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Spline function
In numerical analysis, a B-spline (short for basis spline) is a type of spline function designed to have minimal support (overlap) for a given degree
B-spline
Type of cardinal spline
Catmull–Rom spline is a special case of a cardinal spline. This assumes uniform spacing of the control points p k {\displaystyle {\boldsymbol {p}}_{k}}
Catmull–Rom_spline
Mathematical function defined piecewise by polynomials
In mathematics, a spline is a function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial
Spline_(mathematics)
Wavelet constructed using a spline function
wavelets, a spline wavelet is a wavelet constructed using a spline function. There are different types of spline wavelets. The interpolatory spline wavelets
Spline_wavelet
Method of representing curves and surfaces in computer graphics
Non-uniform rational basis spline (NURBS) is a mathematical model using basis splines (B-splines) that is commonly used in computer graphics for representing
Non-uniform_rational_B-spline
Mathematical method
analysis, spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial called a spline. That is, instead
Spline_interpolation
therefore they integrate well with the existing NURBS (Non-Uniform Rational B-Spline) based industry standard CAD/CAM systems. They are readily amenable to
Rational_motion
Method of defining complex surfaces in computer graphics
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
T-spline
Class of numerical simulation algorithms
method's strengths. These issues can be address by incorporating cubic B-spline functions with C squared continuity across element boundaries as the global
Smoothed finite element method
Smoothed_finite_element_method
Method of evaluating spline curves
polynomial-time and numerically stable algorithm for evaluating spline curves in B-spline form. It is a generalization of de Casteljau's algorithm for Bézier
De_Boor's_algorithm
Function used in signal processing
sample the appropriate normalized B-spline basis functions instead of convolving discrete-time windows. A kth-order B-spline basis function is a piece-wise
Window_function
Type of artificial neural network architecture
the spline function. The spline function can be a sum of B-splines. spline ( x ) = ∑ i c i B i ( x ) {\displaystyle {\text{spline}}(x)=\sum _{i}c_{i}B_{i}(x)}
Kolmogorov–Arnold_Networks
Type of spline in applied mathematics
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
Akima_spline
Computer-aided design approach
functions can be introduced in this context, such as B-splines, NURBS and T-splines. B-splines can be derived recursively from a piecewise constant function
Isogeometric_analysis
Method of representing a 3D object by defining the limits of its volume
or a swept surface, or B-spline surface. The boundaries are defined by lines, conics, polylines, surface curves, or b spline curves ISO 10303-514 Advanced
Boundary_representation
Method of function approximation and data interpolation
dimensions. Special cases include thin plate splines and natural cubic splines in one dimension. A polyharmonic spline is a linear combination of polyharmonic
Polyharmonic_spline
Curved curface derived from a coarse polygon mesh
is analogous to spline surfaces and curves, where Bézier curves are required to interpolate certain control points, while B-Splines are not (and are
Subdivision_surface
Method of smoothing using a spline function
Smoothing splines are function estimates, f ^ ( x ) {\displaystyle {\hat {f}}(x)} , obtained from a set of noisy observations y i {\displaystyle y_{i}}
Smoothing_spline
Variant form of the Catmull-Rom spine
In computer graphics, the centripetal Catmull–Rom spline is a variant form of the Catmull–Rom spline, originally formulated by Edwin Catmull and Raphael
Centripetal Catmull–Rom spline
Centripetal_Catmull–Rom_spline
Geometric shape
modelling and in computer graphics, a composite Bézier curve or Bezier spline is a spline made out of Bézier curves that is at least C 0 {\displaystyle C^{0}}
Composite_Bézier_curve
frequency B-spline wavelets. These frequency B-spline wavelets are complex wavelets whose spectrum are spline. fbsp ( m − f b − f c ) ( t ) := f b sinc m
