A generalization replaces the perpendicular by a line making a fixed angle with the tangent,
where .
For either consistent choice of the angle, the resulting
locus is obtained from the ordinary pedal curve by a rotation through and a dilation
by , both centered at the pedal
point (Sánchez-Ramos et al. 2021, p. 198).
When a closed curve rolls on a line, the area between the line and roulette after a complete revolution by any point
on the curve is twice the area
of the pedal curve (taken with respect to the generating point) of the rolling curve.
with respect to a fixed point 
(called the pedal
point) is the locus of the foot of the perpendicular
from 
to a tangent
to 
. The parametric equations for a curve 
relative to the pedal
point 
are given by
with the tangent,
where 
.
For either consistent choice of the angle, the resulting
locus is obtained from the ordinary pedal curve by a rotation through 
and a dilation
by 
, both centered at the pedal
point (Sánchez-Ramos et al. 2021, p. 198).
is the pedal curve of a curve 
, then 
is the negative pedal curve
of 
(Lawrence 1972, pp. 47-48).
