Python script to generate a "squircle" in svg format.

squircle.py

# Loosely based on the constants found by Liam Rosenfeld
# https://liamrosenfeld.com/posts/apple_icon_quest/

# Node coordinates
n1 = 0.63149379
n2 = 0.07491139
# Handle coordinates
h1 = 0.86840694
h2 = 0.37282383
h3 = 0.16905956


def squircle(size: float, r: float):
    w = size
    h = size

    def top_left(x: float, y: float) -> str:
        return f"{x*r:.2f},{y*r:.2f}"

    def top_right(x: float, y: float) -> str:
        return f"{w-x*r:.2f},{y*r:.2f}"

    def btm_right(x: float, y: float) -> str:
        return f"{w-x*r:.2f},{h-y*r:.2f}"

    def btm_left(x: float, y: float) -> str:
        return f"{x*r:.2f},{h-y*r:.2f}"

    return f"\
M{w/2},{0} \
\
C{top_right(h1, 0)}\
 {top_right(h1, 0)}\
 {top_right(n1, n2)} \
C{top_right(h2, h3)}\
 {top_right(h3, h2)}\
 {top_right(n2, n1)} \
C{top_right(0, h1)}\
 {top_right(0, h1)}\
 {w},{h/2} \
\
C{btm_right(0, h1)}\
 {btm_right(0, h1)}\
 {btm_right(n2, n1)} \
C{btm_right(h3, h2)}\
 {btm_right(h2, h3)}\
 {btm_right(n1, n2)} \
C{btm_right(h1, 0)}\
 {btm_right(h1, 0)}\
 {w/2},{h} \
\
C{btm_left(h1, 0)}\
 {btm_left(h1, 0)}\
 {btm_left(n1, n2)} \
C{btm_left(h2, h3)}\
 {btm_left(h3, h2)}\
 {btm_left(n2, n1)} \
C{btm_left(0, h1)}\
 {btm_left(0, h1)}\
 {0},{h/2} \
\
C{top_left(0, h1)}\
 {top_left(0, h1)}\
 {top_left(n2, n1)} \
C{top_left(h3, h2)}\
 {top_left(h2, h3)}\
 {top_left(n1, n2)} \
C{top_left(h1, 0)}\
 {top_left(h1, 0)}\
 {w/2},{0}"


if __name__ == "__main__":
    import argparse
    parser = argparse.ArgumentParser(
        description="Create a squircle with given size and radius."
    )
    parser.add_argument(
        "size", type=int, help="The size (required).")
    parser.add_argument("--radius", type=int,
                        help="The radius (defaults to 0.45 * size/2).")

    # Parse the arguments
    args = parser.parse_args()
    size = args.size
    r = 0.45*args.size/2 if args.radius is None else args.radius
    print(f'\
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 {size} {size}">\n\
  <path d="{squircle(size, r)}" />\n\
</svg>')

squircle.svg

<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 32 32">
  <path d="M16.0,0 C25.75,0.00 25.75,0.00 27.45,0.54 C29.32,1.22 30.78,2.68 31.46,4.55 C32.00,6.25 32.00,6.25 32,16.0 C32.00,25.75 32.00,25.75 31.46,27.45 C30.78,29.32 29.32,30.78 27.45,31.46 C25.75,32.00 25.75,32.00 16.0,32 C6.25,32.00 6.25,32.00 4.55,31.46 C2.68,30.78 1.22,29.32 0.54,27.45 C0.00,25.75 0.00,25.75 0,16.0 C0.00,6.25 0.00,6.25 0.54,4.55 C1.22,2.68 2.68,1.22 4.55,0.54 C6.25,0.00 6.25,0.00 16.0,0" />
</svg>