Fbsp_wavelet
Technique in 3D computer graphics
Catmull and Jim Clark in 1978 as a generalization of bi-cubic uniform B-spline surfaces to arbitrary topology. In 2005/06, Edwin Catmull, together with
Catmull–Clark subdivision surface
Catmull–Clark_subdivision_surface
Filter in digital signal processing
The Mitchell–Netravali filters or BC-splines are a group of reconstruction filters used primarily in computer graphics, which can be used, for example
Mitchell–Netravali_filters
Cubic function used for interpolation
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
Cubic_Hermite_spline
Computer-aided geometric design
cubic B-spline curves, and in 1979, de Boor independently proposed this algorithm. In 2004, Hongwei Lin and coauthors proved that non-uniform cubic B-spline
Progressive-iterative approximation method
Progressive-iterative_approximation_method
Curve used in computer graphics and related fields
Implementation of Bézier and B-Spline Geometry. SAND2022-7702C. (153 pages) Computer code TinySpline: Open source C-library for NURBS, B-splines and Bézier curves
Bézier_curve
3D computer graphics software
perpetual license. It is pitched as CAD for artists. Non-uniform rational B-spline Solid modeling Polygon mesh modeling Boolean operations Real-time rendering
Plasticity_(software)
Generalization of basis splines (B-splines) to multiple variables
box splines are piecewise polynomial functions of several variables. Box splines are considered as a multivariate generalization of basis splines (B-splines)
Box_spline
Species of mathematical spline
Bézier surfaces are a type of mathematical spline used in computer graphics, computer-aided design, and finite element modeling. As with Bézier curves
Bézier_surface
Polygonal curve Maurer rose Reuleaux triangle Stadium Splines B-spline Nonuniform rational B-spline Blancmange curve De Rham curve Dragon curve Koch curve
List_of_curves
American 3D graphics software company
as a separate corporate entity. The development of non-uniform rational B-spline (NURBS) originated with seminal work at Boeing and Structural Dynamics
Solid_Modeling_Solutions
Tent function, often used in signal processing
wave, a piecewise linear periodic function Trigonometric functions "Basic properties of splines and B-splines" (PDF). INF-MAT5340 Lecture Notes. p. 38.
Triangular_function
transport Parametric curve Bézier curve Spline (mathematics) Hermite spline Beta spline B-spline Higher-order spline NURBS Perimeter Pi Plane curve Pochhammer
List_of_curves_topics
American mathematician
modeling and computer graphics, known for her pioneering research on B-splines. She was a professor in the school of computing at the University of Utah
Elaine_Cohen
Element of a basis for a function space
function nonzero only on part of the domain. B-spline basis functions are a standard example. A spline of degree p can be written in the form S ( x )
Basis_function
3D computer graphics software
founded in 1978. Rhinoceros geometry is based on the non-uniform rational B-spline (NURBS) mathematical model, which focuses on producing mathematically precise
Rhinoceros_3D
Filter in electronics and signal processing
convolution with the constant B-spline (a rectangular pulse). For example, four iterations of a moving average yield a cubic B-spline as a filter window, which
Gaussian_filter
Golden spiral Syntractrix Tractrix Trochoid Bézier curve Splines B-spline Nonuniform rational B-spline Ogee Loess curve Lowess Polygonal curve Maurer rose
List_of_mathematical_shapes
Points used to define the shape of curves and surfaces
of a polynomial curve as well as for the B-spline representation of a spline curve or tensor-product spline surface. Salomon, David (2007), Curves and
Control_point_(mathematics)
Form of computer-aided engineering
closer to that point. Curve types include nonuniform rational B-spline (NURBS), splines, patches, and geometric primitives. Digital sculpting – There
3D_modeling
Type of polygon mesh in computer graphics
generalization of bi-quadratic uniform B-splines, whereas Catmull-Clark was based on generalized bi-cubic uniform B-splines. The subdivision refinement algorithm
Doo–Sabin_subdivision_surface
Industrial design software
