曲線擬合

将函数拟合至数据点(Fitting functions to data points)

最常见的是，一函数符合y=f(x) 的形式。
(Most commonly, one fits a function of the form y=f(x).)

将其他函数拟合至数据点(Fitting other functions to data points)

其他类型的曲线在特定条件下也可使用，诸如三角函数(如正弦或是余弦函数)。
(Other types of curves, such as trigonometric functions (such as sine and cosine), may also be used, in certain cases.)
在光谱学中，数据可以用高斯，罗伦兹，Voigt 和相关函数来拟合。
(In spectroscopy, data may be fitted with Gaussian, Lorentzian, Voigt and related functions.)
在农业中，反向逻辑S函数 (S曲线）用于描述作物产量和生长因子之间的关系。 蓝色图形是将农田中测量数据进行S形回归得出的。 可以看出在初始情况，即土壤低盐度的状况下，作物产量在土壤盐度增加时缓慢降低，而之后降得更快。
(In agriculture the inverted logistic sigmoid function (S-curve) is used to describe the relation between crop yield and growth factors. The blue figure was made by a sigmoid regression of data measured in farm lands. It can be seen that initially, i.e. at low soil salinity, the crop yield reduces slowly at increasing soil salinity, while thereafter the decrease progresses faster.)

将平面曲线拟合至数据点(Fitting plane curves to data points)

If a function of the form  cannot be postulated, one can still try to fit a plane curve.
Other types of curves, such as conic sections (circular, elliptical, parabolic, and hyperbolic arcs) or trigonometric functions (such as sine and cosine), may also be used, in certain cases.  For example, trajectories of objects under the influence of gravity follow a parabolic path, when air resistance is ignored.  Hence, matching trajectory data points to a parabolic curve would make sense.  Tides follow sinusoidal patterns, hence tidal data points should be matched to a sine wave, or the sum of two sine waves of different periods, if the effects of the Moon and Sun are both considered.
For a parametric curve, it is effective to fit each of its coordinates as a separate function of arc length; assuming that data points can be ordered, the chord distance may be used.

Fitting a circle by geometric fit

Coope approaches the problem of trying to find the best visual fit of circle to a set of 2D data points. The method elegantly transforms the ordinarily non-linear problem into a linear problem that can be solved without using iterative numerical methods, and is hence an order of magnitude faster than previous techniques.

Fitting an ellipse by geometric fit

The above technique is extended to general ellipses by adding a non-linear step, resulting in a method that is fast, yet finds visually pleasing ellipses of arbitrary orientation and displacement.