𐍆𐌴𐌹𐌻𐌰:Flag of Canada (construction sheet - leaf geometry).svg

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𐍆𐍂𐌿𐌼𐌹𐍃𐍄 𐍆𐌰𐌾𐌻 ‎(SVG file, nominally 1,400 × 728 pixels, file size: 17 KB)

𐍃𐍉 𐌳𐌰𐍄𐌰 𐌹𐍃𐍄 𐍆𐍂𐌰𐌼 Wikimedia Commons 𐌾𐌰𐌷 𐌼𐌰𐌲 𐌱𐍂𐌿𐌺𐌾𐌰𐌳𐌰 𐍆𐍂𐌰𐌼 𐌰𐌽𐌸𐌰𐍂𐌰𐌹𐌼 𐍆𐌰𐌿𐍂𐌰𐍅𐌰𐌿𐍂𐍀𐍉𐌼. 𐌲𐌰𐍃𐌺𐌴𐌹𐍂𐌴𐌹𐌽𐍃 𐌰𐌽𐌰 𐍃𐌴𐌹𐌽𐌰𐌼𐌼𐌰 𐌳𐌰𐍄𐌰 𐍃𐌺𐌴𐌹𐍂𐌴𐌹𐌽𐌹𐌻𐌰𐌿𐌱𐌰 𐌾𐌰𐌹𐌽𐌰𐍂 𐌰𐍄𐌰𐌿𐌲𐌹𐌸𐍃 𐌹𐍃𐍄 𐌿𐍆.

𐌼𐌰𐌿𐍂𐌲𐌿𐍃 𐍃𐌺𐌴𐌹𐍂𐌴𐌹𐌽𐍃

𐍃𐌺𐌴𐌹𐍂𐌴𐌹𐌽𐍃
English: Construction sheet for the flag of Canada with an unofficial (but highly accurate) mathematical representation of the maple leaf.


The government of Canada has never provided a mathematical or geometric description of the maple leaf on the Canadian flag.
Two government drawings of the flag exist:

  • An official hand drawn design drawing from 1964 complete with grid overlay. It has a few minor asymmetry errors.
  • A modern looking vector image created with aid of a computer; it is basically a tracing of the 1964 drawing with asymmetry corrections applied.


The diagram on this construction sheet is based on careful measurements taken from an image of the 1964 drawing as it appears in CAN/CGSB-98.1-2003; corrections have been applied to remove asymmetries. The result is very close to the government vector image which can be found in CAN/CGSB-98.1-2018.

The maple leaf can be drawn with 25 line segments and 12 minor arcs. Bézier curves are not required. Each line segment (except for the one on the bottom of the stem) is connected to one end of a minor arc. The line segments are tangent to their connected arcs such that each transition from line segment to arc forms a mathematically smooth path.

The full mathematical representation uses a 1920×960 grid and a standard Cartesian coordinate system. The following are defined:

  • Grid coordinates for all eleven points on the leaf.
  • Grid coordinates for the two points that lay at the bottom of the stem.
  • Angles of 24 line segments expressed in whole degrees and measured CCW from the X-axis.
  • Arc radii for all 12 arcs expressed in grid units.

The following can be derived using trigonometry:

  • Coordinates of the points of tangency (these are the points where the line segments and arcs meet).
  • Coordinates of the arc centrepoints (not required by SVG paths but may be useful for other purposes).
  • Arc central angles (not required by SVG paths but may be useful for other purposes)
For anybody not wishing to do the math themselves, the coordinates for the points of tangency and the centrepoints have been calculated and are displayed in the side panels with rounding to 3 decimal places.
Français : Feuille de construction pour le drapeau du Canada avec une représentation mathématique non officielle (mais très précise) de la feuille d'érable.


Le gouvernement du Canada n'a jamais fourni de description mathématique ou géométrique de la feuille d'érable sur le drapeau canadien.
Deux dessins gouvernementaux du drapeau existent:

  • Un dessin de conception officiel dessiné à la main de 1964 avec superposition de grille. Il a quelques erreurs d'asymétrie mineures.
  • Une image vectorielle d'aspect moderne créée à l'aide d'un ordinateur ; il s'agit essentiellement d'un calque du dessin de 1964 avec des corrections d'asymétrie appliquées.


Le schéma de cette feuille de construction est basé sur des mesures minutieuses prises à partir d'une image du dessin de 1964 tel qu'il apparaît dans la norme CAN/CGSB-98.1-2003; des corrections ont été appliquées pour éliminer les asymétries. Le résultat est très proche de l'image vectorielle du gouvernement qui se trouve dans CAN/CGSB-98.1-2018.
Date
𐌱𐍂𐌿𐌽𐌽𐌰 𐍃𐍅𐌴𐍃 𐍅𐌰𐌿𐍂𐍃𐍄𐍅. Very careful measurements taken from an image of the official 1964 drawing of the Canadian flag
𐌱𐍉𐌺𐌰𐍂𐌴𐌹𐍃 MapGrid
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This diagram was created with perl.

