orientation-preserving

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… ►If

h(a)=a^{\prime}

and

h(b)=b^{\prime}

, then the reparametrization is called orientation-preserving, and … ►A parametrization

\boldsymbol{{\Phi}}(u,v)

of an oriented surface

S

is orientation preserving if

\mathbf{T}_{u}\times\mathbf{T}_{v}

has the same direction as the chosen normal at each point of

S

, otherwise it is orientation reversing. ►If

\boldsymbol{{\Phi}}_{1}

and

\boldsymbol{{\Phi}}_{2}

are both orientation preserving or both orientation reversing parametrizations of

S

defined on open sets

D_{1}

and

D_{2}

respectively, then …