generating class A surfaces using Bézier surface and non-uniform rational B-spline (NURBS) modeling method. The product is sold specifically as CAID rather
Autodesk_Alias
CAD software
analysis, parametric modelling, sub-divisional and non-uniform rational B-spline (NURBS) surface modeling, technical drawing (drafting), and numerical control
Creo_Parametric
and a CDF 9/7 wavelet for lossy compression. The primal generator is a B-spline if the simple factorization q prim ( X ) = 1 {\displaystyle q_{\text{prim}}(X)=1}
Cohen–Daubechies–Feauveau wavelet
Cohen–Daubechies–Feauveau_wavelet
interpolation through key points see cardinal spline. For examples which go near key points see nonuniform rational B-spline, or Bézier curve. This is extended to
Interpolation (computer graphics)
Interpolation_(computer_graphics)
Experiment methodology
A/B testing (also known as bucket testing, split-run testing or split testing) is a user-experience research method. A/B tests consist of a randomized
A/B_testing
Ukrainian-American theoretical and computational physicist
Atomic, Molecular & Optical Physics in 2008, for "the development of the B-Spline R-matrix method with non-orthogonal orbital sets for atomic structure calculations
Oleg_Zatsarinny
Set of data points in three-dimensional space
converted to polygon mesh or triangle mesh models, non-uniform rational B-spline (NURBS) surface models, or CAD models through a process commonly referred
Point_cloud
2D vector graphics editor and animation software
existing curves. Arc, Spiral, and Triangle tools create curves B-Spline tool creates B-Spline curves Context-sensitive Node tool provides control over post-editing
DrawPlus
Open-source 3D modelling software
hyperbola, parabola, Bézier, B-spline, offset; analytical surfaces: plane, cylinder, cone, sphere, torus, Bézier, B-spline, revolution, extrusion, offset)
Open_Cascade_Technology
Vector graphics editor
Boolean operations, plotting implicit functions, non-uniform rational B-spline (NURBS) and more. 2Geom is free software released under LGPL 2.1 or MPL
Inkscape
Function defined by multiple sub-functions
sub-functions Spline, a function composed of polynomial sub-functions, often constrained to be smooth at the joints between pieces B-spline f ( x ) = {
Piecewise_function
descriptions that are commonly used today, such as B-spline surfaces, non-uniform rational B-spline (NURB) surfaces, etc. His technique for describing
Steven_Anson_Coons
3D schematic representation of protein structure
fitted cubic polynomial B-spline curves to the peptide planes. Most modern graphics systems provide either B-splines or Hermite splines as a basic drawing
Ribbon_diagram
Closed volume that completely contains the union of a set of objects
useful to speedup the clipping or visibility test of a B-Spline curve. See "Circle and B-Splines clipping algorithms" under the subject Clipping (computer
Bounding_volume
Video software application produced by Apple Inc.
Rectangle, ellipse, Bézier curve and B-spline creation tools. The text tool. Rectangle, ellipse, Bézier and B-spline masking tools (which define the part
Motion_(software)
3D rendering program
usda, .usdc, .usdz) List of 3D rendering software Non-uniform rational B-spline https://www.creativebloq.com/reviews/keyshot-2023 https://develop3d
Keyshot
three-dimensional analogs of parametric curves such as Bézier curves, B-splines, or NURBs. The technique was first described by Thomas W. Sederberg and
Free-form_deformation
Wavelet proportional to the second derivative of a Gaussian
explained in appendix A in Lindeberg (2015). Derivatives of cardinal B-splines can also approximate the Mexican hat wavelet. Since Ricker wavelet is
Ricker_wavelet
Time Protocol NUMA—Non-Uniform Memory Access NURBS—Non-Uniform Rational B-Spline NUT—Network UPS Tools NVD—National Vulnerability Database NVMe—NVM Express
List of computing and IT abbreviations
List_of_computing_and_IT_abbreviations
Computer scientist and co-founder of Pixar (born 1945)
surfaces came from mathematical structures in his mind when he applied B-splines to non-four sided objects. He also independently discovered Z-buffering
Edwin_Catmull
Method of multivariate interpolation on a 3-dimensional regular grid
