In the
differential geometry of
surfaces, an asymptotic curve is a
curve always
tangent to an asymptotic direction of the surface (where they exist). It is sometimes called an asymptotic line, although it need not be a
line. An asymptotic direction is one in which the normal
curvature is zero. Which is to say: for a point on an asymptotic curve, take the
plane which bears both the curve's tangent and the surface's
normal at that point. The curve of intersection of the plane and the surface will have zero curvature at that point. Asymptotic direction only occur when the
Gaussian curvature is negative. There will be two asymptotic directions through every point with negative Gaussian curvature, these directions are symmetric about the
principal directions.
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LINEA ASINTOTICA. ASINTOTO
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