In mathematics, a spline is a special function defined piecewise by polynomials.[1] In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low-degree polynomials, while avoiding Runge's phenomenon for higher degrees.
In the computer science subfields of computer-aided design and computer graphics, the term spline more frequently refers to a piecewise polynomial (parametric) curve. Splines are popular curves in these subfields because of the simplicity of their construction, their ease and accuracy of evaluation, and their capacity to approximate complex shapes through curve fitting and interactive curve design.
The term spline comes from the flexible spline devices used by shipbuilders and draftsmen to draw smooth shapes.
https://en.wikipedia.org/wiki/Spline_(mathematics)
In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point.[1][2][3][4]
https://en.wikipedia.org/wiki/Spiral
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.
Definitions[edit]
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 directions can only occur when the Gaussian curvature is negative (or zero). There will be two asymptotic directions through every point with negative Gaussian curvature, bisected by the principal directions. If the surface is minimal, the asymptotic directions are orthogonal to one another.
Related notions[edit]
The direction of the asymptotic direction are the same as the asymptotes of the hyperbola of the Dupin indicatrix.[1]
A related notion is a curvature line, which is a curve always tangent to a principal direction.
https://en.wikipedia.org/wiki/Asymptotic_curve
No comments:
Post a Comment