvious that this not just a screen rendering artifact (I think).

 

Attached is another example, a 7 way symmetric design using the same 360/7 fraction as the first one but with Pie tool wedges & the first wedge at a start angle of 0°. The canvas is 400 px square but scaling it to various other dimensions with File > Document Setup set to rescale has no effect on eliminating the gap or changing its size relative to the wedge sections.

pie version.afdesign

[dutchshader]

isn't this the same problem as with 2 rectangles placed side by side.
then there is also allways a thin line shining thru.

adding a 0.3p stoke in the same collor makes the line disapear.

(Edit) as you mentiond in the first post.

also at max zoom the thicknes of the line stays the same.

 

placed some other elements, and they all have that gap between them.

 

pie test.afdesign

[R C-R]

I am not sure if it is the same problem. I can export a file with two stroke-less rectangles placed side by side & pixel aligned to a JPEG & there is no gap, but the gap always shows up with the exported angular designs, even where the angle is 0° or 90° & pixel aligned. That suggests that the rectangle gap may be just a display rendering artifact but that something else is happening with the angular stuff.

[JimmyJack]

This seems to be the same old problem.

 

It's the antialiasing between abutting objects. I believe it's better than it was in the past, but to me it's still a big problem. 

 

In the special case of perfectly aligned whole pixel vertical/horizontal edges there is no (hopefully) antialiasing, so no (or much less of a) problem. Everything else.... look out. Including vertical/horizontal lines that aren't so carefully conceived.

We've been told to adjust the coverage map ramp, but that's really just stealing from Peter to pay Paul.

It does help on verts/horizs, but on anything else, the one problem is replaced with a second.... more jagged edges elsewhere.

 

Another simple experiment (that teases out the rotational transform computation aspect):

Draw a box/rectangle (pixel perfect). Convert to curves. Break opposing corners (close the two new shapes... or not). Ta-da! Line.

In the case of pixel aligned edges that have been rotated and meet at a 0 or 90 degree angle, those do appear to be better than the others.

[dutchshader]

​on the first jpg there a no lines on the four squares, but after rotation the lines appear.

 

 

[R C-R]

In the special case of perfectly aligned whole pixel vertical/horizontal edges there is no (hopefully) antialiasing, so no (or much less of a) problem.

Except there is a gap even on the vertical or horizontal edges in all the n-way radially symmetric designs I have tried making & it is the same apparent size as the gaps at the other angles. The gap size also does not change if the overall size is a few hundred pixels or several thousand.

 

Examine the attached n way comparison. Each of the four designs has at least one pair of vertical or horizontal edges, yet they all have the same gaps.

n way comparison.afdesign

[JimmyJack]

This is what I get on a simple png export.

In three of the four the verts and horizontals are better, and on the fourth the verticals actually seem a bit worse.

(if you view them in pixel view mode in AD you can see that some antialiasing has been introduced on the vertical edges of the fourth example...)

 

Bit of a crap shoot. Like I said, It's still a problem.

 

[Alfred]

Bit of a crap shoot.

 

I see you've rolled a four! :D