Metric Pixel Canvas

The Metric Pixel Canvas is a pixel based derivative of the ISO 216 standard developed by Dennis Pennekamp to unite pixel based raster graphics with vector graphics on a square root of two based metric canvas.

Size	Dimensions (pixels)	Dimensions (mm)	Diagonal
dA14	37 × 26	9.25 × 6.5	11.3 mm (0.45")
dA13	52 × 37	13 × 9.25	16.0 mm (0.63")
dA12	74 × 52	18.5 × 13	22.6 mm (0.89")
dA11	104 × 74	26 × 18.5	31.9 mm (1.26")
dA10	148 × 104	37 × 26	45.2 mm (1.78")
dA9	208 × 148	52 × 37	63.8 mm (2.51")
dA8	296 × 208	74 × 52	90.4 mm (3.56")
dA7	416 × 296	104 × 74	128 mm (5.03")
dA6	592 × 416	148 × 104	181 mm (7.12")
dA5	832 × 592	208 × 148	255 mm (10.1")
dA4	1184 × 832	296 × 208	362 mm (14.2")
dA3	1664 × 1184	416 × 296	511 mm (20.1")
dA2	2368 × 1664	592 × 416	724 mm (28.5")
dA1	3328 × 2368	832 × 592	1021 mm (40.2")
dA0	4736 × 3328	1184 × 832	1447 mm (57.0")
d2A0	6656 × 4736	1664 × 1184	2042 mm (80.4")
d3A0	9472 × 6656	2368 × 1664	2894 mm (114")
d4A0	13312 × 9472	3328 × 2368	4084 mm (161")

From the list we can derive the following:

• The base unit is a square pixel of 0.25 x 0.25 mm.

(Which establishes a resolution of approximately 102 dpi.)

• The line thickness is 0.25 mm by default.

(Which is nice as one can buy 0.25 mm pens in a shop.)

• The dA4 size qualifies as an A4 paper size according to the margins allowed by ISO 216.

(Which means you can simply print to A4 even if the A4 was cut on the small side, and if you don't care about minimal distortion you can print it resized to fit to your A4 paper exactly)

• Like ISO 216 it uses a 1:√2 aspect ratio by approximation.

(Which means that a large canvas can be cut in two to create 2 pieces of almost exactly the same aspect ratio, without adding any margins or creating any loss)

• Unlike ISO 216 it does not repeatedly round to the nearest millimetre or allow for increasing margins.

(Which means no pixels are ever lost during two step scaling, while one step scaling creates an approximation error which is always the same percentage and can therefore be nullified when repeated.)

Scaling

For example, to project dA4 onto dA3, multiply the sides in accordance with the aspect ratio:
819 x (52 / 37) = 1664
589 x (37 / 26) = 1184
This creates non square pixels, although to the untrained eye indistinguishable from 0.35 mm squares which means one can again use a standard (0.35 mm) pen to continue drawing the former 0.25 mm lines on a print out. When repeated the fractions are exchanged to nullify the error:
1664 x (37 / 26) = 2368
1184 x (52 / 37) = 1664
The resulting dA2 is exactly twice the size of dA4 with 0.5 mm square pixels. Vice versa, when projecting dA2 onto dA4, we have simply doubled the printing resolution.

Vector graphics

Compatibility with vector graphics is reached by positioning the centre of the first (most lower left) pixel at position (x,y) = (1,1) metre in a two dimensional coordinate system.

This means that the pixel called 0,0 can also be named position 1000,1000 mm, and that a black square centimetre covering the lower left corner of the canvas uses 400 pixels and has its corners located at positions;

A (1000,1000) mm
B (1010,1000) mm
C (1010,1010) mm
D (1000,1010) mm

Practical intermezzo
To alleviate having to type lots of zeros as prefix to every coordinate on your canvas you can reduce the prefix to 'one metre plus' by typing the letter m followed by rest of the coordinate in millimeter.

Type:  Display:
m      [1000+ ]mm
5      [1000+5]mm
       [1005  ]mm

Anti-aliasing

Compatibly sized geometric shapes based on rectangles, horizontal and vertical lines are perfectly interchangeable between vector and pixel based notations (1). You cannot see the resolution until it is said to be representing a 5 by 5 pixel canvas.

File:5by5-pixel-vector-grids.png

Pixel and vector shapes

As square and angled lines don't match on a pixel canvas (2), shapes with angled and curved lines are best kept as vector data. In XML defined as 0.25 mm thick lines with round end markers (3). The end markers fill most of the pixel while remaining within the pixel boundaries. This allows them to be rendered with a single solid colour (4) reminiscent of early computer graphics, or be plotted as if using a round tip metric pen (3) creating perfect alignment with bitmap graphics (5) when rendered with anti-aliasing.

Video

The Metric Pixel Canvas is also well suited as a video standard. The native frame rate is metric friendly with 100 full frames per second, and can easily be scaled down to the common 50 and 25 frame/s. The primary display resolution is dA2 landscape, capable of framing other formats like HDTV without pixel loss. Advantages are many, for example:

• Readably projecting ISO 216 based letters and brochures on the display.
• Displaying objects at their real size.
• Predictable size and resolution upgrade and downgrade paths.
• Rotating an A4 sized handheld unit ninety degrees to view two video channels without borders.
• Borderless printing of a single frame as photograph onto A4 paper.