A heart-shaped curve traced by a point on a coin rolling round another coin. One big circle does almost all the work.
Measuring the shape…
r = 1 − sin θ
Roll a circle around another of the same size and a point on its rim traces a cardioid. You can also see one as the bright curve of light inside a coffee cup. The one sharp point (the cusp) is where the extra circles go.
Each path of the cardioid is traced by a chain of circles, each one spinning on the tip of the one before. A Fourier transform measures the path and works out every circle's size, speed and starting angle. The circles are sorted biggest first, so the first few give the rough shape and the rest add detail.
"Within 1%" means the drawing is, on average, less than 1% of its width away from the real outline. The bars show the circles of the main outline: height is size, position is how many times it turns per loop and in which direction. Click a bar to remove that circle and see what it was doing. Learn how it works.