Constructed from their Support Functions

The support function is

h(t) = 16 + fourier3*cos(3*t) + fourier5*cos(5*t)

c(t) = h(t)*[cos(t),sin(t)] + h'(t)*[-sin(t), cos(t)]

c'(t) = (h(t) + h''(t))*[-sin(t), cos(t)].

The curve is called of "constant width" because the

distance between parallel tangents (a sort of diameter)

is the constant h(t) + h(t+pi).

The curve has singularities where h(t) + h''(t) = 0.

h(t) = 16 + fourier3*cos(3*t) + fourier5*cos(5*t)

c(t) = h(t)*[cos(t),sin(t)] + h'(t)*[-sin(t), cos(t)]

c'(t) = (h(t) + h''(t))*[-sin(t), cos(t)].

The curve is called of "constant width" because the

distance between parallel tangents (a sort of diameter)

is the constant h(t) + h(t+pi).

The curve has singularities where h(t) + h''(t) = 0.