A4 and A3 sheets in Morphic


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Last updated at 8:41 am UTC on 14 January 2022

Exercise with A4 sheets

Create a morph representing an A4 sheet
Add morphs to the sheet, then
Use export as PNG
Print the PNG file

(not complete yet, add some content and show post script export)

A4 paper, a paper size defined by the ISO 216 standard, measuring 210 × 297 mm.

The sheets have an aspect ratio of 2 sqrt.

The main advantage of this system is its scaling. Rectangular paper with an aspect ratio of √2 has the unique property that, when cut or folded in half midway between its shorter sides, each half has the same √2 aspect ratio and half the area of the whole sheet before it was divided. Equivalently, if one lays two same-sized sheets paper with an aspect ratio of √2 side-by-side along their longer side, they form a larger rectangle with the aspect ratio of √2 and double the area of each individual sheet.

Here is a way to create Morphs which represent A4 and A3 sheets.

a4Extent := 210 @ 297 "millimeter". 
scaleFactorForDisplay := 1.2.
a4 := Morph new extent:  a4Extent * scaleFactorForDisplay.
a4 color: Color lightBlue.
a4 openInHand .


a4 := Morph new extent:  a4Extent * scaleFactorForDisplay.
a4 color: Color lightGreen.
a4 openInHand .


a3Extent := a4Extent scaleBy: (2 sqrt @ (2 sqrt)).
a3 := Morph new extent:  a3Extent transposed * scaleFactorForDisplay .
a3 color: Color lightRed.
a3 openInHand .

 a4Extent := 210 @ 297 "millimeter". 
 a4ExtentPrintableArea := 190 @ 277 "millimeter". 
 
 scaleFactorForDisplay := 2.
 a4ExtentForDisplay := a4Extent  * scaleFactorForDisplay.
 a4 := Morph new extent:  a4ExtentForDisplay.
 a4 color: Color lightBlue. 
 

 a4PrintableAreaExtentForDisplay := a4ExtentPrintableArea * scaleFactorForDisplay.
 a4PrintableArea := Morph new extent:  a4PrintableAreaExtentForDisplay.
 a4PrintableArea color: Color white.


 a4 addMorph: a4PrintableArea.
 a4PrintableArea center: a4 center.
 a4 openInHand

12 boxes

An A4 sheet with 12 boxes (submorphs). The layout is done by calculating the center points of the submorphs and then using the positioning method #center: on them.
An alternative would be to use a TableLayout.

a4Extent := 210 @ 297 "millimeter". 
a4ExtentPrintableArea := 190 @ 277 "millimeter". 

scaleFactorForDisplay := 2.
a4ExtentForDisplay := a4Extent * scaleFactorForDisplay.
a4 := Morph new extent:  a4ExtentForDisplay.
a4 color: Color lightBlue.


a4PrintableAreaExtentForDisplay := a4ExtentPrintableArea * scaleFactorForDisplay.
a4PrintableArea := Morph new extent:  a4PrintableAreaExtentForDisplay.
a4PrintableArea color: Color white.


a4 addMorph: a4PrintableArea.

boxHeight := (a4PrintableArea height) /4.

boxWidth := (a4PrintableArea width) /3.
innerBoxWidth := boxHeight / (2 sqrt).

0 to: 3 do: [:row |
	0 to: 2 do: [:col | 
		box:= Morph new extent: innerBoxWidth@boxHeight; color: Color random; borderWidth: 0.
		centerPoint := ((col+0.5) * boxWidth)@((row+0.5) * boxHeight).
		box center: centerPoint.
		a4PrintableArea addMorph: box ]
	].

a4PrintableArea center: a4 center.
a4 openInHand

To consider for continuing the work:

maintain the dimensioning in millimeters
the scaleFactor needs to be a property of the morph so that if it is to be printed the scaling may be done accordingly.
for morphs which are placed on the sheets the position is still given in mm.
if there is the need to go for fractions of mm then the position and extent needs to be added as a property of the morph. The property will be used when printing or exporting.

Also see

SVG minimal document - LODraw export (A4 size SVG export)