If you consider a point on a radius of the rolling curve in generating a cardioid that is not on its circumference, the result is a conchoid called the limaçon of Pascal.
Any of a family of curves defined as the locus of points p, such that each p is on a line that passes through a given fixed point P and intersects a given curve, C, and the distance from p to the point of intersection with C is a specified constant (note that for nontrivial cases two such points p satisfy the criteria, and the resultant curve has two parts).