Licensing

This work is ineligible for copyright and therefore in the public domain because it consists entirely of information that is common property and contains no original authorship.
Trademarked This work includes material that may be protected as a trademark in some jurisdictions. If you want to use it, you have to ensure that you have the legal right to do so and that you do not infringe any trademark rights. See our general disclaimer.
This tag does not indicate the copyright status of the attached work. A normal copyright tag is still required. See Commons:Licensing.
Insignia This image shows a flag, a coat of arms, a seal or some other official insignia. The use of such symbols is restricted in many countries. These restrictions are independent of the copyright status.


This file is saved in human-editable plain text format. Any editing of the image or creation of any derivative work should be performed using a text editor. Please do not upload edits saved or exported with Inkscape or similar vector graphics editors, as well as with automated tools such as SVG Translate.

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Flag of Canada (construction sheet with full maple leaf geometry)

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16 𐌾𐌰𐌽𐌿𐌰𐍂𐌴𐌹𐍃 2019

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𐍆𐌰𐌾𐌻𐌰𐍃𐍀𐌹𐌻𐌻

𐌰𐍄𐍄𐌴𐌺 𐌳𐌰𐌲/𐌼𐌴𐌻 𐌳𐌿 𐌱𐌰𐌽𐌳𐍅𐌾𐌰𐌽 𐍆𐌰𐌾𐌻 𐍃𐍅𐌰𐍃𐍅𐌴 𐌲𐌰𐌱𐌰𐌹𐍂𐌷𐍄𐌹𐌳𐌰 𐌹𐌽 𐌸𐌰𐌼𐌼𐌰 𐌼𐌴𐌻𐌰.

𐌼𐌴𐌻𐌻𐌴𐌹𐍄𐌹𐌻𐌰 𐍆𐍂𐌹𐍃𐌰𐌷𐍄𐍃𐍅𐌰𐌷𐍃𐍄𐌿𐍃𐌱𐍂𐌿𐌺𐌾𐌰𐌽𐌳𐍃/𐌱𐍂𐌿𐌺𐌾𐌰𐌽𐌳𐌹𐍅𐌰𐌿𐍂𐌳
𐌽𐌿06:37, 28 𐌾𐌰𐌽𐌿𐌰𐍂𐌴𐌹𐍃 2024𐌻𐌴𐌹𐍄𐌹𐌻𐌰𐍆𐍂𐌹𐍃𐌰𐌷𐍄𐍃 𐌿𐍃𐌼𐌴𐍂𐌾𐌰 𐌹𐌽 06:37, 28 𐌾𐌰𐌽𐌿𐌰𐍂𐌴𐌹𐍃 20241,400 × 728 (17 KB)Iketsiarc C (et arc J – pour la symétrie du code) déplacés de 3 px; espaces (fines) ajoutées devant les deux-points; français plus idiomatique; casse du titre corrigée; 3 <path> simplifiés; coordonnées intactes. C'est tout.
01:00, 5 𐍆𐌰𐌹𐌱𐍂𐌿𐌰𐍂𐌴𐌹𐍃 2022𐌻𐌴𐌹𐍄𐌹𐌻𐌰𐍆𐍂𐌹𐍃𐌰𐌷𐍄𐍃 𐌿𐍃𐌼𐌴𐍂𐌾𐌰 𐌹𐌽 01:00, 5 𐍆𐌰𐌹𐌱𐍂𐌿𐌰𐍂𐌴𐌹𐍃 20221,400 × 728 (17 KB)MapGridIncreased drawing resolution by 10. Fixed the "central angle" values listed in the side bars; previous version inadvertently showed supplements of the central angles. There is absolutely no change to the flag geometry.
03:28, 4 𐌰𐌿𐌺𐍄𐍉𐌱𐌰𐌹𐍂 2019𐌻𐌴𐌹𐍄𐌹𐌻𐌰𐍆𐍂𐌹𐍃𐌰𐌷𐍄𐍃 𐌿𐍃𐌼𐌴𐍂𐌾𐌰 𐌹𐌽 03:28, 4 𐌰𐌿𐌺𐍄𐍉𐌱𐌰𐌹𐍂 20191,400 × 728 (17 KB)MapGridReduced file size (only slightly). Changed drawing label. Redid the grid with an SVG pattern; hopefully Media Viewer will render it!
04:20, 17 𐌾𐌰𐌽𐌿𐌰𐍂𐌴𐌹𐍃 2019𐌻𐌴𐌹𐍄𐌹𐌻𐌰𐍆𐍂𐌹𐍃𐌰𐌷𐍄𐍃 𐌿𐍃𐌼𐌴𐍂𐌾𐌰 𐌹𐌽 04:20, 17 𐌾𐌰𐌽𐌿𐌰𐍂𐌴𐌹𐍃 20191,400 × 728 (17 KB)MapGridUser created page with UploadWizard

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