Roulette (curve) application of this is that a square wheel could roll without bouncing on a road that is a matched series of catenary arcs. Roulette (curve) In the differential geometry of curves, a roulette is a kind of curve, generalizing cycloids, epicycloids, hypocycloids, trochoids, and involutes. Roughly speaking, a roulette is the curve described by a point (called the "generator" or "pole") attached to a given curve as that curve rolls without slipping, along a second given curve that is fixed. More precisely, given a curve attached to a plane which is moving so that the curve rolls, without slipping, along
Intersection curve has to fulfill the condition formula_29, because formula_28 has to be a tangent vector, which means any contour point is a point of the intersection curve of the two implicit surfaces For quadrics, formula_32 is always a linear function. Hence the contour line of a quadric is always a plane section (i.e. a conic section). The contour line of the surface formula_33 (see picture) was traced by the marching method. "Remark:" The determination of a contour polygon of a parametric surface formula_34 needs tracing an implicit curve in parameter plane. The intersection curve of two polyhedrons is a polygon (see