# Category: Splines (mathematics)

Smoothing spline
Smoothing splines are function estimates, , obtained from a set of noisy observations of the target , in order to balance a measure of goodness of fit of to with a derivative based measure of the smoo
Hermite spline
In the mathematical subfield of numerical analysis, a Hermite spline is a spline curve where each polynomial of the spline is in Hermite form.
Akima spline
In applied mathematics, an Akima spline is a type of non-smoothing spline that gives good fits to curves where the second derivative is rapidly varying. The Akima spline was published by Hiroshi Akima
M-spline
In the mathematical subfield of numerical analysis, an M-spline is a non-negative spline function.
Composite Bézier curve
In geometric modelling and in computer graphics, a composite Bézier curve or Bézier spline is a spline made out of Bézier curves that is at least continuous. In other words, a composite Bézier curve i
Kochanek–Bartels spline
In mathematics, a Kochanek–Bartels spline or Kochanek–Bartels curve is a cubic Hermite spline with tension, bias, and continuity parameters defined to change the behavior of the tangents. Given n + 1
Biarc
A biarc is a smooth curve formed from two circular arcs. In order to make the biarc smooth (G1 continuous), the two arcs should have the same tangent at the connecting point where they meet. Biarcs ar
De Boor's algorithm
In the mathematical subfield of numerical analysis de Boor's algorithm is a polynomial-time and numerically stable algorithm for evaluating spline curves in B-spline form. It is a generalization of de
Coons patch
In mathematics, a Coons patch, is a type of surface patch or manifold parametrization used in computer graphics to smoothly join other surfaces together, and in computational mechanics applications, p
Thin plate energy functional
The exact thin plate energy functional (TPEF) for a function is where and are the principal curvatures of the surface mapping at the point This is the surface integral of hence the in the integrand. M
Variation diminishing property
In mathematics, the variation diminishing property of certain mathematical objects involves diminishing the number of changes in sign (positive to negative or vice versa).
I-spline
In the mathematical subfield of numerical analysis, an I-spline is a monotone spline function.
Centripetal Catmull–Rom spline
In computer graphics, the centripetal Catmull–Rom spline is a variant form of the Catmull–Rom spline, originally formulated by Edwin Catmull and Raphael Rom, which can be evaluated using a recursive a
Non-uniform rational B-spline
Non-uniform rational basis spline (NURBS) is a mathematical model using basis splines (B-splines) that is commonly used in computer graphics for representing curves and surfaces. It offers great flexi
Cubic Hermite spline
In numerical analysis, a cubic Hermite spline or cubic Hermite interpolator is a spline where each piece is a third-degree polynomial specified in Hermite form, that is, by its values and first deriva
Polyharmonic spline
In applied mathematics, polyharmonic splines are used for function approximation and data interpolation. They are very useful for interpolating and fitting scattered data in many dimensions. Special c
Thin plate spline
Thin plate splines (TPS) are a spline-based technique for data interpolation and smoothing. They were introduced to geometric design by Duchon. They are an important special case of a polyharmonic spl
Spline interpolation
In the mathematical field of numerical analysis, spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial called a spline. That is, instead of fi
Spline wavelet
In the mathematical theory of wavelets, a spline wavelet is a wavelet constructed using a spline function. There are different types of spline wavelets. The interpolatory spline wavelets introduced by
Monotone cubic interpolation
In the mathematical field of numerical analysis, monotone cubic interpolation is a variant of cubic interpolation that preserves monotonicity of the data set being interpolated. Monotonicity is preser
B-spline
In the mathematical subfield of numerical analysis, a B-spline or basis spline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition. Any splin
Perfect spline
In the mathematical subfields function theory and numerical analysis, a univariate polynomial spline of order is called a perfect spline if its -th derivative is equal to or between knots and changes
Box spline
In the mathematical fields of numerical analysis and approximation theory, box splines are piecewise polynomial functions of several variables. Box splines are considered as a multivariate generalizat
Spline (mathematics)
In mathematics, a spline is a special function defined piecewise by polynomials.In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar
Interpolation (computer graphics)
In the context of live-action and computer animation, interpolation is inbetweening, or filling in frames between the key frames. It typically calculates the in-between frames through use of (usually)
De Casteljau's algorithm
In the mathematical field of numerical analysis, De Casteljau's algorithm is a recursive method to evaluate polynomials in Bernstein form or Bézier curves, named after its inventor Paul de Casteljau.
Discrete spline interpolation
In the mathematical field of numerical analysis, discrete spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial called a discrete spline. A di
Control point (mathematics)
In computer-aided geometric design a control point is a member of a set of points used to determine the shape of a spline curve or, more generally, a surface or higher-dimensional object. For Bézier c
T-spline
In computer graphics, a T-spline is a mathematical model for defining freeform surfaces. A T-spline surface is a type of surface defined by a network of control points where a row of control points is