# Printing 'Dot Angles'

Here I will look at printing dot angles.

## Introduction

FIGURE 1

Unlike pixels, printing dots can be used at any angle. The square on the left shows lines of dots set at 0°, the same as pixels, but the pattern results in a square or rigid look to the human eye. In contrast the square on the right has lines of dots that have been rotated to an angle of 45°, resulting in a much more pleasing pattern. There is no difference in the dot size, number, or spacing in the two squares; it is just that the human brain loves patterns.  Upright and horizontal lines give a sense of rigidity or solidity. Angles and curves, on the other hand, give a sense of motion, dynamism or fluidity. So when it comes to printing images with dots there is a real advantage to using a pattern of 45° as the dots appear to blend together better.

FIGURE 2

If it helps to visualise the difference with the two patterns then compare the stars between the old and current United States flags. The US flag before 1959 (when there were only 48 states) had the stars in rows and columns, whereas the current US flag (50 states since 1959) has the stars interlaced. The stars are still in rows and columns but now at an angle of 45°. To the eye this has a softer look as the rigid rows and columns are not as obvious.

## Black printer dots

FIGURE 3

Black printer dots may look better at an angle of 45° but a problem arises. The dots aligned with the underlying pixels when horizontal (blue above), but now no longer align when they are rotated to 45° (red above). The underlying pixels at 45° cover a greater distance because they are measured diagonally whereas the printer dots are still measured horizontally but rotated. The result is that the pixel and printer dot resolutions are now mismatched.

The length of a diagonal at 45° is the square root of 2, which equals 1.414 to three decimal places. The image pixel resolution must therefore be multiplied by 1.414 to get the value of the diagonal resolution up to the horizontal value.

Since 1.414 is inconvenient to remember it is easier to round the number up to 1.5, or more commonly 2, as the multiplication factor. The convention of using twice the pixel resolution to create the printing dot resolution is just that, a convention. There is nothing in the laws of physics that states the multiplication factor must be 2, but this convention does have 2 advantages:
• It is an easy number as multiplying by 2 does not require a calculator.
• It has a safety margin.  If a photograph is resized upwards a little in the design then it will not need re-scanning (so long as the resizing does not increase by 1.414 or more).

## Colour printer dots

FIGURE 4

When 4 colours are being used then new angles have to be introduced. They can not all be printed at 45° as that would result in the higher colours covering the dots of the lower colours. The problem is that when two or more patterns are overlaid at different angles to each other an interference, or moir pattern results (see right).  At certain angles this moiré can be quite ugly so angles that give the most pleasant pattern need to be used.

FIGURE 5

As Black is the strongest colour it is kept at 45° being visually the most attractive angle. Yellow is the weakest colour and therefore is given the least attractive angle of no rotation since it will be least noticed. That leaves Cyan and Magenta.  Convention has decided that an angle of 30° either side of Black gives the best result, but there are occasions when these figures can be altered.

## Dot patterns

FIGURE 6

When the 4  colours are added together at the angles of 15, 75, 0, and 45 degrees for each of the CMYK colours, they form a small rosette or flower petal pattern which is pleasant to look at. Squinting helps to view the pattern more clearly. However, printer dots can be set at other angles and the resolution (LPI) can be set at different values for each colour giving a different pattern (above right). Each colour can also be printed slightly offset from one another which would soften the pattern.