at trilinear interpolation, which is equivalent to 3-dimensional tensor B-spline interpolation of order 1, and the trilinear interpolation operator is also
Trilinear_interpolation
Canadian software company
Alias Maya. Sketch provided the basis of the core non-uniform rational B-spline (NURBS) editing tools, which in turn was based on a product that the company
Alias_Systems_Corporation
Use of software to manipulate a digital object
modeling 3D printing List of digital art software NURBS (non-uniform rational B-spline) Polygon mesh Polygonal modeling Sketch-based modeling Subdivision surface
Digital_sculpting
Basic shapes represented in vector graphics
functions, similar to a spline or Bézier curve in two dimensions. The most common structure is the Non-uniform rational B-spline (NURBS), supported by most
Geometric_primitive
Filter used to construct a smooth analog signal from a digital input
various widths, or cardinal B-splines of higher order – the box filter and tent filter being the 0th and 1st order cardinal B-splines. These filters fail to
Reconstruction_filter
Multi-platform game engine by Square Enix
NURBS based geometry for hair and beard, including NURB curves, B-splines and T-splines 50 hair shaders High-dynamic-range rendering, including HDR lighting
Luminous_Engine
Framework for multi-scale signal representation
Scale-Equivariant Steerable Networks (Preprint). arXiv:1910.11093. "Bekkers, E.J.: B-spline CNNs on Lie groups (2020) In: International Conference on Learning Representations"
Scale_space
Surface able to be flattened without distortion
S.; Maekawa, Takashi (September 1998). "Design for Manufacturing Using B-Spline Developable Surfaces". Journal of Ship Research. 42 (3): 207–215. doi:10
Developable_surface
Subdivision surface derived from a triangular mesh
March 2026. Catmull, E.; Clark, J. (November 1978). "Recursively generated B-spline surfaces on arbitrary topological meshes". Computer-Aided Design. 10 (6):
Loop_subdivision_surface
Group of techniques to quickly construct physical objects
approximate the application vendors' internal CAD geometric forms (e.g., B-splines) with a simplified mathematical form, which in turn is expressed in a
Rapid_prototyping
Graphics created using computers
texture coordinates) for polygon surfaces, while non-uniform rational B-spline (NURB) surfaces have their own intrinsic parameterization used as texture
Computer_graphics
Method for estimating new data within known data points
example, if f ∈ C 4 ( [ a , b ] ) {\displaystyle f\in C^{4}([a,b])} (four times continuously differentiable) then cubic spline interpolation has an error
Interpolation
Process by which atoms or molecules acquire charge by gaining or losing electrons
examples of non-perturbative methods and numerous options exist e.g. B-splines, generalized Sturmians or Coulomb wave packets. Another non-perturbative
Ionization
Geometry definition file format
surfaces using several different kinds of interpolation, such as Taylor and B-splines, although support for those features in third party file readers is far
Wavefront_.obj_file
surfaces together M-spline — a non-negative spline I-spline — a monotone spline, defined in terms of M-splines Smoothing spline — a spline fitted smoothly
List of numerical analysis topics
List_of_numerical_analysis_topics
American computer scientist and entrepreneur
Retrieved January 21, 2021. "Encyclopedia of the Great Plains | CLARK, JIM (b. 1944)". plainshumanities.unl.edu. University of Nebraska at Lincoln. August
James_H._Clark
Interdisciplinary field
choices are rigid, affine, and deformable transformation models. B-spline and thin plate spline models are commonly used for parameterized transformation fields
Medical_image_computing
Interpolation on functions of more than one variable
Thin-plate spline Polyharmonic spline (The thin-plate spline is a special case of a polyharmonic spline.) Radial basis function (Polyharmonic splines are a
Multivariate_interpolation
Algorithm for polynomial evaluation
evaluate polynomials in Chebyshev form De Boor's algorithm to evaluate splines in B-spline form De Casteljau's algorithm to evaluate polynomials in Bézier form
Horner's_method
Index of articles associated with the same name
