Roulette (curve) in this case, the point lies on the circle then the roulette is a cycloid. A related concept is a glissette, the curve described by a point attached to a given curve as it slides along two (or more) given curves. Formally speaking, the curves must be differentiable curves in the Euclidean plane. The "fixed curve" is kept invariant; the "rolling curve" is subjected to a continuous congruence transformation such that at all times the curves are tangent at a point of contact that moves with the same speed when taken along either curve (another way to express this constraint
Singular point of a curve or on a parametrised curve, "g"("t") = ("t","t"). Both definitions give a singular point at the origin. However, a node such as that of "y"−"x"−"x" = 0 at the origin is a singularity of the curve considered as an algebraic curve, but if we parameterize it as "g"("t") = ("t"−1,"t"("t"−1)), then "g"′("t") never vanishes, and hence the node is "not" a singularity of the parameterized curve as defined above. Care needs to be taken when choosing a parameterization. For instance the straight line "y" = 0 can be parameterised by "g"("t") = ("t",0) which has a singularity at the origin.