= Hodograph plane
{title2=$q=u-iv$}
The hodograph plane records <velocity> rather than position. For a two-dimensional <potential flow>, the complex coordinate $q=u-iv$ is the <complex velocity>. A straight impermeable wall fixes the <velocity> direction and hence maps to a radial line in this plane. A constant-<speed> <free streamline> maps to a circle centered at zero. Thus a free-<boundary> problem in physical space can become a fixed geometric domain in <velocity> space. Recovering the physical map then uses $dz/dw=1/q(w)$, wherever $q$ is nonzero.
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