Metric Pixel Canvas
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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.
Canvas sizes listed in landscape orientation:
dA14 0037 x 0026 pixels (09.25 x 06.50 mm) dA13 0052 x 0037 pixels (13.00 x 09.25 mm) dA12 0074 x 0052 pixels (18.50 x 13.00 mm) dA11 0104 x 0074 pixels (26.00 x 18.50 mm)
dA10 0148 x 0104 pixels (0037 x 0026 mm) dA9 0208 x 0148 pixels (0052 x 0037 mm) dA8 0296 x 0208 pixels (0074 x 0052 mm) dA7 0416 x 0296 pixels (0104 x 0074 mm) dA6 0592 x 0416 pixels (0148 x 0104 mm)
dA5 0832 x 0592 pixels (0208 x 0148 mm) dA4 1184 x 0832 pixels (0296 x 0208 mm) (diagonal 363 mm or 15 inch) dA3 1664 x 1184 pixels (0416 x 0296 mm) (diagonal 514 mm or 20 inch)
dA2 2368 x 1664 pixels (0592 x 0416 mm) (diagonal 726 mm or 28 inch) dA1 3328 x 2368 pixels (0832 x 0592 mm) dA0 4736 x 3328 pixels (1184 x 0840 mm) d2A0 6656 x 4736 pixels (1664 x 1184 mm) d3A0 9472 x 6720 pixels (2368 x 1664 mm) d4A0 13312 x 9472 pixels (3328 x 2368 mm)
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 therefor be nullified when repeated.)
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[edit] Scaling
For example to project dA4 onto dA3 multiply the sides in accordance with the aspect ratio:
1184 x (52 / 37) = 1664
0832 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.
[edit] 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 zero's 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
[edit] 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.
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.
[edit] 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.
