gauss curvature | Wolfram Resource System

GaussianCurvature

Compute the Gaussian curvature of a surface

Curvature

Compute the curvature of a curve

PrincipalCurvatures

Compute the principal curvatures of a surface

ImplicitCurvature

Compute the implicit curvature of a curve

CurvaturePlot

Plot a curve defined by its curvature

NormalCurvature

Compute the normal curvature of a curve on a surface

MeanCurvature

Compute the mean curvature of a surface

BrioschiCurvature

Compute the Gaussian curvature for a metric

RicciCurvature

Compute the components of the Ricci curvature for a metric

TotalSignedCurvature

Compute the total signed curvature of a curve

ExtrinsicCurvatureTensor

Represent the extrinsic curvature tensor field for a Riemannian submanifold

CurvatureTorsionPlot3D

Plot a curve defined by its curvature and torsion

GeneralizedGaussianQuadratureWeights

Get a numerically sorted list of abscissa-weight pairs for generalized Gaussian quadrature

WolframRicciCurvatureScalar

Compute the Wolfram–Ricci scalar curvature of a graph and its associated properties

WolframRicciCurvatureTensor

Compute projections of the Wolfram–Ricci curvature tensor of a graph and many associated properties

PointsetDerivativeRoots

Get the roots of a derivative for applying the Lucas–Gauss theorem on a set of points

ModifiedGaussianQuadratureWeights

Get a numerically sorted list of abscissa-weight pairs for various modifications of Gaussian quadrature

UnitNormal

Compute the unit normal of a surface

OsculatingCircle

Get the osculating circle of a curve

StieltjesJacobiE

Evaluate the Stieltjes-Jacobi polynomial

FocalSet

Compute the focal set of a surface

GaussianQuadratureWeights

Get a numerically sorted list of abscissa-weight pairs for Gaussian quadrature

OsculatingCircleProperties

Compute the defining properties of the osculating circle for a curve at a point

TangentialAngle

Compute the tangential angle of a curve

FractionalDPolynomialRoots

Compute and visualize the roots of fractional (noninteger) derivatives of polynomials

Smooth the Boundary of a Region

Use the curvature flow image filter to smooth the boundary of a snowflake

CesaroEquation

Compute the Cesàro equation for a planar curve

EinsteinTensor

Represent the Einstein curvature tensor (field) for a Riemannian or pseudo-Riemannian manifold

RicciTensor

Represent the Ricci curvature tensor (field) for a Riemannian or pseudo-Riemannian manifold

RiemannTensor

Represent the Riemann curvature tensor (field) for a Riemannian or pseudo-Riemannian manifold

BinormalVector

Compute the binormal vector of a curve

CurveTorsion

Compute the torsion of a curve

AsymptoticCurves

Compute the asymptotic curves of a parameterized surface

EvolutoidCurve

Compute the evolutoid of a curve

EvoluteCurve

Compute the evolute of a curve

Cos2PiOverFermatPrime

Closed form of cos(2π/p) where p is a Fermat prime (3, 5, 17, 257, 65537) a la Gauss

GaussianHessenbergDecomposition

Compute the Gaussian Hessenberg decomposition of a matrix

GeneralizedHelicoid

Compute the generalized helicoid of a curve

Intrinsic3DCurve

Plot intrinsic curves in 3D

RicciScalar

Compute the Ricci scalar for a metric

NaturalEquations

Compute the natural equations of a curve

CurvedSpacetimeSprinkling

Produce random causal graphs by sprinkling points into a spacetime with a specified algebraic curvature function

ExtrinsicCurvedManifoldToGraph

Produce random spatial graphs by sprinkling points into a Riemannian manifold with an arbitrary extrinsic curvature

IntrinsicCurvedManifoldToGraph

Produce random spatial graphs by sprinkling points into a Riemannian manifold with a specified intrinsic algebraic curvature function

ADMDecomposition

Represent a canonical decomposition of the metric for a Riemannian or pseudo-Riemannian manifold via the ADM formalism

SolveVacuumEinsteinEquations

Determine whether a given Riemannian or pseudo-Riemannian manifold is a solution to the vacuum Einstein field equations

StressEnergyTensor

Represent a stress-energy tensor (field) over a Riemannian or pseudo-Riemannian manifold

SolveEinsteinEquations

Determine whether a given stress-energy tensor (field) is a solution to the Einstein field equations

ChristoffelSymbols

Represent the Christoffel symbols for (the Levi-Civita connection over) a Riemannian or pseudo-Riemannian manifold

SolveVacuumADMEquations

Determine whether a given ADM decomposition is a solution to the vacuum ADM equations

OsculatingParabola

Get the osculating parabola of a plane curve

OsculatingConic

Get the osculating conic of a plane curve

AberrancyCurve

Compute the curve of aberrancy of a plane curve

Geodesic

Compute the geodesics for a parametrized surface

CurveAberrancy

Compute the aberrancy of a plane curve

RadiusOfAberrancy

Compute the radius of aberrancy of a plane curve

ClenshawCurtisQuadratureWeights

Get a numerically sorted list of abscissa-weight pairs for Clenshaw-Curtis quadrature

Image Vectorization

Apply smoothing and quantization to a raster image to make it more suitable for vectorization

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