Image: Flag of Canada (construction sheet - leaf geometry)

Description: 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.
Usage Terms: Public domain