Convex Curves of Constant Width
Constructed from their Support Functions

Modify the curve

fourier3,  0 ... 2:


fourier5,  0 ... 1:










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.
convex curve morph 001
convex curve morph in a square box

Convex_Curve.pdf