  This paper introduces a novel class of fair and interpolatory curves called
$p\kappa$-curves. These curves are comprised of smoothly stitched B\'ezier
curve segments, where the curvature distribution of each segment is made to
closely resemble a parabola, resulting in an aesthetically pleasing shape.
Moreover, each segment passes through an interpolated point at a parameter
where the parabola has an extremum, encouraging the alignment of interpolated
points with curvature extrema. To achieve these properties, we tailor an energy
function that guides the optimization process to obtain the desired curve
characteristics. Additionally, we develop an efficient algorithm and an
initialization method, enabling interactive modeling of the $p\kappa$-curves
without the need for global optimization. We provide various examples and
comparisons with existing state-of-the-art methods to demonstrate the curve
modeling capabilities and visually pleasing appearance of $p\kappa$-curves.
