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Let a patch be given by the map x:U->R^n, where U is an open subset of R^2, or more generally by x:A->R^n, where A is any subset of R^2. Then x(U) (or more generally, x(A)) ...

A line along a normal vector (i.e., perpendicular to some tangent line). If K subset R^d is a centrosymmetric set which has a twice differentiable boundary, then there are ...

The common axis of the three altitude planes of a trihedron.

A curve composed exclusively of circular arcs.

The positions of the geometric centroid of a planar non-self-intersecting polygon with vertices (x_1,y_1), ..., (x_n,y_n) are x^_ = ...

The directions in which the principal curvatures occur.

A tangent vector v_(p)=v_1x_u+v_2x_v is a principal vector iff det[v_2^2 -v_1v_2 v_1^2; E F G; e f g]=0, where e, f, and g are coefficients of the first fundamental form and ...

sigma=1/tau, where tau is the torsion. The symbol phi is also sometimes used instead of sigma.

A transformation consisting of rotations and translations which leaves a given arrangement unchanged.

The curve b(u) in the ruled surface parameterization x(u,v)=b(u)+vd(u) is called the directrix (or base curve).