the degree of the polynomial representation of a non-uniform rational B-spline Order of convergence, a measurement of convergence Order of derivation
Order_(mathematics)
Data analysis software
high-low plots, histograms, loess plots, needle plots, pie charts, penalised b-spline, radar charts, reference lines, scatter plots, series plots, step plots
World_Programming_System
Algorithm for computing polynomial coefficients
derivative of the function f {\displaystyle f} and B n − 1 {\displaystyle B_{n-1}} is a certain B-spline of degree n − 1 {\displaystyle n-1} for the data
Divided_differences
Movement of liquid inside another moving object
Yarmohammadisatri, Sadegh (2015). "Shape design optimization of cylindrical tank using b-spline curves". Computer & Fluids. 109: 100–112. doi:10.1016/j.compfluid.2014
Slosh_dynamics
Organic architectural style
Other computer-aided design functions used are the nonuniform rational B-spline or NURBS, freeform surfaces, and digitizing of sculpted forms similar to
Blobitecture
Classification algorithm
high-dimensional whitening representations using basis function systems (B-splines, Fourier basis, etc.). Decorrelation Principal component analysis Weighted
Whitening_transformation
Geometric modeling kernel developed by Spatial Corporation
editing features that allow for the creation and manipulation of free-form B-spline and NURBS curves and surfaces. Advanced Covering Advanced Covering is a
ACIS
Mathematical curve
In mathematics, a Kochanek–Bartels spline or Kochanek–Bartels curve is a cubic Hermite spline with tension, bias, and continuity parameters defined to
Kochanek–Bartels_spline
Chemical element with atomic number 109 (Mt)
energies and expectation values for the neutral atoms He to Uuo: The B-spline expansion method". Atomic Data and Nuclear Data Tables. 95 (6): 836–870
Meitnerium
Computational human phantoms are models of the human body
models are based on more advanced mathematics, such as non-uniform rational B-spline (NURBS) and polygon meshes, which allow for 4-D phantoms where simulations
Computational_human_phantom
Linear Quadratic Bézier Cubic Bézier B-spline Cardinal spline Hermite spline TCB spline Smoothstep Akima spline NURBS Blender Bézier curve without subdivision
Comparison of 3D computer graphics software
Comparison_of_3D_computer_graphics_software
API standard for rendering 3D computer graphics
introduced more advanced graphics primitives, such as Non-uniform rational B-spline (NURBS) surfaces. An ad hoc ANSI committee was formed around these proposed
PHIGS
Statistics models class
parametric form (for example a polynomial, or an un-penalized regression spline of a variable) or may be specified non-parametrically, or semi-parametrically
Generalized_additive_model
Variant of cubic interpolation that preserves monotonicity
using cubic Hermite spline with the tangents m i {\displaystyle m_{i}} modified to ensure the monotonicity of the resulting Hermite spline. An algorithm is
Monotone_cubic_interpolation
Computer graphics and design system
display screens. It was unique at the time for being able to manipulate B-splines (a type of curve) in real time and to produce camera ready (i.e. ultra-high
Aesthedes
base. It introduced groundbreaking features - booleans, CSG primitives, b-spline curves, physically based animation simulation, morph-based animation techniques
Realsoft_3D
Graphic-art effect
Kragen. "Hmm, aside from my note about how the family of kernels Costella discovered are precisely the uniform cardinal B-splines..." Hacker News. v t e
Box_blur
Overview of and topical guide to geometry
Minkowski space Thurston's conjecture Parametric curve Bézier curve Spline Hermite spline B-spline NURBS Parametric surface Convex hull construction Euclidean
Outline_of_geometry
Polygon mesh composed of triangles
algorithm for ray-triangle intersection Nonobtuse mesh Nonuniform rational B-spline Point cloud Polygon mesh Triangulation (topology) Triangulation (geometry)
Triangle_mesh
B-spline surface to some terrain data using this method. Original terrain data Fitted B-spline surface with large lambda and more smoothing Fitted B-spline
Thin_plate_energy_functional
travel, tourism, insurance
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travel, tourism, insurance