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Parallel curves, frequently called "offset curves" in computer graphics applications, are curves which are displaced from a base curve by a constant offset, either positive ...

The Plateau curves were studied by the Belgian physicist and mathematician Joseph Plateau. They have Cartesian equation x = (asin[(m+n)t])/(sin[(m-n)t]) (1) y = ...

A curve y(x) is osculating to f(x) at x_0 if it is tangent at x_0 and has the same curvature there. Osculating curves therefore satisfy y^((k))(x_0)=f^((k))(x_0) for k=0, 1, ...

Two (or more) intersecting curves that are perpendicular at their intersection are said to be orthogonal.

A set of curves whose equations are of the same form but which have different values assigned to one or more parameters in the equations. Families of curves arise, for ...

Two curves both containing the point P are tangent at P if they share the same tangent line at P.

Two curves which, at any point, have a common principal normal vector are called Bertrand curves. The product of the torsions of Bertrand curves is a constant.

The parallel curves for (outward) offset k of an ellipse with semi-axis lengths a and b are given by x_p = (a+(bk)/(sqrt(a^2sin^2t+b^2cos^2t)))cost (1) y_p = ...

The parallel curves of a circle with radius a with offset k are given by the parametric equations x_p(t) = (a+k)cost (1) y_p(t) = (a+k)sint (2) and are therefore themselves ...

Two curves phi and psi satisfying phi+psi=0 are said to be linearly dependent. Similarly, n curves phi_i, i=1, ..., n are said to be linearly dependent if sum_(i=1)^nphi_i=0.