# Category: Multivariate interpolation

Natural neighbor interpolation
Natural neighbor interpolation is a method of spatial interpolation, developed by Robin Sibson. The method is based on Voronoi tessellation of a discrete set of spatial points. This has advantages ove
Tricubic interpolation
In the mathematical subfield numerical analysis, tricubic interpolation is a method for obtaining values at arbitrary points in 3D space of a function defined on a regular grid. The approach involves
Nearest-neighbor interpolation
Nearest-neighbor interpolation (also known as proximal interpolation or, in some contexts, point sampling) is a simple method of multivariate interpolation in one or more dimensions. Interpolation is
Bilinear interpolation
In mathematics, bilinear interpolation is a method for interpolating functions of two variables (e.g., x and y) using repeated linear interpolation. It is usually applied to functions sampled on a 2D
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
Trend surface analysis
Trend surface analysis is a mathematical technique used in environmental sciences (archeology, geology, soil science, etc.). Trend surface analysis (also called trend surface mapping) is a method base
Bézier triangle
A Bézier triangle is a special type of Bézier surface that is created by (linear, quadratic, cubic or higher degree) interpolation of control points.
Multivariate interpolation
In numerical analysis, multivariate interpolation is interpolation on functions of more than one variable; when the variates are spatial coordinates, it is also known as spatial interpolation. The fun
PDE surface
PDE surfaces are used in geometric modelling and computer graphics for creating smooth surfaces conforming to a given boundary configuration. PDE surfaces use partial differential equations to generat
Nearest neighbor value interpolation
In mathematics applied to computer graphics, nearest neighbor value interpolation is an advanced method of image interpolation. This method uses the pixel value corresponding to the smallest absolute
Subdivision surface
In the field of 3D computer graphics, a subdivision surface (commonly shortened to SubD surface) is a curved surface represented by the specification of a coarser polygon mesh and produced by a recurs
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
Inverse distance weighting
Inverse distance weighting (IDW) is a type of deterministic method for multivariate interpolation with a known scattered set of points. The assigned values to unknown points are calculated with a weig
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
Doo–Sabin subdivision surface
In 3D computer graphics, a Doo–Sabin subdivision surface is a type of subdivision surface based on a generalization of bi-quadratic uniform B-splines, whereas Catmull-Clark was based on generalized bi
Loop subdivision surface
In computer graphics, the Loop method for subdivision surfaces is an approximating subdivision scheme developed by Charles Loop in 1987 for triangular meshes. Prior methods, namely Catmull-Clark and D
Bicubic interpolation
In mathematics, bicubic interpolation is an extension of cubic interpolation (not to be confused with cubic spline interpolation, a method of applying cubic interpolation to a data set) for interpolat
Kriging
In statistics, originally in geostatistics, kriging or Kriging, also known as Gaussian process regression, is a method of interpolation based on Gaussian process governed by prior covariances. Under s
Bézier surface
Bézier surfaces are a species of mathematical spline used in computer graphics, computer-aided design, and finite element modeling. As with Bézier curves, a Bézier surface is defined by a set of contr
Trilinear interpolation
Trilinear interpolation is a method of multivariate interpolation on a 3-dimensional regular grid. It approximates the value of a function at an intermediate point within the local axial rectangular p
Catmull–Clark subdivision surface
The Catmull–Clark algorithm is a technique used in 3D computer graphics to create curved surfaces by using subdivision surface modeling. It was devised by Edwin Catmull and Jim Clark in 1978 as a gene
Lanczos resampling
Lanczos filtering and Lanczos resampling are two applications of a mathematical formula. It can be used as a low-pass filter or used to smoothly interpolate the value of a digital signal between its s